mirror of https://github.com/CGAL/cgal
Merge pull request #8259 from loic-dubois/Hyperbolic_surface_triangulation_2-dubois
Hyperbolic surface triangulation 2 (new package)
This commit is contained in:
Sébastien Loriot
commit
6188aae5e5
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@ -71,6 +71,7 @@
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\package_listing{Triangulation_on_sphere_2}
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\package_listing{Triangulation_on_sphere_2}
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\package_listing{Periodic_2_triangulation_2}
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\package_listing{Periodic_2_triangulation_2}
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\package_listing{Hyperbolic_triangulation_2}
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\package_listing{Hyperbolic_triangulation_2}
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\package_listing{Triangulation_on_hyperbolic_surface_2}
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\package_listing{Periodic_4_hyperbolic_triangulation_2}
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\package_listing{Periodic_4_hyperbolic_triangulation_2}
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\package_listing{Triangulation_3}
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\package_listing{Triangulation_3}
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\package_listing{TDS_3}
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\package_listing{TDS_3}
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@ -22,7 +22,6 @@
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@article{ cgal:afh-pdecm-02,
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@article{ cgal:afh-pdecm-02,
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author = "P. K. Agarwal and E. Flato and D. Halperin",
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author = "P. K. Agarwal and E. Flato and D. Halperin",
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title = "Polygon Decomposition for Efficient Construction of {Minkowski} Sums",
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title = "Polygon Decomposition for Efficient Construction of {Minkowski} Sums",
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@ -130,6 +129,21 @@
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,update = "04.04 kettner"
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,update = "04.04 kettner"
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}
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}
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@book{cgal:b-gdg-83,
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title={The Geometry of Discrete Groups},
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author={Beardon, A.F.},
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|
series={Graduate texts in mathematics},
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year={1983},
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publisher={Springer}
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}
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@book{cgal:b-gscrs-92,
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title={Geometry and Spectra of Compact Riemann Surfaces},
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author={Peter Buser},
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year={1992},
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publisher={Springer}
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}
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@article{ cgal:bbp-iayed-01
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@article{ cgal:bbp-iayed-01
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,author = "H. Br{\"o}nnimann and C. Burnikel and S. Pion"
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,author = "H. Br{\"o}nnimann and C. Burnikel and S. Pion"
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,title = "Interval arithmetic yields efficient dynamic filters
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,title = "Interval arithmetic yields efficient dynamic filters
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@ -689,6 +703,33 @@ Mourrain and Monique Teillaud"
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keywords = "Convex hull problem, Frame, Linear programming, Data envelopment analysis, Redundancy"
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keywords = "Convex hull problem, Frame, Linear programming, Data envelopment analysis, Redundancy"
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}
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}
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@inproceedings{despre2020flipping,
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title={Flipping geometric triangulations on hyperbolic surfaces},
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author={Despr{\'e}, Vincent and Schlenker, Jean-Marc and Teillaud, Monique},
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booktitle={36th International Symposium on Computational Geometry},
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year={2020},
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url={https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.35}
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}
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@article{despre2022experimental,
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title={Experimental analysis of {Delaunay} flip algorithms on genus two hyperbolic surfaces},
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author={Despr{\'e}, Vincent and Dubois, Lo{\"\i}c and Kolbe, Benedikt and Teillaud, Monique},
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year={2022},
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url={https://inria.hal.science/hal-03665888v1/document}
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}
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@article{aigon2005hyperbolic,
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title={Hyperbolic octagons and {Teichm{\"u}ller} space in genus 2},
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author={Aigon-Dupuy, Aline and Buser, Peter and Cibils, Michel and K{\"u}nzle, Alfred F and Steiner, Frank},
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journal={Journal of mathematical physics},
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volume={46},
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number={3},
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year={2005},
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publisher={AIP Publishing},
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url = {https://doi.org/10.1063/1.1850177}
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}
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@article{cgal:dl-cginc-19,
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@article{cgal:dl-cginc-19,
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author = {Despr\'{e}, Vincent and Lazarus, Francis},
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author = {Despr\'{e}, Vincent and Lazarus, Francis},
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title = {Computing the Geometric Intersection Number of Curves},
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title = {Computing the Geometric Intersection Number of Curves},
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@ -230,6 +230,7 @@ def protect_accentuated_letters(authors):
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.replace("ş", r"{\c{s}}")
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.replace("ş", r"{\c{s}}")
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.replace("%", "")
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.replace("%", "")
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.replace("đ", r"{\-d}")
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.replace("đ", r"{\-d}")
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.replace("ï", r"{\"i}")
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)
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)
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try:
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try:
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res.encode("ascii")
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res.encode("ascii")
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@ -170,7 +170,7 @@ public:
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/// @}
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/// @}
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/// \name
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/// \name
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/// The following functions must be provided only if the methods of `Hyperbolic_Delaunay_triangulation_2`
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/// The following functions must be provided only if the methods of `CGAL::Hyperbolic_Delaunay_triangulation_2`
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/// that return elements of the Voronoi diagram are instantiated:
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/// that return elements of the Voronoi diagram are instantiated:
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/// @{
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/// @{
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Construct_hyperbolic_segment_2 construct_hyperbolic_segment_2_object();
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Construct_hyperbolic_segment_2 construct_hyperbolic_segment_2_object();
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@ -15,7 +15,7 @@ namespace CGAL {
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<img src="header.png" style="max-width:50%; width:50%;"/>
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<img src="header.png" style="max-width:50%; width:50%;"/>
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</center>
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</center>
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This package enables the computation of Delaunay triangulations of
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This package enables the computation of hyperbolic Delaunay triangulations of
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point sets in the Poincaré disk model of the hyperbolic plane.
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point sets in the Poincaré disk model of the hyperbolic plane.
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\section HT2_Poincare_model The Poincaré Disk Model of the Hyperbolic Plane
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\section HT2_Poincare_model The Poincaré Disk Model of the Hyperbolic Plane
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@ -6,6 +6,12 @@
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### General Changes
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### General Changes
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- The minimal supported version of Boost is now 1.74.0.
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- The minimal supported version of Boost is now 1.74.0.
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### 2D Triangulations on Hyperbolic Surfaces (new package)
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- This package enables building and handling triangulations of closed orientable hyperbolic surfaces.
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It offers functions for the generation of the triangulation from a convex fundamental domain,
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the Delaunay flip algorithm and the construction of a portion of the lift of the triangulation
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in the Poincaré disk. A method is offered that generates such domains in genus two.
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### [Polygon Mesh Processing](https://doc.cgal.org/6.1/Manual/packages.html#PkgPolygonMeshProcessing)
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### [Polygon Mesh Processing](https://doc.cgal.org/6.1/Manual/packages.html#PkgPolygonMeshProcessing)
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- Added the function `CGAL::Polygon_mesh_processing::discrete_mean_curvature` and `CGAL::Polygon_mesh_processing::discrete_Guassian_curvature` to evaluate the discrete curvature at a vertex of a mesh.
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- Added the function `CGAL::Polygon_mesh_processing::discrete_mean_curvature` and `CGAL::Polygon_mesh_processing::discrete_Guassian_curvature` to evaluate the discrete curvature at a vertex of a mesh.
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- Added the function `CGAL::Polygon_mesh_processing::angle_sum` to compute the sum of the angles around a vertex.
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- Added the function `CGAL::Polygon_mesh_processing::angle_sum` to compute the sum of the angles around a vertex.
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@ -0,0 +1,54 @@
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// Copyright (c) 2016 GeometryFactory SARL (France).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org)
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
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//
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// Author(s) : Andreas Fabri
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//
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// Warning: this file is generated, see include/CGAL/license/README.md
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#ifndef CGAL_LICENSE_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_H
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#define CGAL_LICENSE_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_H
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#include <CGAL/config.h>
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#include <CGAL/license.h>
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#ifdef CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_COMMERCIAL_LICENSE
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# if CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_COMMERCIAL_LICENSE < CGAL_RELEASE_DATE
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# if defined(CGAL_LICENSE_WARNING)
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CGAL_pragma_warning("Your commercial license for CGAL does not cover "
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"this release of the 2D Triangulations on Hyperbolic Surfaces package.")
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# endif
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# ifdef CGAL_LICENSE_ERROR
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# error "Your commercial license for CGAL does not cover this release \
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of the 2D Triangulations on Hyperbolic Surfaces package. \
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You get this error, as you defined CGAL_LICENSE_ERROR."
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# endif // CGAL_LICENSE_ERROR
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# endif // CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_COMMERCIAL_LICENSE < CGAL_RELEASE_DATE
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#else // no CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_COMMERCIAL_LICENSE
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# if defined(CGAL_LICENSE_WARNING)
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CGAL_pragma_warning("\nThe macro CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_COMMERCIAL_LICENSE is not defined."
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"\nYou use the CGAL 2D Triangulations on Hyperbolic Surfaces package under "
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"the terms of the GPLv3+.")
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# endif // CGAL_LICENSE_WARNING
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# ifdef CGAL_LICENSE_ERROR
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# error "The macro CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_COMMERCIAL_LICENSE is not defined.\
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You use the CGAL 2D Triangulations on Hyperbolic Surfaces package under the terms of \
|
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the GPLv3+. You get this error, as you defined CGAL_LICENSE_ERROR."
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# endif // CGAL_LICENSE_ERROR
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#endif // no CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_COMMERCIAL_LICENSE
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#endif // CGAL_LICENSE_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_H
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@ -106,6 +106,7 @@ Three Three
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Triangulation_2 2D Triangulation
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Triangulation_2 2D Triangulation
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Triangulation_3 3D Triangulations
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Triangulation_3 3D Triangulations
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Triangulation dD Triangulations
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Triangulation dD Triangulations
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Triangulation_on_hyperbolic_surface_2 2D Triangulations on Hyperbolic Surfaces
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Triangulation_on_sphere_2 2D Triangulation on Sphere
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Triangulation_on_sphere_2 2D Triangulation on Sphere
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Visibility_2 2D Visibility Computation
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Visibility_2 2D Visibility Computation
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Voronoi_diagram_2 2D Voronoi Diagram Adaptor
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Voronoi_diagram_2 2D Voronoi Diagram Adaptor
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@ -17,9 +17,7 @@ namespace CGAL {
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This package enables the computation of Delaunay triangulations of the Bolza
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This package enables the computation of Delaunay triangulations of the Bolza surface, which is the most symmetric surface of genus 2. The Bolza surface is a hyperbolic closed compact orientable surface. For triangulations on general hyperbolic surfaces, we refer to the package \ref Chapter_Hyperbolic_Surface_Triangulations "2D Triangulations on Hyperbolic Surfaces".
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surface, which is the most symmetric surface of genus 2. The Bolza surface is
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a hyperbolic closed compact orientable surface.
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A triangulation of the Bolza surface can be seen as a periodic
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A triangulation of the Bolza surface can be seen as a periodic
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triangulation of the hyperbolic plane.
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triangulation of the hyperbolic plane.
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@ -11,4 +11,5 @@ Circular_kernel_2
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Triangulation
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Triangulation
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Hyperbolic_triangulation_2
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Hyperbolic_triangulation_2
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Number_types
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Number_types
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Periodic_2_triangulation_2
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Periodic_2_triangulation_2
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Triangulation_on_hyperbolic_surface_2
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@ -0,0 +1,26 @@
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cmake_minimum_required(VERSION 3.12...3.31)
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project( Triangulation_on_hyperbolic_surface_2_Demo )
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# Find includes in corresponding build directories
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set(CMAKE_INCLUDE_CURRENT_DIR ON)
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include_directories(${CMAKE_BINARY_DIR})
|
||||||
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|
||||||
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# Instruct CMake to run moc automatically when needed.
|
||||||
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set(CMAKE_AUTOMOC ON)
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||||||
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|
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|
# CGAL and its components
|
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|
find_package(CGAL REQUIRED COMPONENTS Core Qt6)
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find_package(Qt6 QUIET COMPONENTS Widgets)
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|
if (NOT CGAL_Qt6_FOUND OR NOT Qt6_FOUND)
|
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|
message(STATUS "This project requires the Qt6 library, and will not be compiled.")
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||||||
|
return()
|
||||||
|
endif()
|
||||||
|
|
||||||
|
# ui files, created with Qt Designer
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qt6_wrap_ui(UIS drawing_window_description.ui)
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|
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|
add_executable( Triangulation_on_hyperbolic_surface_2_demo Triangulation_on_hyperbolic_surface_2_demo.cpp window.cpp ${UIS})
|
||||||
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target_link_libraries(Triangulation_on_hyperbolic_surface_2_demo PRIVATE CGAL::CGAL CGAL::CGAL_Qt6 Qt6::Widgets )
|
||||||
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cgal_add_compilation_test(Triangulation_on_hyperbolic_surface_2_demo)
|
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@ -0,0 +1,43 @@
|
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|
#include "window.h"
|
||||||
|
|
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#include <CGAL/Exact_rational.h>
|
||||||
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#include <CGAL/Simple_cartesian.h>
|
||||||
|
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_fundamental_domain_factory_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2.h>
|
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|
|
||||||
|
using namespace CGAL;
|
||||||
|
|
||||||
|
typedef Simple_cartesian<Exact_rational> Kernel;
|
||||||
|
typedef Hyperbolic_Delaunay_triangulation_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef Hyperbolic_fundamental_domain_2<Traits> Domain;
|
||||||
|
typedef Hyperbolic_fundamental_domain_factory_2<Traits> Factory;
|
||||||
|
typedef Triangulation_on_hyperbolic_surface_2<Traits> Triangulation;
|
||||||
|
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
int main(int argc, char** argv)
|
||||||
|
{
|
||||||
|
// 1. Generate the triangulation
|
||||||
|
Factory factory;
|
||||||
|
Domain domain = factory.make_hyperbolic_fundamental_domain_g2(time(NULL));
|
||||||
|
Triangulation triangulation = Triangulation(domain);
|
||||||
|
triangulation.make_Delaunay();
|
||||||
|
|
||||||
|
// 2. Draw the triangulation
|
||||||
|
QApplication app(argc, argv);
|
||||||
|
app.setApplicationName("Hyperbolic surfaces triangulation 2 Demo");
|
||||||
|
|
||||||
|
DemoWindow window;
|
||||||
|
window.item().draw_triangulation(triangulation);
|
||||||
|
window.show();
|
||||||
|
|
||||||
|
QStringList args = app.arguments();
|
||||||
|
args.removeAt(0);
|
||||||
|
return app.exec();
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,44 @@
|
||||||
|
<?xml version="1.0" encoding="UTF-8"?>
|
||||||
|
<ui version="4.0">
|
||||||
|
<class>MainWindow</class>
|
||||||
|
<widget class="QMainWindow" name="MainWindow">
|
||||||
|
<property name="geometry">
|
||||||
|
<rect>
|
||||||
|
<x>0</x>
|
||||||
|
<y>0</y>
|
||||||
|
<width>800</width>
|
||||||
|
<height>720</height>
|
||||||
|
</rect>
|
||||||
|
</property>
|
||||||
|
<property name="sizePolicy">
|
||||||
|
<sizepolicy hsizetype="Expanding" vsizetype="Expanding">
|
||||||
|
<horstretch>0</horstretch>
|
||||||
|
<verstretch>0</verstretch>
|
||||||
|
</sizepolicy>
|
||||||
|
</property>
|
||||||
|
<property name="windowTitle">
|
||||||
|
<string>Hyperbolic flips demo window</string>
|
||||||
|
</property>
|
||||||
|
<widget class="QWidget" name="centralwidget">
|
||||||
|
<widget class="QGraphicsView" name="graphicsView">
|
||||||
|
<property name="geometry">
|
||||||
|
<rect>
|
||||||
|
<x>10</x>
|
||||||
|
<y>10</y>
|
||||||
|
<width>771</width>
|
||||||
|
<height>671</height>
|
||||||
|
</rect>
|
||||||
|
</property>
|
||||||
|
<property name="sizePolicy">
|
||||||
|
<sizepolicy hsizetype="Expanding" vsizetype="Expanding">
|
||||||
|
<horstretch>0</horstretch>
|
||||||
|
<verstretch>0</verstretch>
|
||||||
|
</sizepolicy>
|
||||||
|
</property>
|
||||||
|
</widget>
|
||||||
|
</widget>
|
||||||
|
<widget class="QStatusBar" name="statusbar"/>
|
||||||
|
</widget>
|
||||||
|
<resources/>
|
||||||
|
<connections/>
|
||||||
|
</ui>
|
||||||
|
|
@ -0,0 +1,269 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Monique Teillaud
|
||||||
|
|
||||||
|
#include "window.h"
|
||||||
|
|
||||||
|
DemoWindowItem::DemoWindowItem()
|
||||||
|
: CGAL::Qt::GraphicsItem()
|
||||||
|
{
|
||||||
|
// Clear
|
||||||
|
edges_.clear();
|
||||||
|
|
||||||
|
// Prepare the pens
|
||||||
|
poincare_disk_pen_.setStyle(Qt::SolidLine);
|
||||||
|
poincare_disk_pen_.setWidth(8);
|
||||||
|
poincare_disk_pen_.setBrush(Qt::black);
|
||||||
|
|
||||||
|
edges_pen_.setStyle(Qt::SolidLine);
|
||||||
|
edges_pen_.setWidth(6);
|
||||||
|
edges_pen_.setBrush(Qt::blue);
|
||||||
|
}
|
||||||
|
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
void DemoWindowItem::paint(QPainter *painter,
|
||||||
|
const QStyleOptionGraphicsItem*,
|
||||||
|
QWidget*)
|
||||||
|
{
|
||||||
|
// 1. Draw the poincaré disk
|
||||||
|
QRectF circle_rect = QRectF(-poincare_disk_radius_in_pixels_-3,
|
||||||
|
-poincare_disk_radius_in_pixels_-3,
|
||||||
|
2*poincare_disk_radius_in_pixels_+6,
|
||||||
|
2*poincare_disk_radius_in_pixels_+6);
|
||||||
|
painter->setPen(poincare_disk_pen_);
|
||||||
|
painter->setBrush(QBrush());
|
||||||
|
painter->drawEllipse(circle_rect);
|
||||||
|
|
||||||
|
// 2. Draw the edges
|
||||||
|
painter->setBrush(QBrush());
|
||||||
|
painter->setPen(edges_pen_);
|
||||||
|
for (std::size_t i=0; i<edges_.size(); i++) {
|
||||||
|
draw_edge(painter, edges_[i].first, edges_[i].second);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
QRectF DemoWindowItem::boundingRect() const {
|
||||||
|
return QRectF(-poincare_disk_radius_in_pixels_-3,
|
||||||
|
-poincare_disk_radius_in_pixels_-3,
|
||||||
|
poincare_disk_radius_in_pixels_+6,
|
||||||
|
poincare_disk_radius_in_pixels_+6);
|
||||||
|
}
|
||||||
|
|
||||||
|
void DemoWindowItem::modelChanged() {} // Only used by Qt : we don't need to fill it
|
||||||
|
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
void DemoWindowItem::draw_triangulation(Triangulation& triangulation)
|
||||||
|
{
|
||||||
|
typedef std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,
|
||||||
|
Point, Point, Point> > RealizationVector;
|
||||||
|
|
||||||
|
RealizationVector realized_triangles;
|
||||||
|
realized_triangles = triangulation.lift();
|
||||||
|
|
||||||
|
Point point_1, point_2, point_3;
|
||||||
|
for (typename RealizationVector::iterator it = realized_triangles.begin(); it != realized_triangles.end(); ++it) {
|
||||||
|
point_1 = std::get<1>(*it);
|
||||||
|
point_2 = std::get<2>(*it);
|
||||||
|
point_3 = std::get<3>(*it);
|
||||||
|
|
||||||
|
edges_.push_back(std::make_pair(point_1, point_2));
|
||||||
|
edges_.push_back(std::make_pair(point_2, point_3));
|
||||||
|
edges_.push_back(std::make_pair(point_3, point_1));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
void DemoWindowItem::draw_point(QPainter* painter, Point position)
|
||||||
|
{
|
||||||
|
// First convert the point in doubles, well-scaled
|
||||||
|
double point_x = poincare_disk_radius_in_pixels_ * CGAL::to_double(position.x());
|
||||||
|
double point_y = poincare_disk_radius_in_pixels_ * CGAL::to_double(position.y());
|
||||||
|
|
||||||
|
// Then draw a small circle
|
||||||
|
QRectF circle_rect = QRectF(point_x-1, point_y-1, 3, 3);
|
||||||
|
painter->drawEllipse(circle_rect);
|
||||||
|
}
|
||||||
|
|
||||||
|
void DemoWindowItem::draw_edge(QPainter* painter, Point source, Point target)
|
||||||
|
{
|
||||||
|
// First convert the points coordinates to doubles
|
||||||
|
|
||||||
|
double src_x = CGAL::to_double(source.x());
|
||||||
|
double src_y = CGAL::to_double(source.y());
|
||||||
|
|
||||||
|
double tar_x = CGAL::to_double(target.x());
|
||||||
|
double tar_y = CGAL::to_double(target.y());
|
||||||
|
|
||||||
|
// 0. If src and tar are too colinear or too close from each other then draw a line
|
||||||
|
|
||||||
|
double determinant = src_x*tar_y - src_y*tar_x; // determinant of the matrix whose columns are the vectors src and tar : indicates colinearity
|
||||||
|
double distance_squared = (src_x-tar_x)*(src_x-tar_x) + (src_y-tar_y)*(src_y-tar_y);
|
||||||
|
if ((std::abs(determinant) < computation_treshold_squared) || (distance_squared < computation_treshold_squared)) {
|
||||||
|
// src and tar are too colinear or too close from each other
|
||||||
|
draw_line(painter, src_x, src_y, tar_x, tar_y);
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
// 1. Compute the center of the circle supporting the geodesic between src and tar
|
||||||
|
|
||||||
|
// 1.a Inverse src and tar with respect to the unit circle and find the euclidean midpoints of the segments between respectively
|
||||||
|
// src and its inversion, and tar and its inversion
|
||||||
|
|
||||||
|
double src_norm_2 = src_x*src_x + src_y*src_y; // Can't be too close to zero because determinant was not
|
||||||
|
double tar_norm_2 = tar_x*tar_x + tar_y*tar_y; // Can't be too close to zero because determinant was not
|
||||||
|
|
||||||
|
double src_inv_x = src_x / src_norm_2;
|
||||||
|
double src_inv_y = src_y / src_norm_2;
|
||||||
|
double tar_inv_x = tar_x / tar_norm_2;
|
||||||
|
double tar_inv_y = tar_y / tar_norm_2;
|
||||||
|
|
||||||
|
// coordinates of the euclidean midpoints of the segments [src, src_inv] and [tar, tar_inv]
|
||||||
|
double src_mid_x = (src_x + src_inv_x) / 2;
|
||||||
|
double src_mid_y = (src_y + src_inv_y) / 2;
|
||||||
|
double tar_mid_x = (tar_x + tar_inv_x) / 2;
|
||||||
|
double tar_mid_y = (tar_y + tar_inv_y) / 2;
|
||||||
|
|
||||||
|
// 1.b Solve a system to find the intersection (center_x, center_y) of the bisectors of the two segments [src, src_inv] and [tar, tar_inv]:
|
||||||
|
// (center_x \\ center y) = (a & b \\ c & d)^{-1} \times (u_x \\ u_y)
|
||||||
|
|
||||||
|
// 1.b.i define the system
|
||||||
|
|
||||||
|
double a = src_x;
|
||||||
|
double b = src_y;
|
||||||
|
double c = tar_x;
|
||||||
|
double d = tar_y;
|
||||||
|
|
||||||
|
double u_x = a*src_mid_x + b*src_mid_y;
|
||||||
|
double u_y = c*tar_mid_x + d*tar_mid_y;
|
||||||
|
|
||||||
|
// 1.b.ii solve the system (just a matrix inversion)
|
||||||
|
double det = a*d-b*c; // Can't be too close to zero...
|
||||||
|
double center_x = (d*u_x - b*u_y) / det;
|
||||||
|
double center_y = (-c*u_x + a*u_y) / det;
|
||||||
|
|
||||||
|
// 2. draw the arc supported by the circle whose center is (center_x, center_y) and whose extremities are src and tar
|
||||||
|
draw_arc(painter, src_x, src_y, tar_x, tar_y, center_x, center_y);
|
||||||
|
}
|
||||||
|
|
||||||
|
void DemoWindowItem::draw_line(QPainter* painter,
|
||||||
|
double point_1_x, double point_1_y,
|
||||||
|
double point_2_x, double point_2_y)
|
||||||
|
{
|
||||||
|
// Convert to doubles and scale by the radius of the poincaré disk
|
||||||
|
double src_x = poincare_disk_radius_in_pixels_ * point_1_x;
|
||||||
|
double src_y = poincare_disk_radius_in_pixels_ * point_1_y;
|
||||||
|
double tar_x = poincare_disk_radius_in_pixels_ * point_2_x;
|
||||||
|
double tar_y = poincare_disk_radius_in_pixels_ * point_2_y;
|
||||||
|
|
||||||
|
// Actual drawing
|
||||||
|
QLineF line (src_x, src_y, tar_x, tar_y);
|
||||||
|
painter->drawLine(line);
|
||||||
|
}
|
||||||
|
|
||||||
|
void DemoWindowItem::draw_arc(QPainter* painter,
|
||||||
|
double point_1_x, double point_1_y,
|
||||||
|
double point_2_x, double point_2_y,
|
||||||
|
double center_x, double center_y)
|
||||||
|
{
|
||||||
|
// Draws the arc supported by the circle whose center is (center_x, center_y) and whose extremities are src and tar
|
||||||
|
|
||||||
|
// 1. Scale by the radius of the poincaré disk
|
||||||
|
|
||||||
|
double src_x = poincare_disk_radius_in_pixels_ * point_1_x;
|
||||||
|
double src_y = poincare_disk_radius_in_pixels_ * point_1_y;
|
||||||
|
|
||||||
|
double tar_x = poincare_disk_radius_in_pixels_ * point_2_x;
|
||||||
|
double tar_y = poincare_disk_radius_in_pixels_ * point_2_y;
|
||||||
|
|
||||||
|
double xc = poincare_disk_radius_in_pixels_ * center_x;
|
||||||
|
double yc = poincare_disk_radius_in_pixels_ * center_y;
|
||||||
|
|
||||||
|
// 2. Define the radius of the circle and the box [xm, xM] \times [ym, yM] bounding the circle
|
||||||
|
|
||||||
|
double circle_radius = sqrt((point_1_x-center_x)*(point_1_x-center_x) + (point_1_y-center_y)*(point_1_y-center_y));
|
||||||
|
|
||||||
|
double xm = poincare_disk_radius_in_pixels_ * (center_x - circle_radius);
|
||||||
|
double xM = poincare_disk_radius_in_pixels_ * (center_x + circle_radius);
|
||||||
|
double ym = poincare_disk_radius_in_pixels_ * (center_y - circle_radius);
|
||||||
|
double yM = poincare_disk_radius_in_pixels_ * (center_y + circle_radius);
|
||||||
|
|
||||||
|
// If the source and the target are too close from each other (less than 10 pixels) or if the circle is very big then just draw a line
|
||||||
|
double dist_sq = (src_x-tar_x)*(src_x-tar_x) + (src_y - tar_y)*(src_y-tar_y);
|
||||||
|
double rad_sq = (xM-xc)*(xM-xc) + (yM-yc)*(yM-yc);
|
||||||
|
if ((dist_sq < 100) || (rad_sq > 1000 * dist_sq)) {
|
||||||
|
QLineF line (src_x, src_y, tar_x, tar_y);
|
||||||
|
painter->drawLine(line);
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
// 3. Compute angles (needed because we will draw using QPainter::drawArc)
|
||||||
|
|
||||||
|
// src_angle is the argument, in degrees, of point_1 - center
|
||||||
|
// tar_angle is the argument, in degrees, of point_2 - center
|
||||||
|
double src_angle = deg_angle(src_x - xc, src_y - yc);
|
||||||
|
double tar_angle = deg_angle(tar_x - xc, tar_y - yc);
|
||||||
|
src_angle = 360 - src_angle; // Because of y-axis inversion
|
||||||
|
tar_angle = 360 - tar_angle; // Because of y-axis-inversion
|
||||||
|
|
||||||
|
// Compute the sweep angle (see QPainter::drawArc)
|
||||||
|
double sweep_angle = tar_angle - src_angle;
|
||||||
|
while (sweep_angle > 180)
|
||||||
|
sweep_angle -= 360;
|
||||||
|
while (sweep_angle < -180)
|
||||||
|
sweep_angle += 360;
|
||||||
|
|
||||||
|
// 4. Actual Drawing
|
||||||
|
|
||||||
|
QRectF bbox_rect (xm, ym, xM-xm, yM-ym);
|
||||||
|
painter->drawArc(bbox_rect, src_angle*16, sweep_angle*16);
|
||||||
|
}
|
||||||
|
|
||||||
|
double DemoWindowItem::deg_angle(double x, double y)
|
||||||
|
{
|
||||||
|
// To avoid problems when further division by x (ok since x^2 + y^2 not too small) :
|
||||||
|
if (x*x < computation_treshold_squared) {
|
||||||
|
if (y>0) return 90;
|
||||||
|
return -90;
|
||||||
|
}
|
||||||
|
|
||||||
|
double angle = 180. * std::atan(y / x) / M_PI;
|
||||||
|
if (x < 0) {
|
||||||
|
return angle + 180.;
|
||||||
|
}
|
||||||
|
return angle;
|
||||||
|
}
|
||||||
|
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
DemoWindow::DemoWindow() : DemosMainWindow()
|
||||||
|
{
|
||||||
|
setupUi(this); // Method automatically generated by the ui file and here inherited from Ui::MainWindow. Builds the window and the contents for us...
|
||||||
|
this->graphicsView->setScene(&scene_); // ... in particular graphicsView is already constructed : we just put our scene in it and then do things within the scene
|
||||||
|
scene_.setItemIndexMethod(QGraphicsScene::NoIndex);
|
||||||
|
scene_.setSceneRect(-600, -600, 1200, 1200);
|
||||||
|
item_ = new DemoWindowItem();
|
||||||
|
scene_.addItem(item_);
|
||||||
|
this->graphicsView->scale(0.5, -0.5); // Y-axis inversion
|
||||||
|
|
||||||
|
setWindowTitle("Hyperbolic surfaces triangulation 2 Demo");
|
||||||
|
}
|
||||||
|
|
||||||
|
DemoWindowItem& DemoWindow::item()
|
||||||
|
{
|
||||||
|
return *item_;
|
||||||
|
}
|
||||||
|
|
||||||
|
void DemoWindow::keyPressEvent(QKeyEvent*) {}
|
||||||
|
|
@ -0,0 +1,107 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Monique Teillaud
|
||||||
|
|
||||||
|
#ifndef CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_DEMO_WINDOW
|
||||||
|
#define CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_DEMO_WINDOW
|
||||||
|
|
||||||
|
// Qt headers
|
||||||
|
#include <CGAL/Qt/utility.h>
|
||||||
|
#include <CGAL/Qt/GraphicsItem.h>
|
||||||
|
#include <CGAL/Qt/DemosMainWindow.h>
|
||||||
|
|
||||||
|
// UI generated header
|
||||||
|
#include "ui_drawing_window_description.h"
|
||||||
|
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Simple_cartesian.h>
|
||||||
|
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
|
||||||
|
typedef CGAL::Simple_cartesian<CGAL::Exact_rational> Kernel;
|
||||||
|
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef CGAL::Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef Traits::Hyperbolic_point_2 Point;
|
||||||
|
typedef CGAL::Triangulation_on_hyperbolic_surface_2<Traits> Triangulation;
|
||||||
|
|
||||||
|
class DemoWindowItem
|
||||||
|
: public CGAL::Qt::GraphicsItem
|
||||||
|
{
|
||||||
|
Q_OBJECT // Qt macro for Qt objects
|
||||||
|
// (Q_OBJECT does not support templates)
|
||||||
|
|
||||||
|
private:
|
||||||
|
typedef CGAL::Bbox_2 Bbox_2; // "Bounding box": just a box type used for drawing
|
||||||
|
|
||||||
|
// Edges to draw
|
||||||
|
std::vector<std::pair<Point,Point> > edges_;
|
||||||
|
|
||||||
|
// Pens for drawing
|
||||||
|
QPen poincare_disk_pen_;
|
||||||
|
QPen edges_pen_;
|
||||||
|
|
||||||
|
// radius of the poincaré disk
|
||||||
|
const int poincare_disk_radius_in_pixels_ = 600;
|
||||||
|
|
||||||
|
// Approximation treshold: used to decide when to simplify a computation (ex: draw a line
|
||||||
|
// instead of an arc if an hyperbolic segment is very small)
|
||||||
|
const double computation_treshold = 0.001;
|
||||||
|
const double computation_treshold_squared = computation_treshold*computation_treshold;
|
||||||
|
|
||||||
|
public:
|
||||||
|
// Initializer
|
||||||
|
DemoWindowItem();
|
||||||
|
|
||||||
|
// Qt methods
|
||||||
|
void paint(QPainter *painter, const QStyleOptionGraphicsItem *option, QWidget *widget);
|
||||||
|
QRectF boundingRect() const;
|
||||||
|
void modelChanged();
|
||||||
|
|
||||||
|
// Drawing method
|
||||||
|
void draw_triangulation(Triangulation& triangulation);
|
||||||
|
|
||||||
|
private:
|
||||||
|
// Sub-methods for drawing edges and vertices
|
||||||
|
void draw_point(QPainter* painter, Point position);
|
||||||
|
|
||||||
|
void draw_edge(QPainter* painter, Point source, Point target);
|
||||||
|
void draw_line(QPainter* painter, double point_1_x, double point_1_y, double point_2_x, double point_2_y);
|
||||||
|
void draw_arc(QPainter* painter, double point_1_x, double point_1_y, double point_2_x, double point_2_y, double center_x, double center_y);
|
||||||
|
|
||||||
|
double deg_angle(double x, double y);
|
||||||
|
};
|
||||||
|
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
class DemoWindow
|
||||||
|
: public CGAL::Qt::DemosMainWindow,
|
||||||
|
public Ui::MainWindow
|
||||||
|
{
|
||||||
|
Q_OBJECT // Qt macro for Qt objects
|
||||||
|
// (Q_OBJECT does not support templates)
|
||||||
|
|
||||||
|
private:
|
||||||
|
QGraphicsScene scene_;
|
||||||
|
DemoWindowItem* item_;
|
||||||
|
|
||||||
|
public:
|
||||||
|
DemoWindow();
|
||||||
|
DemoWindowItem& item();
|
||||||
|
|
||||||
|
// Events handling
|
||||||
|
void keyPressEvent(QKeyEvent* event);
|
||||||
|
};
|
||||||
|
|
||||||
|
#endif // CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_DEMO_WINDOW
|
||||||
|
|
@ -0,0 +1,14 @@
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2MainClasses
|
||||||
|
|
||||||
|
\cgalModels{ComplexNumber}
|
||||||
|
|
||||||
|
\tparam FT is the field type and must be a model of `FieldNumberType`.
|
||||||
|
*/
|
||||||
|
template <class FT>
|
||||||
|
class Complex_number {
|
||||||
|
};
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
@ -0,0 +1,116 @@
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2MainClasses
|
||||||
|
|
||||||
|
represents a fundamental domain of a closed orientable hyperbolic surface.
|
||||||
|
The domain is given as a polygon \f$ P \f$ represented by the list of its vertices in the Poincaré disk model,
|
||||||
|
together with a pairing of the sides of \f$ P \f$.
|
||||||
|
The \f$ n \f$-th side of \f$ P \f$ is the side between the \f$ n \f$-th and the \f$ (n+1) \f$-th vertex, where indices are modulo the number of vertices of \f$ P \f$.
|
||||||
|
The side pairings are represented by a list of integers, such that if the \f$ n \f$-th integer of the list is \f$ m \f$, then the \f$ n \f$-th side is paired to the \f$ m \f$-th side.
|
||||||
|
|
||||||
|
\tparam Traits must be a model of `HyperbolicSurfaceTraits_2`.
|
||||||
|
|
||||||
|
\sa `Hyperbolic_fundamental_domain_factory_2`
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
class Hyperbolic_fundamental_domain_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/// \name Types
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Point type.
|
||||||
|
*/
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
/// \name Creation
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Default constructor
|
||||||
|
*/
|
||||||
|
Hyperbolic_fundamental_domain_2();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Constructor from vertices and pairings ranges.
|
||||||
|
|
||||||
|
\tparam PointRange a model of the concepts `RandomAccessContainer` whose `value_type` is `Point`.
|
||||||
|
\tparam PairingRange a model of the concepts `RandomAccessContainer` whose `value_type` is `std::size_t`.
|
||||||
|
*/
|
||||||
|
template<class PointRange, class PairingRange>
|
||||||
|
Hyperbolic_fundamental_domain_2(PointRange & vertices, PairingRange & pairings);
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Access Functions
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the number of vertices (equivalently, the number of sides) of the domain.
|
||||||
|
|
||||||
|
\pre <code> Hyperbolic_fundamental_domain_2< Traits >::is_valid() </code>
|
||||||
|
*/
|
||||||
|
std::size_t size() const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the i-th vertex.
|
||||||
|
|
||||||
|
\pre <code> is_valid() </code>
|
||||||
|
*/
|
||||||
|
const Point& vertex(std::size_t i) const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the index of the side paired to the i-th side.
|
||||||
|
|
||||||
|
\pre <code> is_valid() </code>
|
||||||
|
*/
|
||||||
|
std::size_t paired_side(std::size_t i) const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the isometry that maps the side paired to side \f$ i \f$ to side \f$ i \f$.
|
||||||
|
|
||||||
|
\pre <code> is_valid() </code>
|
||||||
|
*/
|
||||||
|
Hyperbolic_isometry_2<Traits> side_pairing(std::size_t i) const;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Validity
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
checks that the number of vertices is even, that there are as many side pairings as vertices,
|
||||||
|
and that the vertices all lie within the open unit disk.
|
||||||
|
*/
|
||||||
|
bool is_valid() const;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
};
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
||||||
|
/// \name Input/Output
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\brief inserts the domain in a stream.
|
||||||
|
|
||||||
|
The format of the output is the following.
|
||||||
|
The first line prints the number \f$n\f$ of vertices of the domain.
|
||||||
|
For \f$ i=0 \f$ to \f$ n-1 \f$ the index of the side paired to side \f$ i \f$ is printed on a separate line.
|
||||||
|
For \f$ i=0 \f$ to \f$ n-1 \f$ the i-th vertex is printed on a separate line.
|
||||||
|
|
||||||
|
\pre <code> is_valid() </code>
|
||||||
|
*/
|
||||||
|
std::ostream& operator<<(std::ostream& s, const Hyperbolic_fundamental_domain_2<Traits>& domain);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\brief extracts the domain from a stream.
|
||||||
|
|
||||||
|
The format of the input must be the same as the format of the output of 'operator<<()'.
|
||||||
|
*/
|
||||||
|
std::istream& operator>>(std::istream& s, Hyperbolic_fundamental_domain_2<Traits>& domain);
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
@ -0,0 +1,38 @@
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2MainClasses
|
||||||
|
|
||||||
|
Factory class, whose only purpose is to construct random fundamental domains of
|
||||||
|
closed orientable hyperbolic surfaces.
|
||||||
|
|
||||||
|
The function `make_hyperbolic_fundamental_domain_g2()` constructs such a domain for
|
||||||
|
a surface of genus two.
|
||||||
|
|
||||||
|
\tparam Traits must be a model of `HyperbolicSurfaceTraits_2`.
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
class Hyperbolic_fundamental_domain_factory_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/// \name Creation
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Constructor.
|
||||||
|
*/
|
||||||
|
Hyperbolic_fundamental_domain_factory_2();
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Generation of a domain in genus two.
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
randomly generates a convex domain of a closed orientable hyperbolic surface of genus two from a seed.
|
||||||
|
*/
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits> make_hyperbolic_fundamental_domain_g2(unsigned int seed);
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
};
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
@ -0,0 +1,105 @@
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2MainClasses
|
||||||
|
|
||||||
|
represents an isometry in the Poincaré disk model.
|
||||||
|
The isometry \f$ f \f$ is represented by a list \f$ (c_0, c_1, c_2, c_3) \f$ of complex numbers,
|
||||||
|
so that \f$ f(z) = (c_0 z + c_1) / (c_2 z + c_3) \f$ holds on every complex \f$ z \f$ in the open unit disk.
|
||||||
|
|
||||||
|
Functionalities are offered to compose isometries, and apply an isometry to a point.
|
||||||
|
|
||||||
|
\tparam Traits must be a model of `HyperbolicSurfaceTraits_2`.
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
class Hyperbolic_isometry_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/// \name Types
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Complex number type.
|
||||||
|
*/
|
||||||
|
typedef typename Traits::Complex Complex_number;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Point type.
|
||||||
|
*/
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Creation
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Default constructor to the identity.
|
||||||
|
*/
|
||||||
|
Hyperbolic_isometry_2();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Constructor from coefficients.
|
||||||
|
*/
|
||||||
|
Hyperbolic_isometry_2(const Complex_number& c0,
|
||||||
|
const Complex_number& c1,
|
||||||
|
const Complex_number& c2,
|
||||||
|
const Complex_number& c3);
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/*!
|
||||||
|
sets the isometry to the identity.
|
||||||
|
*/
|
||||||
|
void set_to_identity();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
sets the coefficients of the isometry.
|
||||||
|
|
||||||
|
\warning The implementation does not check that the resulting transformation is an isometry.
|
||||||
|
*/
|
||||||
|
void set_coefficients(const Complex_number& c0,
|
||||||
|
const Complex_number& c1,
|
||||||
|
const Complex_number& c2,
|
||||||
|
const Complex_number& c3);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
sets a particular coefficient of the isometry.
|
||||||
|
|
||||||
|
\warning The implementation does not check that the resulting transformation is an isometry.
|
||||||
|
*/
|
||||||
|
void set_coefficient(int index, const Complex_number& coefficient);
|
||||||
|
|
||||||
|
/// \name Access Functions
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the index-th coefficient.
|
||||||
|
*/
|
||||||
|
const Complex_number& get_coefficient(int index) const;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Operations
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
evaluates the isometry at point \f$ p \f$.
|
||||||
|
*/
|
||||||
|
Point evaluate(const Point& p) const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
evaluates the isometry at point \f$ p \f$.
|
||||||
|
*/
|
||||||
|
Point operator()(const Point& p) const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the composition of two isometries.
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> operator*(const Hyperbolic_isometry_2<Traits>& iso1,
|
||||||
|
const Hyperbolic_isometry_2<Traits>& iso2);
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
};
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
@ -0,0 +1,13 @@
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2TraitsClasses
|
||||||
|
|
||||||
|
\tparam HyperbolicTraits must be a model of `HyperbolicDelaunayTriangulationTraits_2`.
|
||||||
|
|
||||||
|
\cgalModels{HyperbolicSurfaceTraits_2}
|
||||||
|
*/
|
||||||
|
template<class HyperbolicTraits>
|
||||||
|
class Hyperbolic_surface_traits_2 : public HyperbolicTraits {};
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
@ -0,0 +1,258 @@
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2MainClasses
|
||||||
|
|
||||||
|
This item defines attributes of edges that are of type `Complex_number` reprensenting cross-ratios.
|
||||||
|
|
||||||
|
\tparam Traits must be a model of `HyperbolicSurfaceTraits_2`.
|
||||||
|
|
||||||
|
\cgalModels{GenericMapItems}
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
struct Combinatorial_map_with_cross_ratios_item
|
||||||
|
{
|
||||||
|
template <class CMap>
|
||||||
|
struct Dart_wrapper
|
||||||
|
{
|
||||||
|
typedef Cell_attribute<CMap, Complex_number<typename Traits::FT> > Edge_attrib;
|
||||||
|
typedef std::tuple<void, Edge_attrib, void> Attributes;
|
||||||
|
};
|
||||||
|
};
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2MainClasses
|
||||||
|
|
||||||
|
represents a triangulation of a closed orientable hyperbolic surface.
|
||||||
|
|
||||||
|
The class provides functions such as the generation of the triangulation from a convex fundamental domain,
|
||||||
|
the Delaunay flip algorithm, and the construction of a portion of the lift of the triangulation in the hyperbolic plane.
|
||||||
|
|
||||||
|
\tparam Traits must be a model of `HyperbolicSurfaceTraits_2`.
|
||||||
|
\tparam Attributes must be a model of `GenericMapItems` whose edges are
|
||||||
|
decorated with complex numbers to represent cross ratios.
|
||||||
|
*/
|
||||||
|
template<class Traits, class Attributes = Combinatorial_map_with_cross_ratios_item<Traits> >
|
||||||
|
class Triangulation_on_hyperbolic_surface_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/// \name Types
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Type of combinatorial map whose edges are decorated with complex numbers.
|
||||||
|
*/
|
||||||
|
typedef Combinatorial_map<2, Attributes> Combinatorial_map_with_cross_ratios;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Combinatorial map dart descriptor type.
|
||||||
|
*/
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::Dart_descriptor Dart_descriptor;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Combinatorial map dart const descriptor type.
|
||||||
|
*/
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::Dart_const_descriptor Dart_const_descriptor;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Range of one dart for each vertex (that is 0-cell) of the combinatorial map.
|
||||||
|
*/
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_range<0> Vertex_range;
|
||||||
|
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Range of one dart for each edge (that is 1-cell) of the combinatorial map.
|
||||||
|
*/
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_range<1> Edge_range;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Range of one dart for each face (that is 2-cell) of the combinatorial map.
|
||||||
|
*/
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_range<2> Face_range;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Range of one dart for each vertex (that is 0-cell) of the combinatorial map.
|
||||||
|
*/
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_const_range<0> Vertex_const_range;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Range of one dart for each edge (that is 1-cell) of the combinatorial map.
|
||||||
|
*/
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_const_range<1> Edge_const_range;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Range of one dart for each face (that is 2-cell) of the combinatorial map.
|
||||||
|
*/
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_const_range<2> Face_const_range;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Point type.
|
||||||
|
*/
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
stores a dart \f$ d \f$ of the combinatorial map, belonging to a triangle \f$ t \f$,
|
||||||
|
and stores the three vertices of a lift of \f$ t \f$ in the hyperbolic plane.
|
||||||
|
*/
|
||||||
|
struct Anchor
|
||||||
|
{
|
||||||
|
typename Combinatorial_map_with_cross_ratios::Dart_descriptor dart;
|
||||||
|
typename Traits::Hyperbolic_point_2 vertices[3];
|
||||||
|
};
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Creation
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Default constructor.
|
||||||
|
*/
|
||||||
|
Triangulation_on_hyperbolic_surface_2() {};
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Constructor from a convex fundamental domain: triangulates the polygon of
|
||||||
|
the domain. (The triangulation is defined by adding an internal edge
|
||||||
|
between domain.vertex(size-1) and the other vertices. The anchor has the
|
||||||
|
three vertices of indices size-1, 0 and 1 and the dart is the one between
|
||||||
|
the vertices of indices size-1 and 0.)
|
||||||
|
*/
|
||||||
|
Triangulation_on_hyperbolic_surface_2(const Hyperbolic_fundamental_domain_2<Traits>& domain);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Constructor from a decorated combinatorial map and an anchor.
|
||||||
|
*/
|
||||||
|
Triangulation_on_hyperbolic_surface_2(Combinatorial_map_with_cross_ratios& cmap, Anchor& an_anchor);
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Assignment
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\pre <code> other.is_valid() </code>
|
||||||
|
*/
|
||||||
|
Triangulation_on_hyperbolic_surface_2& operator=(Triangulation_on_hyperbolic_surface_2 other);
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Access Functions
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the decorated combinatorial map.
|
||||||
|
*/
|
||||||
|
Combinatorial_map_with_cross_ratios& combinatorial_map();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns whether the triangulation has an anchor or not.
|
||||||
|
\pre <code> is_valid() </code>
|
||||||
|
*/
|
||||||
|
bool has_anchor() const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the anchor.
|
||||||
|
\pre <code> is_valid() && has_anchor() </code>
|
||||||
|
*/
|
||||||
|
Anchor& anchor();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the anchor.
|
||||||
|
\pre <code> is_valid() && has_anchor() </code>
|
||||||
|
*/
|
||||||
|
const Anchor& anchor() const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the range of vertices.
|
||||||
|
*/
|
||||||
|
Vertex_range vertices_range();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the range of edges.
|
||||||
|
*/
|
||||||
|
Edge_range edges_range();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the range of faces.
|
||||||
|
*/
|
||||||
|
Face_range faces_range();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the range of vertices.
|
||||||
|
*/
|
||||||
|
Vertex_const_range vertices_const_range() const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the range of edges.
|
||||||
|
*/
|
||||||
|
Edge_const_range edges_const_range() const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the range of faces.
|
||||||
|
*/
|
||||||
|
Face_const_range faces_const_range() const;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Delaunay Flip Algorithm
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns whether the edge supported by the dart is Delaunay flippable or not. An edge \f$ e \f$
|
||||||
|
is Delaunay flippable if the imaginary part of its cross ratio is positive.
|
||||||
|
|
||||||
|
\pre <code> is_valid() </code>
|
||||||
|
*/
|
||||||
|
bool is_Delaunay_flippable(Dart_descriptor dart) const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
flips the edge supported by the dart.
|
||||||
|
|
||||||
|
\pre <code> is_valid() </code>
|
||||||
|
*/
|
||||||
|
void flip(Dart_descriptor dart);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
determines if the triangulation is a valid Delaunay triangulation.
|
||||||
|
*/
|
||||||
|
bool is_Delaunay() const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
applies the Delaunay flip algorithm: flips Delaunay-flippable edges until there is no such edge anymore.
|
||||||
|
\pre <code> is_valid() </code>
|
||||||
|
*/
|
||||||
|
int make_Delaunay();
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Lifting
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
lifts the triangulation in the hyperbolic plane.
|
||||||
|
|
||||||
|
Returns, for every triangle \f$ t \f$ of the triangulation, one of the darts of \f$ t \f$ in the combinatorial map of the triangulation, together with a triple \f$ p,q,r \f$ of points in the hyperbolic plane.
|
||||||
|
The points \f$ p,q,r \f$ are the vertices of a lift of \f$ t \f$ in the hyperbolic plane.
|
||||||
|
If the center parameter is set to true, then one of the vertices of the anchor is translated to the origin \f$ 0 \f$.
|
||||||
|
|
||||||
|
\pre <code> is_valid() && has_anchor() </code>
|
||||||
|
*/
|
||||||
|
std::vector<std::tuple<Dart_const_descriptor, Point, Point, Point>> lift(bool center=true) const;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Validity
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
checks that the underlying combinatorial map \f$ M \f$ has no boundary and calls the is_valid method of \f$ M \f$.
|
||||||
|
|
||||||
|
If there is an anchor, then checks that the dart descriptor of the anchor does indeed point to a dart of \f$ M \f$,
|
||||||
|
and checks that the three vertices of the anchor lie within the open unit disk.
|
||||||
|
*/
|
||||||
|
bool is_valid() const;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
};
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
@ -0,0 +1,63 @@
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2InputOutput
|
||||||
|
|
||||||
|
inserts the triangulation in a stream.
|
||||||
|
|
||||||
|
The format of the output is the following.
|
||||||
|
Each dart of the triangulation is given an index between \f$ 0 \f$ and \f$ n-1 \f$, where \f$ n \f$
|
||||||
|
is the number of darts of the triangulation.
|
||||||
|
The first line contains the number \f$ n \f$ of darts.
|
||||||
|
The next line contains either 'yes' or 'no' and tells whether the triangulation has an anchor.
|
||||||
|
If the triangulation has an anchor, then the four next lines print the index of the dart of the anchor,
|
||||||
|
and the three vertices of the anchor.
|
||||||
|
Then, for every triangle \f$ t \f$, the indices of the three darts of \f$ t \f$ are printed on three distinct lines.
|
||||||
|
Finally, for every edge \f$ e \f$, the indices of the two darts of \f$ e \f$ are printed on two distinct lines, followed by a third line on which the cross ratio of \f$ e \f$ is printed.
|
||||||
|
|
||||||
|
\pre <code> Triangulation_on_hyperbolic_surface_2<Traits>::is_valid() </code>
|
||||||
|
*/
|
||||||
|
std::ostream& operator<<(std::ostream& s, const Triangulation_on_hyperbolic_surface_2<Traits>& triangulation);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2InputOutput
|
||||||
|
|
||||||
|
extracts the triangulation from a stream.
|
||||||
|
|
||||||
|
The format of the input should be the same as the format of the output of
|
||||||
|
the '<<' operator for Triangulation_on_hyperbolic_surface_2.
|
||||||
|
*/
|
||||||
|
std::istream& operator>>(std::istream& s, Triangulation_on_hyperbolic_surface_2<Traits>& triangulation);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2InputOutput
|
||||||
|
|
||||||
|
inserts the domain in a stream.
|
||||||
|
|
||||||
|
The format of the output is the following.
|
||||||
|
The first line prints the number \f$n\f$ of vertices of the domain.
|
||||||
|
For \f$ i=0 \f$ to \f$ n-1 \f$ the index of the side paired to side \f$ i \f$ is printed on a separate line.
|
||||||
|
For \f$ i=0 \f$ to \f$ n-1 \f$ the i-th vertex is printed on a separate line.
|
||||||
|
|
||||||
|
\pre <code> Hyperbolic_fundamental_domain_2< Traits >::is_valid() </code>
|
||||||
|
*/
|
||||||
|
std::ostream& operator<<(std::ostream& s, const Hyperbolic_fundamental_domain_2<Traits>& domain);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2InputOutput
|
||||||
|
|
||||||
|
extracts the domain from a stream.
|
||||||
|
|
||||||
|
The format of the input must be the same as the format of the output of
|
||||||
|
the '<<' operator for Hyperbolic_fundamental_domain_2.
|
||||||
|
*/
|
||||||
|
std::istream& operator>>(std::istream& s, Hyperbolic_fundamental_domain_2<Traits>& domain);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2InputOutput
|
||||||
|
|
||||||
|
inserts the isometry in a stream.
|
||||||
|
*/
|
||||||
|
std::ostream& operator<<(std::ostream& s, const Hyperbolic_isometry_2<Traits>& isometry);
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
@ -0,0 +1,113 @@
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2Concepts
|
||||||
|
\cgalConcept
|
||||||
|
|
||||||
|
Describes a complex number type over a `FieldNumberType` for its real and imaginary parts.
|
||||||
|
|
||||||
|
\cgalRefines{Field}
|
||||||
|
|
||||||
|
\cgalHasModelsBegin
|
||||||
|
\cgalHasModels{CGAL::Complex_number}
|
||||||
|
\cgalHasModelsEnd
|
||||||
|
*/
|
||||||
|
class ComplexNumber
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/// \name Types
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Number type for real and imaginary parts: must be a model of `FieldNumberType`.
|
||||||
|
*/
|
||||||
|
typedef unspecified_type FT;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Creation
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Default constructor, sets the both the real part and the imaginary part to \f$ 0 \f$.
|
||||||
|
*/
|
||||||
|
ComplexNumber();
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Constructor, sets the real part to <code> real_part </code> and the imaginary part to \f$ 0 \f$.
|
||||||
|
*/
|
||||||
|
ComplexNumber(const FT& real_part);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Constructor, sets the real part to <code> real_part </code> and the imaginary part to <code> imaginary_part </code>.
|
||||||
|
*/
|
||||||
|
ComplexNumber(const FT& real_part, const FT& imaginary_part);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Constructor, sets the real part to <code> real_part </code> and the
|
||||||
|
imaginary part to <code> imaginary_part </code>. FT must be
|
||||||
|
constructible from U and V.
|
||||||
|
*/
|
||||||
|
template<class U,class V>
|
||||||
|
ComplexNumber(U&& real_part, V&& imaginary_part);
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Getter and Setter
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
sets the real part to <code> real_part </code>.
|
||||||
|
*/
|
||||||
|
void real(const FT& real_part);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
sets the imaginary part to <code> imaginary_part </code>.
|
||||||
|
*/
|
||||||
|
void imag(const FT& imaginary_part);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the real part.
|
||||||
|
*/
|
||||||
|
FT real() const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the imaginary part.
|
||||||
|
*/
|
||||||
|
FT imag() const;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \name Operations
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
Copy operator.
|
||||||
|
*/
|
||||||
|
ComplexNumber operator=(const ComplexNumber& other) const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
writes the complex in a stream.
|
||||||
|
*/
|
||||||
|
std::ostream& operator<<(std::ostream& s, const ComplexNumber& z);
|
||||||
|
|
||||||
|
/*!
|
||||||
|
reads the complex from a stream.
|
||||||
|
*/
|
||||||
|
void operator>>(std::istream& s, ComplexNumber& z);
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
|
||||||
|
/// \relates ComplexNumber
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the square of the modulus.
|
||||||
|
*/
|
||||||
|
FT norm(ComplexNumber z) const;
|
||||||
|
|
||||||
|
/*!
|
||||||
|
returns the conjugate.
|
||||||
|
*/
|
||||||
|
ComplexNumber conj(ComplexNumber z) const;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
};
|
||||||
|
|
@ -0,0 +1,26 @@
|
||||||
|
/*!
|
||||||
|
\ingroup PkgHyperbolicSurfaceTriangulation2Concepts
|
||||||
|
\cgalConcept
|
||||||
|
|
||||||
|
This traits class must have a type for complex numbers.
|
||||||
|
|
||||||
|
\cgalRefines{HyperbolicDelaunayTriangulationTraits_2}
|
||||||
|
|
||||||
|
\cgalHasModelsBegin
|
||||||
|
\cgalHasModels{CGAL::Hyperbolic_surface_traits_2}
|
||||||
|
\cgalHasModelsEnd
|
||||||
|
*/
|
||||||
|
class HyperbolicSurfaceTraits_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
/// \name Types
|
||||||
|
/// @{
|
||||||
|
|
||||||
|
/*!
|
||||||
|
represents a complex number, model of `ComplexNumber`,
|
||||||
|
over the field `HyperbolicSurfaceTraits_2::FT` for its real and imaginary parts.
|
||||||
|
*/
|
||||||
|
typedef unspecified_type Complex;
|
||||||
|
|
||||||
|
/// @}
|
||||||
|
};
|
||||||
|
|
@ -0,0 +1,12 @@
|
||||||
|
@INCLUDE = ${CGAL_DOC_PACKAGE_DEFAULTS}
|
||||||
|
|
||||||
|
EXTRACT_PRIVATE = NO
|
||||||
|
|
||||||
|
PROJECT_NAME = "CGAL ${CGAL_CREATED_VERSION_NUM} - 2D Triangulations on Hyperbolic Surfaces"
|
||||||
|
|
||||||
|
IMAGE_PATH += ${CGAL_PACKAGE_DOC_DIR}/fig/cover.svg
|
||||||
|
|
||||||
|
# custom options for this package
|
||||||
|
#EXTRACT_ALL = true
|
||||||
|
#HIDE_UNDOC_MEMBERS = true
|
||||||
|
#HIDE_UNDOC_CLASSES = true
|
||||||
|
|
@ -0,0 +1,60 @@
|
||||||
|
/// \defgroup PkgHyperbolicSurfaceTriangulation2Ref 2D Triangulations on Hyperbolic Surfaces Reference
|
||||||
|
|
||||||
|
/// \defgroup PkgHyperbolicSurfaceTriangulation2Concepts Concepts
|
||||||
|
/// \ingroup PkgHyperbolicSurfaceTriangulation2Ref
|
||||||
|
|
||||||
|
/// \defgroup PkgHyperbolicSurfaceTriangulation2MainClasses Main Classes
|
||||||
|
/// \ingroup PkgHyperbolicSurfaceTriangulation2Ref
|
||||||
|
|
||||||
|
/// \defgroup PkgHyperbolicSurfaceTriangulation2TraitsClasses Traits Classes
|
||||||
|
/// \ingroup PkgHyperbolicSurfaceTriangulation2Ref
|
||||||
|
|
||||||
|
/// \defgroup PkgHyperbolicSurfaceTriangulation2InputOutput Input/Output Functions
|
||||||
|
/// \ingroup PkgHyperbolicSurfaceTriangulation2Ref
|
||||||
|
|
||||||
|
/*!
|
||||||
|
\addtogroup PkgHyperbolicSurfaceTriangulation2Ref
|
||||||
|
|
||||||
|
\cgalPkgDescriptionBegin{2D Triangulations on Hyperbolic Surfaces,PkgHyperbolicSurfaceTriangulation2}
|
||||||
|
\cgalPkgPicture{cover.svg}
|
||||||
|
|
||||||
|
\cgalPkgSummaryBegin
|
||||||
|
\cgalPkgAuthors{Vincent Despré, Loïc Dubois, Marc Pouget and Monique Teillaud}
|
||||||
|
\cgalPkgDesc{This package enables building and handling triangulations of closed orientable hyperbolic surfaces. It offers functions for the generation of the triangulation from a convex fundamental domain, the Delaunay flip algorithm and the construction of a portion of the lift of the triangulation in the Poincaré disk. A method is offered that generates such domains in genus two.}
|
||||||
|
\cgalPkgManuals{Chapter_Hyperbolic_Surface_Triangulations,PkgHyperbolicSurfaceTriangulation2Ref}
|
||||||
|
\cgalPkgSummaryEnd
|
||||||
|
|
||||||
|
\cgalPkgShortInfoBegin
|
||||||
|
\cgalPkgSince{6.1}
|
||||||
|
\cgalPkgDependsOn{\ref PkgCombinatorialMaps}
|
||||||
|
\cgalPkgBib{cgal:y-t2}
|
||||||
|
\cgalPkgLicense{\ref licensesGPL "GPL"}
|
||||||
|
\cgalPkgDemo{2D Triangulations on Hyperbolic Surfaces,nofilefornow.zip}
|
||||||
|
\cgalPkgShortInfoEnd
|
||||||
|
|
||||||
|
\cgalPkgDescriptionEnd
|
||||||
|
|
||||||
|
\cgalClassifedRefPages
|
||||||
|
|
||||||
|
\cgalCRPSection{Concepts}
|
||||||
|
|
||||||
|
- `HyperbolicSurfaceTraits_2` is the concept for the template parameter of most classes of the package.
|
||||||
|
- `ComplexNumber` describes a complex number type.
|
||||||
|
|
||||||
|
\cgalCRPSection{Classes}
|
||||||
|
|
||||||
|
- `CGAL::Triangulation_on_hyperbolic_surface_2` represents a triangulation of a closed orientable hyperbolic surface. It offers functions for the generation of the triangulation from a convex fundamental domain, the Delaunay flip algorithm and the construction of a portion of the lift of the triangulation in the Poincaré disk.
|
||||||
|
|
||||||
|
- `CGAL::Hyperbolic_fundamental_domain_2` represents a fundamental domain of a closed orientable hyperbolic surface.
|
||||||
|
|
||||||
|
- `CGAL::Hyperbolic_fundamental_domain_factory_2` is a factory class, whose purpose is to generate some convex domains of surfaces of genus two.
|
||||||
|
|
||||||
|
- `CGAL::Hyperbolic_isometry_2` represents an isometry in the Poincaré disk model. Facilities are offered to compose isometries, and apply an isometry to a point.
|
||||||
|
|
||||||
|
Models for `HyperbolicSurfaceTraits_2` and `ComplexNumber` are provided: `CGAL::Hyperbolic_surface_traits_2` and `CGAL::Complex_number`.
|
||||||
|
|
||||||
|
\cgalCRPSection{Input/Output Functions}
|
||||||
|
|
||||||
|
- `operator<<` and `operator>>` are overloaded for several classes of the package.
|
||||||
|
|
||||||
|
*/
|
||||||
|
|
@ -0,0 +1,161 @@
|
||||||
|
|
||||||
|
\page Chapter_Hyperbolic_Surface_Triangulations Triangulations of Hyperbolic Surfaces
|
||||||
|
|
||||||
|
namespace CGAL {
|
||||||
|
/*!
|
||||||
|
|
||||||
|
\mainpage User Manual
|
||||||
|
\anchor Chapter_Hyperbolic_Surface_Triangulations
|
||||||
|
|
||||||
|
\cgalAutoToc
|
||||||
|
\authors Vincent Despré, Loïc Dubois, Marc Pouget and Monique Teillaud
|
||||||
|
|
||||||
|
<center>
|
||||||
|
<img src="header.svg" style="max-width:80%; width:80%;"/>
|
||||||
|
</center>
|
||||||
|
|
||||||
|
This package introduces a data structure and algorithms for triangulations of closed orientable hyperbolic surfaces. The triangulation is represented by an enriched CGAL::Combinatorial_map with complex number attributes on edges.
|
||||||
|
Such a triangulation can be constructed from a surface given by a convex fundamental domain (see Section \ref Section_Hyperbolic_Surface_Triangulations_domains "Fundamental Domains and Triangulations"). A method is offered that randomly generates such domains for surfaces of genus two. On the other hand, the package works for any genus surface that may be provided by the user either as a fundamental domain or as an already computed triangulation.
|
||||||
|
Functionalities are offered such as the Delaunay flip algorithm and the construction of a portion of the lift of the triangulation in the Poincaré disk model of the hyperbolic plane.
|
||||||
|
|
||||||
|
For the case of the Bolza surface, which is the most symmetric surface of genus two, we refer the user to the specific package \ref Chapter_2D_Periodic_Hyperbolic_Triangulations "2D Periodic Hyperbolic Triangulations".
|
||||||
|
|
||||||
|
|
||||||
|
\section Section_Hyperbolic_Surface_Triangulations_Background Hyperbolic Surfaces
|
||||||
|
|
||||||
|
We assume some familiarity with basic notions from covering space theory and from the theory of hyperbolic surfaces. See for instance \cgalCite{cgal:b-gdg-83}\cgalCite{cgal:b-gscrs-92}.
|
||||||
|
The <em>Poincaré disk</em> \f$ \mathbb{D} \f$ is a model of the hyperbolic plane whose point set is the open unit disk of the complex plane \f$ \mathbb{C} \f$.
|
||||||
|
In this package, every hyperbolic surface \f$ S \f$ is closed (compact and without boundary) and orientable.
|
||||||
|
The Poincaré disk \f$ \mathbb{D} \f$ is a universal covering space for \f$ S \f$, whose projection map \f$ \pi: \mathbb{D} \to S \f$ is a local isometry.
|
||||||
|
For a point \f$ x \in S \f$, the infinite set \f$ \pi^{-1}(x) \f$ consists of lifts of \f$ x \f$, denoted \f$ \widetilde x \f$. This notion extends to paths and triangulations of S that can be lifted in \f$ \mathbb{D} \f$.
|
||||||
|
|
||||||
|
\subsection Section_Hyperbolic_Surface_Triangulations_domains Fundamental Domains and Triangulations
|
||||||
|
|
||||||
|
Let \f$ S \f$ be a hyperbolic surface. For representing \f$ S \f$, we cut it into topologically simple pieces.
|
||||||
|
For a graph \f$ G \f$ embedded on \f$ S \f$, a face is a connected component of \f$ S \setminus G \f$.
|
||||||
|
A graph \f$ G \f$ embedded on \f$ S \f$ defines a <em>cellular decomposition</em> of \f$ S \f$ if every face is a topological disk.
|
||||||
|
In this document, every edge of a graph \f$ G \f$ embedded on \f$ S \f$ is a geodesic on \f$ S \f$.
|
||||||
|
We consider two types of cellular decompositions of \f$ S \f$:
|
||||||
|
<ul>
|
||||||
|
<li>Decompositions with only one face, and
|
||||||
|
<li>Triangulations.
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
A decomposition of \f$ S \f$ that have only one face is a classical representation of the surface.
|
||||||
|
Cutting \f$ S \f$ open along the edges of \f$ G \f$ results in a hyperbolic polygon \f$ P \f$ that is a <em>fundamental domain</em> for \f$ S \f$.
|
||||||
|
Each edge of \f$ G \f$ is split into a pair of edges in \f$ P \f$.
|
||||||
|
Every hyperbolic surface admits a fundamental domain \f$ P \f$ that is <em>convex</em>, meaning that the interior angles of \f$ P \f$ do not exceed \f$ \pi \f$.
|
||||||
|
|
||||||
|
A decomposition defined by the graph \f$ G \f$ is a <em>triangulation</em> of \f$ S \f$ if every face of \f$ G \f$ is a triangle: it is bounded by three edges of \f$ G \f$.
|
||||||
|
Observe that this definition allows for triangulations with only one vertex.
|
||||||
|
A triangulation of \f$ S \f$ can be obtained from a convex fundamental domain \f$ P \f$ of \f$ S \f$ by triangulating the interior of \f$ P \f$, and by gluing back the boundary edges that are paired in \f$ P \f$.
|
||||||
|
The assumption that \f$ P \f$ is convex ensures that the interior of \f$ P \f$ can be triangulated naively by insertion of any maximal set of pairwise interior disjoint arcs of \f$ P \f$.
|
||||||
|
|
||||||
|
\subsection Section_Hyperbolic_Surface_Triangulations_generation Generation of Convex Fundamental Domains
|
||||||
|
|
||||||
|
In order to perform fast and exact computations with a fundamental domain, every vertex must be a complex number whose type supports fast and exact computations. Under this constraint, it is still a research problem to generate domains of surfaces of genus greater than two. In genus two, this package generates fundamental domains whose vertices belong to \f$ \mathbb{Q} + i \mathbb{Q} \f$ (their real and imaginary parts are rational numbers). The exact generation process can be found in \cgalCite{despre2022experimental}, together with a proof that the surfaces that can be generated in this way are dense in the space of hyperbolic surfaces genus two.
|
||||||
|
|
||||||
|
|
||||||
|
\section Subsection_Hyperbolic_Surface_Triangulations_Representation Representation
|
||||||
|
|
||||||
|
\subsection Subsection_Hyperbolic_Surface_Triangulations_DS_Domains Data Structure for Domains
|
||||||
|
|
||||||
|
We represent every fundamental domain as a polygon in the Poincaré disk, given by the list of its vertices in counter-clockwise order and by the list of its side pairings.
|
||||||
|
This package can generate a random convex fundamental domain \f$ P \f$ of a surface of genus two, with eight vertices \f$ z_0, \dots, z_7 \in \mathbb{C} \f$.
|
||||||
|
The vertices and the sides are in counter-clockwise order, the side between \f$ z_0 \f$ and \f$ z_1 \f$ is \f$ A \f$, the side between \f$ z_4 \f$ and \f$ z_5 \f$ is \f$ \overline{A} \f$ and so on as on \cgalFigureRef{THS2-octagon}. The side pairings are \f$ A \f$ with \f$\overline{A} \f$ , \f$ B \f$ with \f$ \overline{B} \f$ , \f$ C \f$ with \f$ \overline{C} \f$ and \f$ D \f$ with \f$ \overline{D} \f$.
|
||||||
|
|
||||||
|
These octagons are symmetric, i.e. \f$ z_i = -z_{i+4} \f$ for every \f$ i \f$, where indices are modulo eight.
|
||||||
|
Such octagons are described in \cgalCite{aigon2005hyperbolic}.
|
||||||
|
|
||||||
|
\cgalFigureAnchor{THS2-octagon}
|
||||||
|
<center>
|
||||||
|
<img src="octagon.svg" style="max-width:30%; width:30%; display: inline-block;"/>
|
||||||
|
</center>
|
||||||
|
\cgalFigureCaptionBegin{THS2-octagon}
|
||||||
|
Fundamental convex polygonal domain of a genus two surface.
|
||||||
|
\cgalFigureCaptionEnd
|
||||||
|
|
||||||
|
|
||||||
|
\subsection Subsection_Hyperbolic_Surface_Triangulations_DS_Triangulations Data Structure for Triangulations
|
||||||
|
|
||||||
|
Our representation is edge-based instead of the usual CGAL::TriangulationDataStructure_2 used for instance in the package \ref Chapter_2D_Periodic_Hyperbolic_Triangulations "2D Periodic Hyperbolic Triangulations". This edge-based representation is more intrinsic to the surface and can handle non-simplicial triangulations, for instance a triangulation with only one vertex.
|
||||||
|
We represent a triangulation \f$ T \f$ of a hyperbolic surface by an instance of CGAL::Combinatorial_map whose edges have complex number attributes that are cross ratios (defined shortly in the following).
|
||||||
|
While the triangulation \f$ T \f$ is unambiguously determined by the combinatorial map and its cross ratios, the internal representation of \f$ T \f$ contains an additional data: the anchor, to be able to lift the triangulation in the Poincaré disk \f$ \mathbb{D} \f$.
|
||||||
|
The anchor is a lift \f$ \widetilde t \f$ in \f$ \mathbb{D} \f$ of a triangle of \f$ T \f$. The anchor is represented by the three vertices \f$ \widetilde v_0, \widetilde v_1, \widetilde v_2 \f$ of \f$ \widetilde t \f$ in \f$ \mathbb{D} \f$, and by the dart in the combinatorial map of \f$ T \f$ corresponding to the oriented edge \f$ v_0v_1 \f$.
|
||||||
|
A lift function is provided that computes a lift of each triangle of \f$ T \f$ in the Poincaré disk \f$ \mathbb{D} \f$, it starts from the anchor and then recursively constructs lifts of neighboring triangles using the cross ratios. See \cgalCite{despre2022experimental} for details.
|
||||||
|
|
||||||
|
The attribute of an edge \f$ e \f$ of \f$ T \f$ is the complex number \f$ R_T(e) \in \mathbb{C} \f$ called the <em>cross ratio</em> of \f$ e \f$ in \f$ T \f$, defined as follows.
|
||||||
|
Consider the lift \f$ \widetilde T \f$ of \f$ T \f$ in the Poincaré disk \f$ \mathbb{D} \f$.
|
||||||
|
In \f$ \widetilde T \f$, let \f$ \widetilde e \f$ be a lift of \f$ e \f$, see \cgalFigureRef{THS2-crossratio}.
|
||||||
|
Orient \f$ \widetilde e \f$ arbitrarily, and let \f$ z_0 \in \mathbb{D} \f$ and \f$ z_2 \in \mathbb{D} \f$ be respectively the source and target vertices of \f$ \widetilde e \f$.
|
||||||
|
In \f$ \widetilde T \f$, consider the triangle on the right of \f$ \widetilde e \f$, and let \f$ z_1 \in \mathbb{D} \f$ be the vertex distinct from \f$ z_0 \f$ and \f$ z_2 \f$ of this triangle.
|
||||||
|
Similarly, consider the triangle on the left of \f$ \widetilde e \f$, and let \f$ z_3 \in \mathbb{D} \f$ be the vertex distinct from \f$ z_0 \f$ and \f$ z_2 \f$ of this triangle.
|
||||||
|
Then \f$ R_T(e) = (z_3-z_1)(z_2-z_0) / ((z_3-z_0)(z_2-z_1)) \f$.
|
||||||
|
This definition does not depend on the choice of the lift \f$ \widetilde e \f$, nor on the orientation of \f$ \widetilde e \f$.
|
||||||
|
See \cgalCite{despre2022experimental} for details.
|
||||||
|
|
||||||
|
\cgalFigureAnchor{THS2-crossratio}
|
||||||
|
<center>
|
||||||
|
<img src="crossratio.svg" style="max-width:20%; width:20%; display: inline-block;"/>
|
||||||
|
</center>
|
||||||
|
\cgalFigureCaptionBegin{THS2-crossratio}
|
||||||
|
Computation of the cross ratio of an edge.
|
||||||
|
\cgalFigureCaptionEnd
|
||||||
|
|
||||||
|
|
||||||
|
\subsection Subsection_Hyperbolic_Surface_Triangulations_Delaunay Delaunay Flip Algorithm
|
||||||
|
|
||||||
|
Let \f$ T \f$ be a triangulation of a hyperbolic surface. An edge \f$ e \f$ of \f$ T \f$ satisfies the <em>Delaunay criterion</em> if the imaginary part of its cross ratio \f$R_T(e)\f$ is non-positive.
|
||||||
|
This definition is equivalent to the usual formulation for the triangulation lifted in \f$ \mathbb{D} \f$: there exists a disk containing \f$ \widetilde e \f$ and that does not contain any other vertices of \f$ \widetilde T \f$ in its interior.
|
||||||
|
Then \f$ T \f$ is a <em>Delaunay triangulation</em> if every edge of \f$ T \f$ satisfies the Delaunay criterion.
|
||||||
|
If an edge \f$e \f$ of \f$ T \f$ does not satisfy the Delaunay criterion, then \f$e \f$ is called Delaunay flippable, and then the two triangles incident to \f$ e \f$ form a strictly convex quadrilateral, so \f$ e \f$ can be deleted from \f$ T \f$ and replaced by the other diagonal of the quadrilateral.
|
||||||
|
This operation is called a Delaunay <em>flip</em>.
|
||||||
|
When a flip occurs, the cross ratios of the involved edges are modified via simple formulas.
|
||||||
|
The <em>Delaunay flip algorithm</em> flips edges that do not satisfy the Delaunay until no more edges violate the criterion, with no preference on the order of the flips.
|
||||||
|
This algorithm terminates, and outputs a Delaunay triangulation of \f$ S \f$ \cgalCite{despre2020flipping}.
|
||||||
|
|
||||||
|
\section Section_Hyperbolic_Surface_Triangulations_Software_Design Software Design
|
||||||
|
|
||||||
|
The concept `ComplexNumber` describes a complex number type modeled by `CGAL::Complex_number`. Complex numbers are used to encode the cross ratios, for the coefficients of isometries and implicitly to work with points in the Poincaré disk.
|
||||||
|
Most classes of the package are templated by the concept `HyperbolicSurfaceTraits_2`. It is a refinement of `HyperbolicDelaunayTriangulationTraits_2` and is modeled by `CGAL::Hyperbolic_surface_traits_2`. It defines the geometric objects (points, segments...) forming the lifted triangulation in the Poincaré disk.
|
||||||
|
|
||||||
|
|
||||||
|
The package offers three main classes:
|
||||||
|
- `CGAL::Triangulation_on_hyperbolic_surface_2` represents a triangulation of a hyperbolic surface. It offers functions for the generation of the triangulation from a convex fundamental domain, the Delaunay flip algorithm and the construction of a portion of the lift of the triangulation in the Poincaré disk.
|
||||||
|
|
||||||
|
- `CGAL::Hyperbolic_fundamental_domain_2` represents a convex fundamental domain of a hyperbolic surface.
|
||||||
|
|
||||||
|
- `CGAL::Hyperbolic_fundamental_domain_factory_2` generates random convex fundamental domains of surfaces of genus two.
|
||||||
|
|
||||||
|
The secondary class `CGAL::Hyperbolic_isometry_2` defines isometries in the Poincaré disk together with operations to work with them.
|
||||||
|
|
||||||
|
|
||||||
|
\section Visualization_Triangulation_lift Visualization of a Triangulation
|
||||||
|
|
||||||
|
The function `CGAL::Triangulation_on_hyperbolic_surface_2::lift()` computes the lift of each triangle in the hyperbolic plane, enabling its visualization (see \cgalFigureRef{THS2-demo-output}). This package contains a demo (found in the folder Triangulation_on_hyperbolic_surface_2/demo), which can be used to display triangulations.
|
||||||
|
|
||||||
|
\cgalFigureAnchor{THS2-demo-output}
|
||||||
|
<center>
|
||||||
|
<img src="demo-output.png" style="max-width:25%; width:25%; display: inline-block;"/>
|
||||||
|
</center>
|
||||||
|
\cgalFigureCaptionBegin{THS2-demo-output}
|
||||||
|
Lift, in the Poincaré disk, of a Delaunay triangulation of a genus two hyperbolic surface with one vertex.
|
||||||
|
\cgalFigureCaptionEnd
|
||||||
|
|
||||||
|
|
||||||
|
\section Section_Hyperbolic_Surface_Triangulations_Example Example
|
||||||
|
|
||||||
|
The example below generates a convex fundamental domain of a surface of genus two, triangulates the domain, applies the Delaunay flip algorithm to the resulting triangulation, saves and prints the Delaunay triangulation.
|
||||||
|
\cgalExample{Triangulation_on_hyperbolic_surface_2/Triangulation_on_hyperbolic_surface_2.cpp}
|
||||||
|
|
||||||
|
\section Section_Hyperbolic_Surface_Implementation_History Design and Implementation History
|
||||||
|
|
||||||
|
This package implements the Delaunay flip algorithm described in the hyperbolic setting by Vincent Despré, Jean-Marc Schlenker and Monique Teillaud in \cgalCite{despre2020flipping} using the data structure for representing triangulations presented in \cgalCite{despre2022experimental}).
|
||||||
|
It also implements the generation of domains described by Vincent Despré, Loïc Dubois, Benedikt Kolbe and Monique Teillaud in \cgalCite{despre2022experimental}, based on results of Aline Aigon-Dupuy, Peter Buser, Michel Cibils, Alfred F Künzle and Frank Steiner \cgalCite{aigon2005hyperbolic}.
|
||||||
|
The code and the documentation of the package were written by Loïc Dubois, under regular discussions with Vincent Despré, Marc Pouget and Monique Teillaud.
|
||||||
|
The authors acknowledge support from the grants <a href="https://sos.loria.fr/">SoS</a> and <a href="https://perso.math.u-pem.fr/sabourau.stephane/min-max/min-max.html">MIN-MAX</a> of the French National Research Agency ANR.
|
||||||
|
|
||||||
|
*/
|
||||||
|
} /* namespace CGAL */
|
||||||
|
|
||||||
|
\\\\\\\\\\\\
|
||||||
|
|
@ -0,0 +1,7 @@
|
||||||
|
Manual
|
||||||
|
Stream_support
|
||||||
|
Number_types
|
||||||
|
Combinatorial_map
|
||||||
|
Hyperbolic_triangulation_2
|
||||||
|
Algebraic_foundations
|
||||||
|
Periodic_4_hyperbolic_triangulation_2
|
||||||
|
|
@ -0,0 +1,3 @@
|
||||||
|
/*!
|
||||||
|
\example Triangulation_on_hyperbolic_surface_2/Triangulation_on_hyperbolic_surface_2.cpp
|
||||||
|
*/
|
||||||
|
|
@ -0,0 +1,260 @@
|
||||||
|
<?xml version="1.0" encoding="UTF-8"?>
|
||||||
|
<svg width="29.702mm" height="29.753mm" version="1.1" viewBox="0 0 29.702 29.753" xmlns="http://www.w3.org/2000/svg" xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
|
||||||
|
<metadata>
|
||||||
|
<rdf:RDF>
|
||||||
|
<cc:Work rdf:about="">
|
||||||
|
<dc:format>image/svg+xml</dc:format>
|
||||||
|
<dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
|
||||||
|
<dc:title/>
|
||||||
|
</cc:Work>
|
||||||
|
</rdf:RDF>
|
||||||
|
</metadata>
|
||||||
|
<g transform="translate(-188.95 -154.1)">
|
||||||
|
<g transform="matrix(.20048 0 0 .20048 135.37 157.17)" fill="#387ba5" fill-opacity=".77869">
|
||||||
|
<path d="m303.35 107.68c0-0.0548 0.12154-0.51486 0.27008-1.0223 0.54238-1.8529 1.0251-4.7658 1.2488-7.5353 0.77845-9.6387-2.4399-19.925-8.6418-27.62-4.1357-5.1315-9.7772-9.3038-15.943-11.791l-1.5121-0.60999 1.2041-0.12588c9.0412-0.9452 16.414-2.247 24.403-4.3085 25.544-6.5917 49.386-19.908 68.343-38.172 1.3584-1.3087 2.4698-2.3258 2.4698-2.2601 0 0.11466-71.07 92.71-71.589 93.271-0.13929 0.15067-0.25326 0.2291-0.25326 0.17427z" style="paint-order:stroke markers fill"/>
|
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<g transform="matrix(.3 0 0 -.3 -52.5 222.75)" fill-rule="evenodd" stroke="#000" stroke-miterlimit="10.433" stroke-width="0" xml:space="preserve"><polyline points="456 446 498.72 446 498.72 448.04 456 448.04" fill-rule="nonzero"/><path d="m463.44 410.09-0.04-0.18-0.05-0.17-0.04-0.16-0.05-0.15-0.04-0.15-0.05-0.13-0.04-0.13-0.05-0.12-0.12-0.22-0.06-0.1-0.07-0.09-0.08-0.09-0.09-0.07-0.09-0.08-0.11-0.06-0.11-0.07-0.12-0.05-0.14-0.05-0.15-0.05-0.16-0.04-0.09-0.02-0.08-0.01-0.2-0.04-0.2-0.02-0.11-0.01-0.11-0.02-0.24-0.02h-0.13l-0.26-0.02h-0.15l-0.14-0.01h-0.15l-0.16-0.01h-0.85c-0.84 0-1.39 0-1.39-0.96 0-0.59 0.44-0.59 1.39-0.59h16.48l-0.89 1.55h-5.62c-0.7 0-0.8 0-1.11 0.04-0.48 0.05-0.64 0.1-0.64 0.5 0 0.14 0 0.25 0.25 1.14l6.83 27.36c0.43 1.74 0.54 1.89 2.68 1.89h5.33c4.89 0 9.02-2.64 9.02-9.22 0-2.43-1-10.6-5.24-16.09-1.43-1.84-5.37-5.62-11.5-5.62l0.89-1.55c10.36 0 20.19 10.51 20.19 21.42 0 7.03-4.23 12.61-11.72 12.61h-16.73c-0.95 0-1.5 0-1.5-0.95 0-0.6 0.45-0.6 1.45-0.6 0.64 0 1.55-0.04 2.14-0.09 0.8-0.11 1.1-0.25 1.1-0.8 0-0.2-0.05-0.36-0.21-0.95z"/></g>
|
||||||
|
</g>
|
||||||
|
</g>
|
||||||
|
</g>
|
||||||
|
</svg>
|
||||||
|
After Width: | Height: | Size: 33 KiB |
|
|
@ -0,0 +1,15 @@
|
||||||
|
cmake_minimum_required(VERSION 3.12...3.31)
|
||||||
|
|
||||||
|
project( Triangulation_on_hyperbolic_surface_2_Examples )
|
||||||
|
|
||||||
|
# CGAL and its components
|
||||||
|
find_package( CGAL REQUIRED )
|
||||||
|
|
||||||
|
# create a target per cppfile
|
||||||
|
file(
|
||||||
|
GLOB cppfiles
|
||||||
|
RELATIVE ${CMAKE_CURRENT_SOURCE_DIR}
|
||||||
|
${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
|
||||||
|
foreach(cppfile ${cppfiles})
|
||||||
|
create_single_source_cgal_program("${cppfile}")
|
||||||
|
endforeach()
|
||||||
|
|
@ -0,0 +1,38 @@
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Simple_cartesian.h>
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_fundamental_domain_factory_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2_IO.h>
|
||||||
|
#include <time.h>
|
||||||
|
|
||||||
|
typedef CGAL::Exact_rational Rational;
|
||||||
|
typedef CGAL::Simple_cartesian<Rational> Kernel;
|
||||||
|
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef CGAL::Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_2<Traits> Domain;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_factory_2<Traits> Factory;
|
||||||
|
typedef CGAL::Triangulation_on_hyperbolic_surface_2<Traits> Triangulation;
|
||||||
|
|
||||||
|
int main() {
|
||||||
|
// Generates the domain:
|
||||||
|
Factory factory = Factory();
|
||||||
|
Domain domain = factory.make_hyperbolic_fundamental_domain_g2(time(NULL)); // get a random seed with time(NULL)
|
||||||
|
|
||||||
|
// Triangulates the domain:
|
||||||
|
Triangulation triangulation = Triangulation(domain);
|
||||||
|
|
||||||
|
// Applies the Delaunay flip algorithm to the triangulation:
|
||||||
|
triangulation.make_Delaunay();
|
||||||
|
|
||||||
|
// Saves the triangulation:
|
||||||
|
std::ofstream output_file = std::ofstream ("OutputTriangulation.txt");
|
||||||
|
output_file << triangulation;
|
||||||
|
output_file.close();
|
||||||
|
|
||||||
|
// Prints the triangulation:
|
||||||
|
std::cout << triangulation << std::endl;
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,175 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallée (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Marc Pouget, Monique Teillaud
|
||||||
|
|
||||||
|
#ifndef CGAL_COMPLEX_NUMBER_H
|
||||||
|
#define CGAL_COMPLEX_NUMBER_H
|
||||||
|
|
||||||
|
#include <fstream>
|
||||||
|
#include <sstream>
|
||||||
|
#include <utility>
|
||||||
|
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*
|
||||||
|
Templated by a field FT. Represents a complex number over FT.
|
||||||
|
*/
|
||||||
|
template <class FT>
|
||||||
|
class Complex_number
|
||||||
|
{
|
||||||
|
typedef Complex_number<FT> Self;
|
||||||
|
|
||||||
|
FT real_, imag_;
|
||||||
|
|
||||||
|
public:
|
||||||
|
Complex_number(const FT& real_part)
|
||||||
|
: real_(real_part),
|
||||||
|
imag_(0)
|
||||||
|
{}
|
||||||
|
|
||||||
|
Complex_number(const FT& real_part, const FT& imaginary_part)
|
||||||
|
: real_(real_part),
|
||||||
|
imag_(imaginary_part)
|
||||||
|
{}
|
||||||
|
|
||||||
|
Complex_number()
|
||||||
|
: Complex_number(FT(0), FT(0))
|
||||||
|
{}
|
||||||
|
|
||||||
|
template<class U,class V>
|
||||||
|
Complex_number(U&& real_part, V&& imaginary_part)
|
||||||
|
: real_(std::forward<U>(real_part)),
|
||||||
|
imag_(std::forward<V>(imaginary_part))
|
||||||
|
{}
|
||||||
|
|
||||||
|
void real(const FT& real_part) {
|
||||||
|
real_ = real_part;
|
||||||
|
}
|
||||||
|
|
||||||
|
void imag(const FT& imaginary_part) {
|
||||||
|
imag_ = imaginary_part;
|
||||||
|
}
|
||||||
|
|
||||||
|
FT real() const {
|
||||||
|
return real_;
|
||||||
|
}
|
||||||
|
|
||||||
|
FT imag() const {
|
||||||
|
return imag_;
|
||||||
|
}
|
||||||
|
|
||||||
|
Self& operator+=(const Self& other);
|
||||||
|
Self& operator-=(const Self& other);
|
||||||
|
Self& operator*=(const Self& other);
|
||||||
|
Self& operator/=(const Self& other);
|
||||||
|
|
||||||
|
// These member versions are not working ?
|
||||||
|
/* Self operator+(const Self& z) const; */
|
||||||
|
/* Self operator-(const Self& z) const; */
|
||||||
|
|
||||||
|
// Hidden friends
|
||||||
|
friend Self operator+(const Self& z) {
|
||||||
|
return z;
|
||||||
|
}
|
||||||
|
|
||||||
|
friend Self operator-(const Self& z) {
|
||||||
|
return Self(-z.real_,-z.imag_);
|
||||||
|
}
|
||||||
|
|
||||||
|
friend bool operator==(const Self& z1, const Self& z2) {
|
||||||
|
return (z1.real_==z2.real_ && z1.imag_==z2.imag_);
|
||||||
|
}
|
||||||
|
|
||||||
|
friend bool operator!=(const Self& z1, const Self& z2) {
|
||||||
|
return !operator==(z1, z2);
|
||||||
|
}
|
||||||
|
|
||||||
|
friend Self operator+(const Self& z1, const Self& z2) {
|
||||||
|
return Self(z1.real_+z2.real_, z1.imag_+z2.imag_);
|
||||||
|
}
|
||||||
|
|
||||||
|
friend Self operator-(const Self& z1, const Self& z2) {
|
||||||
|
return Self(z1.real_-z2.real_, z1.imag_-z2.imag_);
|
||||||
|
}
|
||||||
|
|
||||||
|
friend Self operator*(const Self& z1, const Self& z2) {
|
||||||
|
return Self(z1.real_*z2.real_-z1.imag_*z2.imag_, z1.real_*z2.imag_+z1.imag_*z2.real_);
|
||||||
|
}
|
||||||
|
|
||||||
|
friend Self operator/(const Self& z1, const Self& z2) {
|
||||||
|
FT m2 = norm(z2);
|
||||||
|
return Self(z1.real_/m2, z1.imag_/m2)*conj(z2);
|
||||||
|
}
|
||||||
|
|
||||||
|
friend std::ostream& operator<<(std::ostream& s, const Self& z) {
|
||||||
|
s << z.real_ << std::endl << z.imag_ << std::endl;
|
||||||
|
return s;
|
||||||
|
}
|
||||||
|
|
||||||
|
friend void operator>>(std::istream& s, Self& z) {
|
||||||
|
FT ft;
|
||||||
|
s >> ft;
|
||||||
|
z.real(ft);
|
||||||
|
s >> ft;
|
||||||
|
z.imag(ft);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
template<class FT>
|
||||||
|
Complex_number<FT>& Complex_number<FT>::operator+=(const Complex_number<FT>& other)
|
||||||
|
{
|
||||||
|
real_ += other.real();
|
||||||
|
imag_ += other.imag();
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class FT>
|
||||||
|
Complex_number<FT>& Complex_number<FT>::operator-=(const Complex_number<FT>& other)
|
||||||
|
{
|
||||||
|
real_ -= other.real();
|
||||||
|
imag_ -= other.imag();
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class FT>
|
||||||
|
Complex_number<FT>& Complex_number<FT>::operator*=(const Complex_number<FT>& other)
|
||||||
|
{
|
||||||
|
real_ = real_*other.real() - imag_*other.imag();
|
||||||
|
imag_ = real_*other.imag() + imag_*other.real();
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class FT>
|
||||||
|
Complex_number<FT>& Complex_number<FT>::operator/=(const Complex_number<FT>& other)
|
||||||
|
{
|
||||||
|
FT m2 = norm(other);
|
||||||
|
real_ /= m2;
|
||||||
|
imag_ /= m2;
|
||||||
|
this *= conj(other);
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class FT>
|
||||||
|
FT norm(const Complex_number<FT>& z)
|
||||||
|
{
|
||||||
|
return z.real()*z.real() + z.imag()*z.imag();
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class FT>
|
||||||
|
Complex_number<FT> conj(const Complex_number<FT>& z)
|
||||||
|
{
|
||||||
|
return Complex_number<FT>(z.real(), -z.imag());
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
||||||
|
#endif // CGAL_COMPLEX_NUMBER_H
|
||||||
|
|
@ -0,0 +1,221 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Marc Pouget, Monique Teillaud
|
||||||
|
|
||||||
|
#ifndef CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_2_H
|
||||||
|
#define CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_2_H
|
||||||
|
|
||||||
|
#include <CGAL/license/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/Hyperbolic_isometry_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/assertions.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*
|
||||||
|
Represents a convex geodesic hyperbolic domain D of a closed orientable hyperbolic surface.
|
||||||
|
The domain D is given as a convex geodesic hyperbolic polygon P given by the list of its vertices in the hyperbolic plane,
|
||||||
|
together with a pairing of the sides of P, such that every two paired sides have the same length, and such that
|
||||||
|
identifying every two paired sides in a way that respects the orientation of P would result in a closed
|
||||||
|
orientable hyperbolic surface.
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
class Hyperbolic_fundamental_domain_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
|
||||||
|
Hyperbolic_fundamental_domain_2() {};
|
||||||
|
|
||||||
|
template<class PointRange, class PairingRange>
|
||||||
|
Hyperbolic_fundamental_domain_2(PointRange & vertices, PairingRange & pairings)
|
||||||
|
{
|
||||||
|
vertices_ = std::vector<Point>(vertices.begin(), vertices.end());
|
||||||
|
pairings_ = std::vector<std::size_t>(pairings.begin(), pairings.end());
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns the number of vertices (equivalently, the number of sides)
|
||||||
|
std::size_t size() const;
|
||||||
|
|
||||||
|
// returns the index-th vertex
|
||||||
|
const Point& vertex(std::size_t index) const;
|
||||||
|
|
||||||
|
// returns the index of the side paired to side A, where A is the index-th side
|
||||||
|
std::size_t paired_side(std::size_t index) const;
|
||||||
|
|
||||||
|
// returns the isometry that maps side A to side B, where B is the index-th side, and A is the side paired to B
|
||||||
|
Hyperbolic_isometry_2<Traits> side_pairing(std::size_t index) const;
|
||||||
|
|
||||||
|
std::istream& from_stream(std::istream& s);
|
||||||
|
std::ostream& to_stream(std::ostream& s) const;
|
||||||
|
|
||||||
|
bool is_valid() const;
|
||||||
|
|
||||||
|
private:
|
||||||
|
std::vector<Point> vertices_;
|
||||||
|
std::vector<std::size_t> pairings_;
|
||||||
|
};
|
||||||
|
|
||||||
|
//template<class Traits> std::ostream& operator<<(std::ostream& s, const Hyperbolic_fundamental_domain_2<Traits>& domain);
|
||||||
|
//template<class Traits> std::istream& operator>>(std::istream& s, Hyperbolic_fundamental_domain_2<Traits>& domain);
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
std::size_t
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits>::
|
||||||
|
size() const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid());
|
||||||
|
return vertices_.size();
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
const typename Hyperbolic_fundamental_domain_2<Traits>::Point&
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits>::
|
||||||
|
vertex(std::size_t index) const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid());
|
||||||
|
return vertices_[index];
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
std::size_t
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits>::
|
||||||
|
paired_side(std::size_t index) const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid());
|
||||||
|
return pairings_[index];
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits>
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits>::
|
||||||
|
side_pairing(std::size_t index) const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid());
|
||||||
|
std::size_t n = size();
|
||||||
|
std::size_t paired_index = paired_side(index);
|
||||||
|
|
||||||
|
//const Point& p1,p2,q1,q2;
|
||||||
|
const Point& q1 = vertex(index);
|
||||||
|
const Point& q2 = vertex((index+1)%n);
|
||||||
|
const Point& p2 = vertex(paired_index);
|
||||||
|
const Point& p1 = vertex((paired_index+1)%n);
|
||||||
|
|
||||||
|
Hyperbolic_isometry_2<Traits> isom = isometry_pairing_the_sides<Traits>(p1,p2,q1,q2);
|
||||||
|
return isom;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
std::ostream&
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits>::
|
||||||
|
to_stream(std::ostream& s) const
|
||||||
|
{
|
||||||
|
std::size_t n = size();
|
||||||
|
|
||||||
|
s << std::to_string(n) << std::endl;
|
||||||
|
|
||||||
|
for (std::size_t k=0; k<n; ++k) {
|
||||||
|
s << paired_side(k) << std::endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
for (std::size_t k=0; k<n; ++k) {
|
||||||
|
s << vertex(k) << std::endl;
|
||||||
|
}
|
||||||
|
return s;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
std::istream&
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits>::
|
||||||
|
from_stream(std::istream& s)
|
||||||
|
{
|
||||||
|
vertices_.clear();
|
||||||
|
pairings_.clear();
|
||||||
|
|
||||||
|
std::string line;
|
||||||
|
s >> line;
|
||||||
|
std::size_t size = std::stoi(line);
|
||||||
|
vertices_.reserve(size);
|
||||||
|
pairings_.reserve(size);
|
||||||
|
|
||||||
|
for (std::size_t k=0; k<size; ++k) {
|
||||||
|
s >> line;
|
||||||
|
pairings_.push_back(std::stoi(line));
|
||||||
|
}
|
||||||
|
|
||||||
|
for (std::size_t k=0; k<size; ++k) {
|
||||||
|
Point p;
|
||||||
|
s >> p;
|
||||||
|
vertices_.push_back(p);
|
||||||
|
}
|
||||||
|
return s;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
bool
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits>::
|
||||||
|
is_valid()const
|
||||||
|
{
|
||||||
|
// Get the number of vertices
|
||||||
|
std::size_t n = vertices_.size();
|
||||||
|
|
||||||
|
// Check that the number of vertices is even
|
||||||
|
if (n%2) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Check that there are as many side pairings as vertices
|
||||||
|
if (pairings_.size() != n) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Check that the pairings_ vector encodes a perfect matching of the set {0,1,\dots,n-1}
|
||||||
|
std::vector<bool> already_paired(n);
|
||||||
|
for (std::size_t k=0; k<n; ++k) {
|
||||||
|
already_paired[k] = false;
|
||||||
|
}
|
||||||
|
for (std::size_t k=0; k<n; ++k) {
|
||||||
|
std::size_t paired_side = pairings_[k];
|
||||||
|
if (paired_side>=n) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
if (already_paired[paired_side]) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
already_paired[paired_side] = true;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Check that the vertices all lie within the open unit disk
|
||||||
|
for (std::size_t k=0; k<n; ++k) {
|
||||||
|
if (norm(Complex_number(vertices_[k].x(), vertices_[k].y())) >= typename Traits::FT(1)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
||||||
|
#endif // CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_2_H
|
||||||
|
|
@ -0,0 +1,284 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Marc Pouget, Monique Teillaud
|
||||||
|
|
||||||
|
#ifndef CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_FACTORY_2_H
|
||||||
|
#define CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_FACTORY_2_H
|
||||||
|
|
||||||
|
#include <CGAL/license/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/Hyperbolic_fundamental_domain_2.h>
|
||||||
|
#include <CGAL/Random.h>
|
||||||
|
|
||||||
|
#include <cmath>
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*
|
||||||
|
Factory class, whose only purpose is to construct random fundamental domains of
|
||||||
|
closed orientable hyperbolic surfaces. The function
|
||||||
|
`make_hyperbolic_fundamental_domain_g2()` constructs such a domain for a surface of
|
||||||
|
genus 2.
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
class Hyperbolic_fundamental_domain_factory_2
|
||||||
|
{
|
||||||
|
private:
|
||||||
|
typedef typename Traits::FT FT;
|
||||||
|
typedef typename Traits::Complex Cmplx;
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
|
||||||
|
Random random_;
|
||||||
|
|
||||||
|
public:
|
||||||
|
Hyperbolic_fundamental_domain_factory_2();
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits> make_hyperbolic_fundamental_domain_g2(unsigned int seed);
|
||||||
|
|
||||||
|
private:
|
||||||
|
float random_positive_float(); // returns number in [0,1]
|
||||||
|
float random_float(); // returns number in [-1,1]
|
||||||
|
Complex_number<float> random_complex_float(); // returns complex z such that modulus(z) < 1 and imag(z) > 0
|
||||||
|
|
||||||
|
FT exact_number_from_float(float x);
|
||||||
|
Cmplx exact_complex_from_float_complex(const Complex_number<float>& z);
|
||||||
|
|
||||||
|
bool try_to_compute_inexact_z0_from_z1_z2_z3(Complex_number<float>& z0, Complex_number<float>& z1, Complex_number<float>& z2, Complex_number<float>& z3);
|
||||||
|
bool try_to_compute_exact_z3_from_z0_z1_z2(Cmplx& z0, Cmplx& z1, Cmplx& z2, Cmplx& z3);
|
||||||
|
|
||||||
|
bool sanity_check(Cmplx& z0, Cmplx& z1, Cmplx& z2, Cmplx& z3);
|
||||||
|
|
||||||
|
const int CGAL_DENOMINATOR_FOR_GENERATION = 10000;
|
||||||
|
};
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_fundamental_domain_factory_2<Traits>::Hyperbolic_fundamental_domain_factory_2() {}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits>
|
||||||
|
Hyperbolic_fundamental_domain_factory_2<Traits>::
|
||||||
|
make_hyperbolic_fundamental_domain_g2(unsigned int seed)
|
||||||
|
{
|
||||||
|
random_ = Random(seed);
|
||||||
|
bool is_domain_generated = false;
|
||||||
|
Cmplx exact_z0, exact_z1, exact_z2, exact_z3;
|
||||||
|
|
||||||
|
while (!is_domain_generated) {
|
||||||
|
// 1. Generate inexact z0,z1,z2,z3
|
||||||
|
Complex_number<float> z0, z1, z2, z3;
|
||||||
|
z1 = random_complex_float();
|
||||||
|
z2 = random_complex_float();
|
||||||
|
z3 = random_complex_float();
|
||||||
|
while (! try_to_compute_inexact_z0_from_z1_z2_z3(z0,z1,z2,z3)) {
|
||||||
|
z1 = random_complex_float();
|
||||||
|
z2 = random_complex_float();
|
||||||
|
z3 = random_complex_float();
|
||||||
|
}
|
||||||
|
|
||||||
|
// 2. Compute exact z0,z1,z2,z3 nearby
|
||||||
|
exact_z0 = exact_complex_from_float_complex(z0);
|
||||||
|
exact_z1 = exact_complex_from_float_complex(z1);
|
||||||
|
exact_z2 = exact_complex_from_float_complex(z2);
|
||||||
|
exact_z3 = exact_complex_from_float_complex(z3);
|
||||||
|
|
||||||
|
// 3. Modify z3 to fix the area...
|
||||||
|
is_domain_generated = try_to_compute_exact_z3_from_z0_z1_z2(exact_z0, exact_z1, exact_z2, exact_z3);
|
||||||
|
if (is_domain_generated) {
|
||||||
|
// ... and perform a sanity check
|
||||||
|
is_domain_generated = sanity_check(exact_z0, exact_z1, exact_z2, exact_z3);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
Cmplx exact_zero(FT(0), FT(0));
|
||||||
|
std::vector<Point> vertices;
|
||||||
|
vertices.push_back(Point(exact_z0.real(), exact_z0.imag()));
|
||||||
|
vertices.push_back(Point(exact_z1.real(), exact_z1.imag()));
|
||||||
|
vertices.push_back(Point(exact_z2.real(), exact_z2.imag()));
|
||||||
|
vertices.push_back(Point(exact_z3.real(), exact_z3.imag()));
|
||||||
|
vertices.push_back(Point(-exact_z0.real(), -exact_z0.imag()));
|
||||||
|
vertices.push_back(Point(-exact_z1.real(), -exact_z1.imag()));
|
||||||
|
vertices.push_back(Point(-exact_z2.real(), -exact_z2.imag()));
|
||||||
|
vertices.push_back(Point(-exact_z3.real(), -exact_z3.imag()));
|
||||||
|
|
||||||
|
std::vector<int> pairings;
|
||||||
|
for (int k=0; k<8; ++k) {
|
||||||
|
pairings.push_back((k+4)%8);
|
||||||
|
}
|
||||||
|
|
||||||
|
Hyperbolic_fundamental_domain_2<Traits> domain(vertices, pairings);
|
||||||
|
return domain;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
float Hyperbolic_fundamental_domain_factory_2<Traits>::random_positive_float() {
|
||||||
|
return random_.uniform_01<float>();
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
float Hyperbolic_fundamental_domain_factory_2<Traits>::random_float() {
|
||||||
|
return random_.uniform_01<float>() * 2 - 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Complex_number<float>
|
||||||
|
Hyperbolic_fundamental_domain_factory_2<Traits>::
|
||||||
|
random_complex_float()
|
||||||
|
{
|
||||||
|
Complex_number<float> result (random_float(), random_positive_float());
|
||||||
|
while (norm(result) >= 1) {
|
||||||
|
result.real(random_float());
|
||||||
|
result.imag(random_positive_float());
|
||||||
|
}
|
||||||
|
|
||||||
|
return result;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
typename Traits::FT
|
||||||
|
Hyperbolic_fundamental_domain_factory_2<Traits>::
|
||||||
|
exact_number_from_float(float x)
|
||||||
|
{
|
||||||
|
if (x < 0) {
|
||||||
|
return FT(0)-exact_number_from_float(-x);
|
||||||
|
}
|
||||||
|
return FT(int(x*CGAL_DENOMINATOR_FOR_GENERATION)%CGAL_DENOMINATOR_FOR_GENERATION)/FT(CGAL_DENOMINATOR_FOR_GENERATION);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
typename Traits::Complex
|
||||||
|
Hyperbolic_fundamental_domain_factory_2<Traits>::
|
||||||
|
exact_complex_from_float_complex(const Complex_number<float>& z)
|
||||||
|
{
|
||||||
|
return Cmplx(exact_number_from_float(z.real()), exact_number_from_float(z.imag()));
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
bool Hyperbolic_fundamental_domain_factory_2<Traits>::
|
||||||
|
try_to_compute_inexact_z0_from_z1_z2_z3(Complex_number<float>& z0,
|
||||||
|
Complex_number<float>& z1,
|
||||||
|
Complex_number<float>& z2,
|
||||||
|
Complex_number<float>& z3)
|
||||||
|
{
|
||||||
|
if (((z2/z1).imag()<=0) || ((z3/z2).imag()<=0)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
Complex_number<float> one(1.0f, 0.0f);
|
||||||
|
Complex_number<float> u = (one - conj(z1*z2)) * (one - conj(z2*z3));
|
||||||
|
float a = -(conj(u*z1)*z3).imag();
|
||||||
|
float b = (u*(conj(z3-z1))).imag();
|
||||||
|
float c = u.imag();
|
||||||
|
|
||||||
|
const float COMPUTATION_TRESHOLD = 0.00001f;
|
||||||
|
if (a+b+c> 0 - COMPUTATION_TRESHOLD) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
z0.real(2.0f * c / (std::sqrt(b * b - 4.0f * a * c) - b));
|
||||||
|
z0.imag(0.0f);
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
bool
|
||||||
|
Hyperbolic_fundamental_domain_factory_2<Traits>::
|
||||||
|
try_to_compute_exact_z3_from_z0_z1_z2(Cmplx& z0, Cmplx& z1, Cmplx& z2, Cmplx& z3)
|
||||||
|
{
|
||||||
|
FT zero_number (0);
|
||||||
|
FT one_number (1);
|
||||||
|
if ((z0.real()<=zero_number) || (z1.imag()<=zero_number) || (z2.imag()<=zero_number) || (z3.imag()<=zero_number)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
if ((norm(z0)>=one_number) || (norm(z1)>=one_number) || (norm(z2)>=one_number) || (norm(z3)>=one_number)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
if (((z1/z0).imag()<=zero_number) || ((z2/z1).imag()<=zero_number) || ((z3/z2).imag()<=zero_number)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
Cmplx one_cmplx (FT(1), FT(0));
|
||||||
|
Cmplx two_cmplx(FT(2), FT(0));
|
||||||
|
|
||||||
|
Cmplx f_of_z0 = two_cmplx * z0 / (z0*z0 + one_cmplx);
|
||||||
|
Cmplx f_of_z1 = (z0 + z1) / (z0*z1 + one_cmplx);
|
||||||
|
Cmplx f_of_z2 = (z0 + z2) / (z0*z2 + one_cmplx);
|
||||||
|
Cmplx f_of_z3 = (z0 + z3) / (z0*z3 + one_cmplx);
|
||||||
|
|
||||||
|
Cmplx intermediate = (one_cmplx - f_of_z0*conj(f_of_z1)) * (one_cmplx - f_of_z1*conj(f_of_z2));
|
||||||
|
FT P_of_zero = intermediate.imag();
|
||||||
|
FT P_of_one = (intermediate * (one_cmplx-f_of_z2*conj(f_of_z3))).imag();
|
||||||
|
|
||||||
|
if (P_of_one == P_of_zero) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
FT lbda = P_of_zero / (P_of_zero - P_of_one);
|
||||||
|
Cmplx V (lbda*(f_of_z3.real()), lbda*(f_of_z3.imag()));
|
||||||
|
|
||||||
|
if ((V.imag()<=zero_number) || (norm(V)>=one_number) || ((V/f_of_z2).imag()<=zero_number)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
z3 = (V - z0) / (one_cmplx - z0*V);
|
||||||
|
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
bool
|
||||||
|
Hyperbolic_fundamental_domain_factory_2<Traits>::
|
||||||
|
sanity_check(Cmplx& z0, Cmplx& z1, Cmplx& z2, Cmplx& z3)
|
||||||
|
{
|
||||||
|
FT zero_number(0);
|
||||||
|
FT one_number(1);
|
||||||
|
|
||||||
|
// 1. Check the positions
|
||||||
|
if ((z0.imag()!=zero_number) || (z0.real()<=zero_number) || (z1.imag()<=zero_number) || (z2.imag()<=zero_number) || (z3.imag()<=zero_number)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
if ((norm(z0)>=one_number) || (norm(z1)>=one_number) || (norm(z2)>=one_number) || (norm(z3)>=one_number)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
if (((z2/z1).imag()<=zero_number) || ((z3/z2).imag()<=zero_number)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
// 2. Check the area
|
||||||
|
Cmplx one_cmplx (one_number, zero_number);
|
||||||
|
Cmplx Z = (one_cmplx-z0*conj(z1)) * (one_cmplx-z1*conj(z2)) *(one_cmplx-z2*conj(z3)) *(one_cmplx+z3*conj(z0));
|
||||||
|
if (Z.imag()!=zero_number) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
||||||
|
#endif // CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_FACTORY_2_H
|
||||||
|
|
@ -0,0 +1,235 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Marc Pouget, Monique Teillaud
|
||||||
|
|
||||||
|
#ifndef CGAL_HYPERBOLIC_ISOMETRY_2_H
|
||||||
|
#define CGAL_HYPERBOLIC_ISOMETRY_2_H
|
||||||
|
|
||||||
|
#include <CGAL/license/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/Complex_number.h>
|
||||||
|
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*
|
||||||
|
Represents a hyperbolic isometry in the Poincare disk model the hyperbolic plane.
|
||||||
|
The isometry f is stored as list (c0, c1, c2, c3) of 4 complex numbers,
|
||||||
|
so that f(z) = (c0 z + c1) / (c2 z + c3) holds on every complex z in the open unit disk.
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
class Hyperbolic_isometry_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef Hyperbolic_isometry_2<Traits> Self;
|
||||||
|
typedef typename Traits::FT FT;
|
||||||
|
typedef typename Traits::Complex Complex_number;
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
|
||||||
|
Hyperbolic_isometry_2();
|
||||||
|
Hyperbolic_isometry_2(const Complex_number& c0, const Complex_number& c1, const Complex_number& c2, const Complex_number& c3);
|
||||||
|
|
||||||
|
void set_to_identity();
|
||||||
|
|
||||||
|
// Can be used to set the coefficients manually. Warning: the implementation does not check that the resulting moebius transform fixes the unit circle.
|
||||||
|
void set_coefficients(const Complex_number& c0, const Complex_number& c1, const Complex_number& c2, const Complex_number& c3);
|
||||||
|
void set_coefficient(int index, const Complex_number& coefficient);
|
||||||
|
|
||||||
|
// returns the index-th coefficient
|
||||||
|
const Complex_number& get_coefficient(int index) const;
|
||||||
|
|
||||||
|
// evaluates the isometry at point
|
||||||
|
Point evaluate(const Point& point) const;
|
||||||
|
Point operator()(const Point& point) const;
|
||||||
|
|
||||||
|
private:
|
||||||
|
Complex_number coefficients_[4];
|
||||||
|
};
|
||||||
|
|
||||||
|
// returns the composition of two isometries.
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> operator*(const Hyperbolic_isometry_2<Traits>& iso1, const Hyperbolic_isometry_2<Traits>& iso2);
|
||||||
|
|
||||||
|
// template<class Traits> std::ostream& operator<<(std::ostream& s, const Hyperbolic_isometry_2<Traits>& isometry);
|
||||||
|
|
||||||
|
// When inverse is 'false', returns the hyperbolic translation that maps -p to zero, and zero to p.
|
||||||
|
// Otherwise, returns the hyperbolic translation that maps p to zero, and zero to -p.
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> hyperbolic_translation(const typename Traits::Hyperbolic_point_2& p,
|
||||||
|
bool inverse = false);
|
||||||
|
|
||||||
|
// When inverse is 'false', returns the hyperbolic rotation around zero that maps p to q.
|
||||||
|
// Otherwise, returns the hyperbolic rotation around zero that maps q to p.
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> hyperbolic_rotation(const typename Traits::Hyperbolic_point_2& p,
|
||||||
|
const typename Traits::Hyperbolic_point_2& q,
|
||||||
|
bool inverse = false);
|
||||||
|
|
||||||
|
// returns the hyperbolic isometry that maps p1 to q1 and p2 to q2
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> isometry_pairing_the_sides(const typename Traits::Hyperbolic_point_2& p1,
|
||||||
|
const typename Traits::Hyperbolic_point_2& p2,
|
||||||
|
const typename Traits::Hyperbolic_point_2& q1,
|
||||||
|
const typename Traits::Hyperbolic_point_2& q2);
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits>::
|
||||||
|
Hyperbolic_isometry_2()
|
||||||
|
{
|
||||||
|
set_to_identity();
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits>::
|
||||||
|
Hyperbolic_isometry_2(const Complex_number& c0,
|
||||||
|
const Complex_number& c1,
|
||||||
|
const Complex_number& c2,
|
||||||
|
const Complex_number& c3)
|
||||||
|
{
|
||||||
|
set_coefficients(c0,c1,c2,c3);
|
||||||
|
}
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
void
|
||||||
|
Hyperbolic_isometry_2<Traits>::
|
||||||
|
set_to_identity()
|
||||||
|
{
|
||||||
|
set_coefficients(Complex_number(FT(1)),
|
||||||
|
Complex_number(FT(0)),
|
||||||
|
Complex_number(FT(0)),
|
||||||
|
Complex_number(FT(1)));
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
void
|
||||||
|
Hyperbolic_isometry_2<Traits>::
|
||||||
|
set_coefficients(const Complex_number& c0,
|
||||||
|
const Complex_number& c1,
|
||||||
|
const Complex_number& c2,
|
||||||
|
const Complex_number& c3)
|
||||||
|
{
|
||||||
|
set_coefficient(0, c0);
|
||||||
|
set_coefficient(1, c1);
|
||||||
|
set_coefficient(2, c2);
|
||||||
|
set_coefficient(3, c3);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
void
|
||||||
|
Hyperbolic_isometry_2<Traits>::
|
||||||
|
set_coefficient(int index, const Complex_number& coefficient)
|
||||||
|
{
|
||||||
|
coefficients_[index] = coefficient;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
const typename Traits::Complex&
|
||||||
|
Hyperbolic_isometry_2<Traits>::
|
||||||
|
get_coefficient(int index) const
|
||||||
|
{
|
||||||
|
return coefficients_[index];
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
typename Traits::Hyperbolic_point_2
|
||||||
|
Hyperbolic_isometry_2<Traits>::
|
||||||
|
evaluate(const Point& point) const
|
||||||
|
{
|
||||||
|
Complex_number z(point.x(), point.y());
|
||||||
|
Complex_number numerator_of_the_result = coefficients_[0] * z + coefficients_[1];
|
||||||
|
Complex_number denominator_of_the_result = coefficients_[2] * z + coefficients_[3];
|
||||||
|
Complex_number result = numerator_of_the_result / denominator_of_the_result;
|
||||||
|
return Point(result.real(), result.imag());
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
typename Traits::Hyperbolic_point_2
|
||||||
|
Hyperbolic_isometry_2<Traits>::
|
||||||
|
operator()(const Point& point) const
|
||||||
|
{
|
||||||
|
return evaluate(point);
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> operator*(const Hyperbolic_isometry_2<Traits>& iso1,
|
||||||
|
const Hyperbolic_isometry_2<Traits>& iso2)
|
||||||
|
{
|
||||||
|
Hyperbolic_isometry_2<Traits> result;
|
||||||
|
for (int i=0; i<2; i++) {
|
||||||
|
for (int j=0; j<2; j++) {
|
||||||
|
result.set_coefficient(2*i+j,
|
||||||
|
iso1.get_coefficient(2*i) * iso2.get_coefficient(j) + iso1.get_coefficient(2*i+1) * iso2.get_coefficient(2+j));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return result;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> hyperbolic_translation(const typename Traits::Hyperbolic_point_2& p,
|
||||||
|
bool inverse)
|
||||||
|
{
|
||||||
|
typename Traits::Complex one (typename Traits::FT(1));
|
||||||
|
typename Traits::Complex z;
|
||||||
|
if (inverse) {
|
||||||
|
z = typename Traits::Complex(p.x(), p.y());
|
||||||
|
} else {
|
||||||
|
z = - typename Traits::Complex(p.x(), p.y());
|
||||||
|
}
|
||||||
|
Hyperbolic_isometry_2<Traits> result;
|
||||||
|
result.set_coefficients(one, z, conj(z), one);
|
||||||
|
return result;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> hyperbolic_rotation(const typename Traits::Hyperbolic_point_2& p,
|
||||||
|
const typename Traits::Hyperbolic_point_2& q,
|
||||||
|
bool inverse)
|
||||||
|
{
|
||||||
|
typename Traits::Complex zero (typename Traits::FT(0));
|
||||||
|
|
||||||
|
Hyperbolic_isometry_2<Traits> result;
|
||||||
|
if (inverse) {
|
||||||
|
result.set_coefficients(typename Traits::Complex(p.x(), p.y()), zero, zero, typename Traits::Complex(q.x(), q.y()));
|
||||||
|
} else {
|
||||||
|
result.set_coefficients(typename Traits::Complex(q.x(), q.y()), zero, zero, typename Traits::Complex(p.x(), p.y()));
|
||||||
|
}
|
||||||
|
return result;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
Hyperbolic_isometry_2<Traits> isometry_pairing_the_sides(const typename Traits::Hyperbolic_point_2& p1,
|
||||||
|
const typename Traits::Hyperbolic_point_2& p2,
|
||||||
|
const typename Traits::Hyperbolic_point_2& q1,
|
||||||
|
const typename Traits::Hyperbolic_point_2& q2)
|
||||||
|
{
|
||||||
|
Hyperbolic_isometry_2<Traits> A,B,Binv,C;
|
||||||
|
A = hyperbolic_translation<Traits>(p1);
|
||||||
|
B = hyperbolic_translation<Traits>(q1);
|
||||||
|
Binv = hyperbolic_translation<Traits>(q1, true);
|
||||||
|
C = hyperbolic_rotation<Traits>(A.evaluate(p2), B.evaluate(q2));
|
||||||
|
return (Binv*C)*A;
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
||||||
|
#endif // CGAL_HYPERBOLIC_ISOMETRY_2_H
|
||||||
|
|
@ -0,0 +1,34 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Marc Pouget, Monique Teillaud
|
||||||
|
|
||||||
|
#ifndef CGAL_HYPERBOLIC_SURFACE_TRAITS_2
|
||||||
|
#define CGAL_HYPERBOLIC_SURFACE_TRAITS_2
|
||||||
|
|
||||||
|
#include <CGAL/license/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/Complex_number.h>
|
||||||
|
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
template<class HyperbolicTraitsClass>
|
||||||
|
class Hyperbolic_surface_traits_2
|
||||||
|
: public HyperbolicTraitsClass
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef typename HyperbolicTraitsClass::FT FT;
|
||||||
|
typedef typename HyperbolicTraitsClass::Hyperbolic_point_2 Hyperbolic_point_2;
|
||||||
|
typedef Complex_number<FT> Complex;
|
||||||
|
};
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
||||||
|
#endif // CGAL_HYPERBOLIC_SURFACE_TRAITS_2
|
||||||
|
|
@ -0,0 +1,835 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Marc Pouget, Monique Teillaud
|
||||||
|
|
||||||
|
#ifndef CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_H
|
||||||
|
#define CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_H
|
||||||
|
|
||||||
|
#include <CGAL/license/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/Combinatorial_map.h>
|
||||||
|
#include <CGAL/Hyperbolic_fundamental_domain_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/assertions.h>
|
||||||
|
|
||||||
|
#include <fstream>
|
||||||
|
#include <iostream>
|
||||||
|
#include <map>
|
||||||
|
#include <queue>
|
||||||
|
#include <vector>
|
||||||
|
#include <tuple>
|
||||||
|
#include <unordered_map>
|
||||||
|
#include <utility>
|
||||||
|
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
/*
|
||||||
|
Represents a geodesic triangulation of a closed orientable hyperbolic surface.
|
||||||
|
The triangulation is stored as combinatorial map decorated with one cross-ratio per edge.
|
||||||
|
It is also possible to specify an anchor for the triangulation. An anchor consists in 1) a dart of the combinatorial map, belonging by definition to a vertex V and a triangle T, together with
|
||||||
|
2) three points A,B,C in the hyperbolic plane. The points A,B,C are the three vertices in counter-clockwise order of a triangle. This triangle is a lift
|
||||||
|
of T, and A is a lift of V.
|
||||||
|
*/
|
||||||
|
template<class Traits>
|
||||||
|
struct Combinatorial_map_with_cross_ratios_item
|
||||||
|
{
|
||||||
|
template <class CMap>
|
||||||
|
struct Dart_wrapper
|
||||||
|
{
|
||||||
|
typedef Cell_attribute<CMap, Complex_number<typename Traits::FT> > Edge_attrib;
|
||||||
|
typedef std::tuple<void, Edge_attrib, void> Attributes;
|
||||||
|
};
|
||||||
|
};
|
||||||
|
|
||||||
|
template<class Traits, class Attributes = Combinatorial_map_with_cross_ratios_item<Traits> >
|
||||||
|
class Triangulation_on_hyperbolic_surface_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef Combinatorial_map<2, Attributes> Combinatorial_map_with_cross_ratios;
|
||||||
|
|
||||||
|
struct Anchor
|
||||||
|
{
|
||||||
|
typename Combinatorial_map_with_cross_ratios::Dart_descriptor dart;
|
||||||
|
typename Traits::Hyperbolic_point_2 vertices[3];
|
||||||
|
|
||||||
|
Anchor(){};
|
||||||
|
|
||||||
|
Anchor(typename Combinatorial_map_with_cross_ratios::Dart_descriptor dart,
|
||||||
|
typename Traits::Hyperbolic_point_2 a, typename Traits::Hyperbolic_point_2 b, typename Traits::Hyperbolic_point_2 c)
|
||||||
|
{
|
||||||
|
this->dart = dart;
|
||||||
|
vertices[0] = a;
|
||||||
|
vertices[1] = b;
|
||||||
|
vertices[2] = c;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::Dart_descriptor Dart_descriptor;
|
||||||
|
// typedef typename Combinatorial_map_with_cross_ratios::Dart_range Dart_range;
|
||||||
|
// typedef typename Combinatorial_map_with_cross_ratios::Dart_range::iterator Dart_iterator;
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_range<0> Vertex_range;
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_range<1> Edge_range;
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_range<2> Face_range;
|
||||||
|
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::Dart_const_descriptor Dart_const_descriptor;
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::Dart_const_range Dart_const_range;
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_const_range<0> Vertex_const_range;
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_const_range<1> Edge_const_range;
|
||||||
|
typedef typename Combinatorial_map_with_cross_ratios::template One_dart_per_cell_const_range<2> Face_const_range;
|
||||||
|
|
||||||
|
typedef typename Traits::FT Number;
|
||||||
|
typedef typename Traits::Complex Complex_number;
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
typedef Hyperbolic_isometry_2<Traits> Isometry;
|
||||||
|
typedef Hyperbolic_fundamental_domain_2<Traits> Domain;
|
||||||
|
|
||||||
|
Triangulation_on_hyperbolic_surface_2() {};
|
||||||
|
Triangulation_on_hyperbolic_surface_2(const Hyperbolic_fundamental_domain_2<Traits>& domain);
|
||||||
|
// Triangulation_on_hyperbolic_surface_2(Combinatorial_map_with_cross_ratios& cmap);
|
||||||
|
Triangulation_on_hyperbolic_surface_2(Combinatorial_map_with_cross_ratios& cmap, Anchor& anchor);
|
||||||
|
|
||||||
|
Combinatorial_map_with_cross_ratios& combinatorial_map();
|
||||||
|
bool has_anchor() const;
|
||||||
|
Anchor& anchor();
|
||||||
|
const Anchor& anchor() const;
|
||||||
|
|
||||||
|
void to_stream(std::ostream& s) const;
|
||||||
|
void from_stream(std::istream& s);
|
||||||
|
|
||||||
|
bool is_Delaunay_flippable(Dart_const_descriptor dart) const;
|
||||||
|
void flip(Dart_descriptor dart);
|
||||||
|
bool is_Delaunay() const;
|
||||||
|
int make_Delaunay();
|
||||||
|
std::vector<std::tuple<Dart_const_descriptor, Point, Point, Point> > lift(bool center=true) const;
|
||||||
|
|
||||||
|
bool is_valid() const;
|
||||||
|
|
||||||
|
// The following methods are not documented but they are non private for internal future use.
|
||||||
|
Dart_descriptor ccw(Dart_descriptor dart);
|
||||||
|
Dart_descriptor cw(Dart_descriptor dart);
|
||||||
|
Dart_descriptor opposite(Dart_descriptor dart);
|
||||||
|
Dart_const_descriptor const_ccw(Dart_const_descriptor dart) const;
|
||||||
|
Dart_const_descriptor const_cw(Dart_const_descriptor dart) const;
|
||||||
|
Dart_const_descriptor const_opposite(Dart_const_descriptor dart) const;
|
||||||
|
|
||||||
|
Complex_number get_cross_ratio(Dart_const_descriptor dart) const;
|
||||||
|
|
||||||
|
// returns the cross ratio of the points a,b,c,d
|
||||||
|
Complex_number cross_ratio(const Point& a, const Point& b, const Point& c, const Point& d) const;
|
||||||
|
// returns the point d such that the cross ratio of a,b,c,d is cratio
|
||||||
|
Point fourth_point_from_cross_ratio(const Point& a, const Point& b, const Point& c, const Complex_number& cratio) const;
|
||||||
|
|
||||||
|
// Wrapper around the Cmap for iterating over vertices, edges or faces.
|
||||||
|
Vertex_range vertices_range() {
|
||||||
|
return combinatorial_map_.template one_dart_per_cell<0>();
|
||||||
|
}
|
||||||
|
Edge_range edges_range() {
|
||||||
|
return combinatorial_map_.template one_dart_per_cell<1>();
|
||||||
|
}
|
||||||
|
Face_range faces_range() {
|
||||||
|
return combinatorial_map_.template one_dart_per_cell<2>();
|
||||||
|
}
|
||||||
|
Vertex_const_range vertices_const_range() const {
|
||||||
|
return combinatorial_map_.template one_dart_per_cell<0>();
|
||||||
|
}
|
||||||
|
Edge_const_range edges_const_range() const {
|
||||||
|
return combinatorial_map_.template one_dart_per_cell<1>();
|
||||||
|
}
|
||||||
|
Face_const_range faces_const_range() const {
|
||||||
|
return combinatorial_map_.template one_dart_per_cell<2>();
|
||||||
|
}
|
||||||
|
|
||||||
|
protected:
|
||||||
|
Combinatorial_map_with_cross_ratios combinatorial_map_;
|
||||||
|
bool has_anchor_ = false;
|
||||||
|
Anchor anchor_;
|
||||||
|
|
||||||
|
Dart_descriptor pick_edge_to_flip();
|
||||||
|
Dart_const_descriptor pick_edge_to_flip() const;
|
||||||
|
|
||||||
|
void copy_from(Combinatorial_map_with_cross_ratios& cmap);
|
||||||
|
void copy_from(Combinatorial_map_with_cross_ratios& cmap, const Anchor& anchor);
|
||||||
|
};
|
||||||
|
|
||||||
|
// template<class Traits, class Attributes> std::ostream& operator<<(std::ostream& s, const Triangulation_on_hyperbolic_surface_2<Traits, Attributes>& triangulation);
|
||||||
|
// template<class Traits, class Attributes> void operator>>(std::istream& s, Triangulation_on_hyperbolic_surface_2<Traits, Attributes>& triangulation);
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits,Attributes>::
|
||||||
|
Triangulation_on_hyperbolic_surface_2(const Domain& domain)
|
||||||
|
{
|
||||||
|
// (Triangulates by adding an internal edge between domain.vertex(size-1) and the other vertices)
|
||||||
|
combinatorial_map_.clear();
|
||||||
|
std::size_t size = domain.size();
|
||||||
|
|
||||||
|
// Make the triangles
|
||||||
|
std::vector<Dart_descriptor> dart_of_triangle(size-2);
|
||||||
|
for (std::size_t k=0; k<size-2; ++k) {
|
||||||
|
dart_of_triangle[k] = combinatorial_map_.make_combinatorial_polygon(3);
|
||||||
|
}
|
||||||
|
|
||||||
|
// Sew the internal edges and set their cross ratios
|
||||||
|
Dart_descriptor dart_1, dart_2;
|
||||||
|
Point p0, p1, p2, p3;
|
||||||
|
|
||||||
|
for (std::size_t k=1; k<size-2; ++k) {
|
||||||
|
dart_1 = dart_of_triangle[k];
|
||||||
|
dart_2 = cw(dart_of_triangle[k-1]);
|
||||||
|
|
||||||
|
p0 = domain.vertex(size-1);
|
||||||
|
p1 = domain.vertex(k-1);
|
||||||
|
p2 = domain.vertex(k);
|
||||||
|
p3 = domain.vertex(k+1);
|
||||||
|
|
||||||
|
combinatorial_map_.template sew<2>(dart_1, dart_2);
|
||||||
|
combinatorial_map_.template set_attribute<1>(dart_1, combinatorial_map_.template create_attribute<1>(cross_ratio(p0,p1,p2,p3)));
|
||||||
|
}
|
||||||
|
|
||||||
|
// Sew the boundary edges and set their cross ratios
|
||||||
|
for (std::size_t k1=0; k1<size; k1++) {
|
||||||
|
std::size_t k2 = domain.paired_side(k1);
|
||||||
|
|
||||||
|
p0 = domain.vertex((k1+1)%size);
|
||||||
|
p2 = domain.vertex(k1);
|
||||||
|
|
||||||
|
if (k1 == size-1) {
|
||||||
|
dart_1 = dart_of_triangle[0];
|
||||||
|
p1 = domain.vertex(1);
|
||||||
|
} else if (k1 == size-2) {
|
||||||
|
dart_1 = cw(dart_of_triangle[size-3]);
|
||||||
|
p1 = domain.vertex(size-3);
|
||||||
|
} else {
|
||||||
|
dart_1 = ccw(dart_of_triangle[k1]);
|
||||||
|
p1 = domain.vertex(size-1);
|
||||||
|
}
|
||||||
|
|
||||||
|
if (k2 == size-1) {
|
||||||
|
dart_2 = dart_of_triangle[0];
|
||||||
|
p3 = domain.vertex(1);
|
||||||
|
} else if (k2 == size-2) {
|
||||||
|
dart_2 = cw(dart_of_triangle[size-3]);
|
||||||
|
p3 = domain.vertex(size-3);
|
||||||
|
} else {
|
||||||
|
dart_2 = ccw(dart_of_triangle[k2]);
|
||||||
|
p3 = domain.vertex(size-1);
|
||||||
|
}
|
||||||
|
|
||||||
|
p3 = domain.side_pairing(k1).evaluate(p3);
|
||||||
|
|
||||||
|
if (combinatorial_map_.template is_sewable<2>(dart_1, dart_2)) {
|
||||||
|
combinatorial_map_.template sew<2>(dart_1, dart_2);
|
||||||
|
combinatorial_map_.template set_attribute<1>(dart_1, combinatorial_map_.template create_attribute<1>(cross_ratio(p0,p1,p2,p3)));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// Set the anchor
|
||||||
|
anchor_.dart = dart_of_triangle[0];
|
||||||
|
anchor_.vertices[0] = domain.vertex(size-1);
|
||||||
|
anchor_.vertices[1] = domain.vertex(0);
|
||||||
|
anchor_.vertices[2] = domain.vertex(1);
|
||||||
|
has_anchor_ = true;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* template<class Traits, class Attributes> */
|
||||||
|
/* Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Triangulation_on_hyperbolic_surface_2(Combinatorial_map_with_cross_ratios& cmap) { */
|
||||||
|
/* copy_from(cmap); */
|
||||||
|
/* } */
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
Triangulation_on_hyperbolic_surface_2(Combinatorial_map_with_cross_ratios& cmap,
|
||||||
|
Anchor& anchor)
|
||||||
|
{
|
||||||
|
copy_from(cmap, anchor);
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Combinatorial_map_with_cross_ratios&
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
combinatorial_map()
|
||||||
|
{
|
||||||
|
return combinatorial_map_;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
bool
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
has_anchor() const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid());
|
||||||
|
return has_anchor_;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Anchor&
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
anchor()
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid() && has_anchor());
|
||||||
|
return anchor_;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
const typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Anchor&
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
anchor() const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid() && has_anchor());
|
||||||
|
return anchor_;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
bool
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
is_Delaunay_flippable(Dart_const_descriptor dart) const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid());
|
||||||
|
return (get_cross_ratio(dart).imag() > Number(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
void
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
flip(Dart_descriptor dart)
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid());
|
||||||
|
|
||||||
|
// First gather all the information needed
|
||||||
|
|
||||||
|
Dart_descriptor a = opposite(dart); // Get a fresh descriptor
|
||||||
|
Dart_descriptor b = ccw(a);
|
||||||
|
Dart_descriptor c = cw(a);
|
||||||
|
|
||||||
|
Dart_descriptor d = opposite(a);
|
||||||
|
Dart_descriptor e = ccw(d);
|
||||||
|
Dart_descriptor f = cw(d);
|
||||||
|
|
||||||
|
Complex_number cross_ratio_AB = get_cross_ratio(e);
|
||||||
|
Complex_number cross_ratio_BC = get_cross_ratio(f);
|
||||||
|
Complex_number cross_ratio_CD = get_cross_ratio(b);
|
||||||
|
Complex_number cross_ratio_DA = get_cross_ratio(c);
|
||||||
|
Complex_number cross_ratio_AC = get_cross_ratio(a);
|
||||||
|
|
||||||
|
// Modify the anchor
|
||||||
|
|
||||||
|
if (anchor_.dart == a) {
|
||||||
|
anchor_.dart = e;
|
||||||
|
anchor_.vertices[1] = Point(fourth_point_from_cross_ratio(anchor_.vertices[1], anchor_.vertices[2], anchor_.vertices[0], cross_ratio_AC));
|
||||||
|
} else if (anchor_.dart == b) {
|
||||||
|
anchor_.vertices[2] = Point(fourth_point_from_cross_ratio(anchor_.vertices[0], anchor_.vertices[1], anchor_.vertices[2], cross_ratio_AC));
|
||||||
|
} else if (anchor_.dart == c) {
|
||||||
|
anchor_.vertices[2] = Point(fourth_point_from_cross_ratio(anchor_.vertices[2], anchor_.vertices[0], anchor_.vertices[1], cross_ratio_AC));
|
||||||
|
} else if (anchor_.dart == d) {
|
||||||
|
anchor_.dart = b;
|
||||||
|
anchor_.vertices[1] = Point(fourth_point_from_cross_ratio(anchor_.vertices[1], anchor_.vertices[2], anchor_.vertices[0], cross_ratio_AC));
|
||||||
|
} else if (anchor_.dart == e) {
|
||||||
|
anchor_.vertices[2] = Point(fourth_point_from_cross_ratio(anchor_.vertices[0], anchor_.vertices[1], anchor_.vertices[2], cross_ratio_AC));
|
||||||
|
} else if (anchor_.dart == f) {
|
||||||
|
anchor_.vertices[2] = Point(fourth_point_from_cross_ratio(anchor_.vertices[2], anchor_.vertices[0], anchor_.vertices[1], cross_ratio_AC));
|
||||||
|
}
|
||||||
|
|
||||||
|
// Compute the new cross ratios
|
||||||
|
|
||||||
|
Complex_number one (Number(1), Number(0));
|
||||||
|
Complex_number cross_ratio_BD = (cross_ratio_AC) / ((cross_ratio_AC) - one);
|
||||||
|
Complex_number cross_ratio_AB_2 = one - (one - (cross_ratio_AB)) * (cross_ratio_AC);
|
||||||
|
Complex_number cross_ratio_BC_2 = one - (one - (cross_ratio_BC)) / (cross_ratio_BD);
|
||||||
|
Complex_number cross_ratio_CD_2 = one - (one - (cross_ratio_CD)) * (cross_ratio_AC);
|
||||||
|
Complex_number cross_ratio_DA_2 = one - (one - (cross_ratio_DA)) / (cross_ratio_BD);
|
||||||
|
|
||||||
|
// Make the topological flip
|
||||||
|
|
||||||
|
combinatorial_map_.template unlink_beta<1>(a);
|
||||||
|
combinatorial_map_.template unlink_beta<1>(b);
|
||||||
|
combinatorial_map_.template unlink_beta<1>(c);
|
||||||
|
|
||||||
|
combinatorial_map_.template unlink_beta<1>(d);
|
||||||
|
combinatorial_map_.template unlink_beta<1>(e);
|
||||||
|
combinatorial_map_.template unlink_beta<1>(f);
|
||||||
|
|
||||||
|
|
||||||
|
combinatorial_map_.template link_beta<1>(b, a);
|
||||||
|
combinatorial_map_.template link_beta<1>(a, f);
|
||||||
|
combinatorial_map_.template link_beta<1>(f, b);
|
||||||
|
|
||||||
|
combinatorial_map_.template link_beta<1>(e, d);
|
||||||
|
combinatorial_map_.template link_beta<1>(d, c);
|
||||||
|
combinatorial_map_.template link_beta<1>(c, e);
|
||||||
|
|
||||||
|
// And give the new cross ratios to the edges
|
||||||
|
|
||||||
|
combinatorial_map_.template info<1>(a) = cross_ratio_BD;
|
||||||
|
combinatorial_map_.template info<1>(e) = cross_ratio_AB_2;
|
||||||
|
combinatorial_map_.template info<1>(f) = cross_ratio_BC_2;
|
||||||
|
combinatorial_map_.template info<1>(b) = cross_ratio_CD_2;
|
||||||
|
combinatorial_map_.template info<1>(c) = cross_ratio_DA_2;
|
||||||
|
|
||||||
|
// Take care of the particular cases where we need to "flip again"
|
||||||
|
|
||||||
|
if (opposite(e) == b) {
|
||||||
|
combinatorial_map_.template info<1>(e) = one - (one - cross_ratio_AB_2) * (cross_ratio_AC);
|
||||||
|
}
|
||||||
|
|
||||||
|
if (opposite(f) == c) {
|
||||||
|
combinatorial_map_.template info<1>(f) = one - (one - cross_ratio_BC_2) / (cross_ratio_BD);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
bool
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
is_Delaunay() const
|
||||||
|
{
|
||||||
|
if (! is_valid()) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
return (pick_edge_to_flip() == nullptr);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
int
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
make_Delaunay()
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid());
|
||||||
|
int number_of_flips_done = 0;
|
||||||
|
|
||||||
|
Dart_descriptor edge_to_flip = pick_edge_to_flip();
|
||||||
|
while (edge_to_flip != nullptr) {
|
||||||
|
flip(edge_to_flip);
|
||||||
|
edge_to_flip = pick_edge_to_flip();
|
||||||
|
number_of_flips_done++;
|
||||||
|
}
|
||||||
|
|
||||||
|
return number_of_flips_done;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
std::vector<std::tuple<typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_const_descriptor,
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Point,
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Point,
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Point> >
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
lift(bool center) const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid() && has_anchor());
|
||||||
|
|
||||||
|
std::vector<std::tuple<Dart_const_descriptor, Point, Point, Point> > realizations;
|
||||||
|
|
||||||
|
size_t visited_darts_mark = combinatorial_map_.get_new_mark();
|
||||||
|
combinatorial_map_.unmark_all(visited_darts_mark);
|
||||||
|
|
||||||
|
struct Compare
|
||||||
|
{
|
||||||
|
bool operator()(const std::pair<Dart_const_descriptor,double>& x,
|
||||||
|
const std::pair<Dart_const_descriptor,double>& y)
|
||||||
|
{
|
||||||
|
return x.second > y.second;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
std::priority_queue<std::pair<Dart_const_descriptor, double>,
|
||||||
|
std::vector<std::pair<Dart_const_descriptor, double> >, Compare> queue;
|
||||||
|
|
||||||
|
std::unordered_map<Dart_const_descriptor, Point> positions;
|
||||||
|
|
||||||
|
Dart_const_range darts = combinatorial_map_.darts();
|
||||||
|
|
||||||
|
combinatorial_map_.mark(anchor_.dart, visited_darts_mark);
|
||||||
|
combinatorial_map_.mark(const_ccw(anchor_.dart), visited_darts_mark);
|
||||||
|
combinatorial_map_.mark(const_cw(anchor_.dart), visited_darts_mark);
|
||||||
|
|
||||||
|
if (center) {
|
||||||
|
Isometry center_the_drawing = hyperbolic_translation<Traits>(anchor_.vertices[0]);
|
||||||
|
positions[anchor_.dart] = center_the_drawing.evaluate(anchor_.vertices[0]);
|
||||||
|
positions[const_ccw(anchor_.dart)] = center_the_drawing.evaluate(anchor_.vertices[1]);
|
||||||
|
positions[const_cw(anchor_.dart)] = center_the_drawing.evaluate(anchor_.vertices[2]);
|
||||||
|
} else {
|
||||||
|
positions[anchor_.dart] = anchor_.vertices[0];
|
||||||
|
positions[const_ccw(anchor_.dart)] = anchor_.vertices[1];
|
||||||
|
positions[const_cw(anchor_.dart)] = anchor_.vertices[2];
|
||||||
|
}
|
||||||
|
|
||||||
|
std::tuple<Dart_const_descriptor, Point, Point, Point> value =
|
||||||
|
std::make_tuple(anchor_.dart,
|
||||||
|
positions[anchor_.dart],
|
||||||
|
positions[const_ccw(anchor_.dart)],
|
||||||
|
positions[const_cw(anchor_.dart)]);
|
||||||
|
realizations.push_back(value);
|
||||||
|
|
||||||
|
Complex_number anchor_z0(anchor_.vertices[0].x(), anchor_.vertices[0].y());
|
||||||
|
Complex_number anchor_z1(anchor_.vertices[1].x(), anchor_.vertices[1].y());
|
||||||
|
Complex_number anchor_z2(anchor_.vertices[2].x(), anchor_.vertices[2].y());
|
||||||
|
|
||||||
|
double weight_of_anchor_dart = CGAL::to_double(norm(anchor_z0) + norm(anchor_z1));
|
||||||
|
double weight_of_ccw_anchor_dart = CGAL::to_double(norm(anchor_z1) + norm(anchor_z2));
|
||||||
|
double weight_of_cw_anchor_dart = CGAL::to_double(norm(anchor_z2) + norm(anchor_z0));
|
||||||
|
|
||||||
|
queue.push(std::make_pair(anchor_.dart, weight_of_anchor_dart));
|
||||||
|
queue.push(std::make_pair(const_ccw(anchor_.dart), weight_of_ccw_anchor_dart));
|
||||||
|
queue.push(std::make_pair(const_cw(anchor_.dart), weight_of_cw_anchor_dart));
|
||||||
|
|
||||||
|
while (! queue.empty()) {
|
||||||
|
Dart_const_descriptor invader = queue.top().first;
|
||||||
|
queue.pop();
|
||||||
|
|
||||||
|
Dart_const_descriptor invaded = const_opposite(invader);
|
||||||
|
|
||||||
|
if (!combinatorial_map_.is_marked(invaded, visited_darts_mark)) {
|
||||||
|
combinatorial_map_.mark(invaded, visited_darts_mark);
|
||||||
|
combinatorial_map_.mark(const_ccw(invaded), visited_darts_mark);
|
||||||
|
combinatorial_map_.mark(const_cw(invaded), visited_darts_mark);
|
||||||
|
|
||||||
|
const Point& a = positions[const_ccw(invader)];
|
||||||
|
const Point& b = positions[const_cw(invader)];
|
||||||
|
const Point& c = positions[invader];
|
||||||
|
Complex_number cross_ratio = get_cross_ratio(invader);
|
||||||
|
|
||||||
|
positions[invaded] = a;
|
||||||
|
positions[const_ccw(invaded)] = c;
|
||||||
|
Point d = fourth_point_from_cross_ratio(a, b, c, cross_ratio);
|
||||||
|
positions[const_cw(invaded)] = d;
|
||||||
|
|
||||||
|
Complex_number za(a.x(), a.y());
|
||||||
|
Complex_number zc(c.x(), c.y());
|
||||||
|
double invaded_distance_to_zero = CGAL::to_double(norm(za));
|
||||||
|
double invaded_ccw_distance_to_zero = CGAL::to_double(norm(zc));
|
||||||
|
Complex_number znew(positions[const_cw(invaded)].x(), positions[const_cw(invaded)].y());
|
||||||
|
double invaded_cw_distance_to_zero = CGAL::to_double(norm(znew));
|
||||||
|
|
||||||
|
double invaded_ccw_weight = invaded_ccw_distance_to_zero + invaded_cw_distance_to_zero;
|
||||||
|
double invaded_cw_weight = invaded_cw_distance_to_zero + invaded_distance_to_zero;
|
||||||
|
|
||||||
|
queue.push(std::make_pair(const_ccw(invaded), invaded_ccw_weight));
|
||||||
|
queue.push(std::make_pair(const_cw(invaded), invaded_cw_weight));
|
||||||
|
|
||||||
|
value = std::make_tuple(invaded, Point(a), Point(c), Point(d));
|
||||||
|
realizations.push_back(value);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
combinatorial_map_.free_mark(visited_darts_mark);
|
||||||
|
|
||||||
|
return realizations;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
bool
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
is_valid() const
|
||||||
|
{
|
||||||
|
// 1. Check the combinatorial map
|
||||||
|
|
||||||
|
// Check that the combinatorial map is valid
|
||||||
|
if (!combinatorial_map_.is_valid()) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Check that the combinatorial map has no 1,2-boundary
|
||||||
|
for (int k=1; k<3; ++k) {
|
||||||
|
if (!combinatorial_map_.is_without_boundary(k)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// 2. Check the anchor, if any
|
||||||
|
|
||||||
|
if (has_anchor_) {
|
||||||
|
// Check that the dart descriptor of the anchor points to a dart of the combinatorial map
|
||||||
|
if (!combinatorial_map_.is_dart_used(anchor_.dart)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Check that the three vertices of the anchor lie within the open unit disk
|
||||||
|
for (int k=0; k<3; ++k) {
|
||||||
|
// if (anchor_.vertices[k].get_z() >= Number(1)) {
|
||||||
|
if (norm(Complex_number(anchor_.vertices[k].x(),anchor_.vertices[k].y())) >= Number(1)) {
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
void
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
to_stream(std::ostream& s) const
|
||||||
|
{
|
||||||
|
CGAL_precondition(is_valid() && has_anchor());
|
||||||
|
|
||||||
|
// Give indices to the darts
|
||||||
|
std::map<Dart_const_descriptor, int> darts_indices;
|
||||||
|
int current_dart_index = 0;
|
||||||
|
for (typename Dart_const_range::const_iterator it=combinatorial_map_.darts().begin(); it!=combinatorial_map_.darts().end(); ++it) {
|
||||||
|
darts_indices[it] = current_dart_index;
|
||||||
|
current_dart_index++;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Store the number of darts
|
||||||
|
s << current_dart_index << std::endl;
|
||||||
|
|
||||||
|
// Store the anchor, if any
|
||||||
|
if (has_anchor_) {
|
||||||
|
s << "yes" << std::endl;
|
||||||
|
s << darts_indices[anchor_.dart] << std::endl;
|
||||||
|
s << anchor_.vertices[0] << std::endl;
|
||||||
|
s << anchor_.vertices[1] << std::endl;
|
||||||
|
s << anchor_.vertices[2] << std::endl;
|
||||||
|
} else {
|
||||||
|
s << "no" << std::endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Store the triangles
|
||||||
|
for (typename Face_const_range::const_iterator it = faces_const_range().begin(); it != faces_const_range().end(); ++it) {
|
||||||
|
s << darts_indices[it] << std::endl;
|
||||||
|
s << darts_indices[const_cw(it)] << std::endl;
|
||||||
|
s << darts_indices[const_ccw(it)] << std::endl;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Store the edges
|
||||||
|
for (typename Edge_const_range::const_iterator it = edges_const_range().begin(); it != edges_const_range().end(); ++it) {
|
||||||
|
s << darts_indices[it] << std::endl;
|
||||||
|
s << darts_indices[const_opposite(it)] << std::endl;
|
||||||
|
s << get_cross_ratio(it);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
void
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
from_stream(std::istream& s)
|
||||||
|
{
|
||||||
|
combinatorial_map_.clear();
|
||||||
|
|
||||||
|
// Load the number of darts
|
||||||
|
std::string line;
|
||||||
|
s >> line;
|
||||||
|
int nb_darts = std::stoi(line);
|
||||||
|
|
||||||
|
// Load the anchor
|
||||||
|
int anchor_dart_id = 0;
|
||||||
|
s >> line;
|
||||||
|
if (!line.compare("yes")) {
|
||||||
|
has_anchor_ = true;
|
||||||
|
|
||||||
|
s >> line;
|
||||||
|
anchor_dart_id = std::stoi(line); // (*) anchor_.dart_id is set at the end of the function
|
||||||
|
|
||||||
|
s >> anchor_.vertices[0];
|
||||||
|
s >> anchor_.vertices[1];
|
||||||
|
s >> anchor_.vertices[2];
|
||||||
|
} else {
|
||||||
|
has_anchor_ = false;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Load the triangles
|
||||||
|
std::vector<Dart_descriptor> darts_by_id (nb_darts);
|
||||||
|
int index1, index2, index3;
|
||||||
|
for (int k=0; k<nb_darts/3; ++k) {
|
||||||
|
Dart_descriptor triangle_dart = combinatorial_map_.make_combinatorial_polygon(3);
|
||||||
|
|
||||||
|
s >> line;
|
||||||
|
index1 = std::stoi(line);
|
||||||
|
s >> line;
|
||||||
|
index2 = std::stoi(line);
|
||||||
|
s >> line;
|
||||||
|
index3 = std::stoi(line);
|
||||||
|
|
||||||
|
darts_by_id[index1] = triangle_dart;
|
||||||
|
darts_by_id[index2] = cw(triangle_dart);
|
||||||
|
darts_by_id[index3] = ccw(triangle_dart);
|
||||||
|
}
|
||||||
|
|
||||||
|
// Load the edges
|
||||||
|
Dart_descriptor dart_1, dart_2;
|
||||||
|
Complex_number cross_ratio;
|
||||||
|
for (int k=0; k<nb_darts/2; ++k) {
|
||||||
|
s >> line;
|
||||||
|
index1 = std::stoi(line);
|
||||||
|
s >> line;
|
||||||
|
index2 = std::stoi(line);
|
||||||
|
dart_1 = darts_by_id[index1];
|
||||||
|
dart_2 = darts_by_id[index2];
|
||||||
|
combinatorial_map_.template sew<2>(dart_1, dart_2);
|
||||||
|
s >> cross_ratio;
|
||||||
|
combinatorial_map_.template set_attribute<1>(dart_1, combinatorial_map_.template create_attribute<1>(cross_ratio));
|
||||||
|
}
|
||||||
|
|
||||||
|
// (*) here
|
||||||
|
if (has_anchor_) {
|
||||||
|
anchor_.dart = darts_by_id[anchor_dart_id];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_descriptor Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::ccw(Dart_descriptor dart) {
|
||||||
|
return combinatorial_map_.beta(dart, 1);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_descriptor Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::cw(Dart_descriptor dart) {
|
||||||
|
return combinatorial_map_.beta(dart, 0);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_descriptor Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::opposite(Dart_descriptor dart) {
|
||||||
|
return combinatorial_map_.opposite(dart);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_const_descriptor Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::const_ccw(Dart_const_descriptor dart) const {
|
||||||
|
return combinatorial_map_.beta(dart, 1);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_const_descriptor Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::const_cw(Dart_const_descriptor dart) const {
|
||||||
|
return combinatorial_map_.beta(dart, 0);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_const_descriptor Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::const_opposite(Dart_const_descriptor dart) const {
|
||||||
|
return combinatorial_map_.opposite(dart);
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Complex_number Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::get_cross_ratio(Dart_const_descriptor dart) const {
|
||||||
|
return combinatorial_map_.template info_of_attribute<1>(combinatorial_map_.template attribute<1>(dart));
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_descriptor Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
pick_edge_to_flip()
|
||||||
|
{
|
||||||
|
auto& cm = combinatorial_map_.darts();
|
||||||
|
for (auto it=cm.begin(); it!=cm.end(); ++it) {
|
||||||
|
if (is_Delaunay_flippable(it)) {
|
||||||
|
return it;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return nullptr;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Dart_const_descriptor
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
pick_edge_to_flip() const
|
||||||
|
{
|
||||||
|
const auto& cm = combinatorial_map_.darts();
|
||||||
|
for (auto it=cm.begin(); it!=cm.end(); ++it) {
|
||||||
|
if (is_Delaunay_flippable(it) ) {
|
||||||
|
return it;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return nullptr;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
void
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
copy_from(Combinatorial_map_with_cross_ratios& cmap)
|
||||||
|
{
|
||||||
|
//combinatorial_map_.copy_from_const(cmap);
|
||||||
|
combinatorial_map_.copy(cmap);
|
||||||
|
has_anchor_ = false;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
void
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
copy_from(Combinatorial_map_with_cross_ratios& cmap,
|
||||||
|
const Anchor& anchor)
|
||||||
|
{
|
||||||
|
// Because of the anchor, we must operate the copy ourself
|
||||||
|
combinatorial_map_.clear();
|
||||||
|
|
||||||
|
// Copy the triangles and fill the darts conversion table
|
||||||
|
std::map<Dart_const_descriptor, Dart_descriptor> darts_table;
|
||||||
|
for (typename Face_const_range::const_iterator it=cmap.template one_dart_per_cell<2>().begin(); it!=cmap.template one_dart_per_cell<2>().end(); ++it) {
|
||||||
|
Dart_descriptor new_dart = combinatorial_map_.make_combinatorial_polygon(3);
|
||||||
|
darts_table[it] = new_dart;
|
||||||
|
darts_table[cmap.beta(it,0)] = combinatorial_map_.beta(new_dart,0);
|
||||||
|
darts_table[cmap.beta(it,1)] = combinatorial_map_.beta(new_dart,1);
|
||||||
|
}
|
||||||
|
|
||||||
|
// Sew the edges and set their cross-ratios
|
||||||
|
for (typename Edge_const_range::const_iterator it=cmap.template one_dart_per_cell<1>().begin(); it!=cmap.template one_dart_per_cell<1>().end(); ++it) {
|
||||||
|
Dart_descriptor dart_1 = darts_table[it];
|
||||||
|
Dart_descriptor dart_2 = darts_table[cmap.opposite(it)];
|
||||||
|
Complex_number cratio = cmap.template info_of_attribute<1>(cmap.template attribute<1>(it));
|
||||||
|
|
||||||
|
combinatorial_map_.template sew<2>(dart_1, dart_2);
|
||||||
|
combinatorial_map_.template set_attribute<1>(dart_1, combinatorial_map_.template create_attribute<1>(cratio));
|
||||||
|
}
|
||||||
|
|
||||||
|
cmap.opposite(anchor.dart);
|
||||||
|
|
||||||
|
// Set the anchor
|
||||||
|
anchor_.dart = darts_table[anchor.dart];
|
||||||
|
for (int k=0; k<3; ++k) {
|
||||||
|
anchor_.vertices[k] = anchor.vertices[k];
|
||||||
|
}
|
||||||
|
has_anchor_ = true;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Traits::Complex
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
cross_ratio(const Point& a, const Point& b, const Point& c, const Point& d) const
|
||||||
|
{
|
||||||
|
Complex_number za (a.x(), a.y());
|
||||||
|
Complex_number zb (b.x(), b.y());
|
||||||
|
Complex_number zc (c.x(), c.y());
|
||||||
|
Complex_number zd (d.x(), d.y());
|
||||||
|
return (zd-zb)*(zc-za) / ((zd-za)*(zc-zb));
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
typename Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::Point
|
||||||
|
Triangulation_on_hyperbolic_surface_2<Traits, Attributes>::
|
||||||
|
fourth_point_from_cross_ratio(const Point& a, const Point& b, const Point& c,
|
||||||
|
const Complex_number& cratio) const
|
||||||
|
{
|
||||||
|
Complex_number za (a.x(), a.y());
|
||||||
|
Complex_number zb (b.x(), b.y());
|
||||||
|
Complex_number zc (c.x(), c.y());
|
||||||
|
Complex_number result = ( cratio*za*(zc-zb) + zb*(za-zc) ) / ( cratio*(zc-zb) + (za-zc));
|
||||||
|
return Point(result.real(), result.imag());
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
||||||
|
#endif // CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_H
|
||||||
|
|
@ -0,0 +1,66 @@
|
||||||
|
// Copyright (c) 2024
|
||||||
|
// INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France).
|
||||||
|
// All rights reserved.
|
||||||
|
//
|
||||||
|
// This file is part of CGAL (www.cgal.org)
|
||||||
|
//
|
||||||
|
// $URL$
|
||||||
|
// $Id$
|
||||||
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||||||
|
//
|
||||||
|
// Author(s) : Vincent Despré, Loïc Dubois, Marc Pouget, Monique Teillaud
|
||||||
|
|
||||||
|
#ifndef CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_IO_H
|
||||||
|
#define CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_IO_H
|
||||||
|
|
||||||
|
#include <CGAL/license/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/assertions.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
|
||||||
|
namespace CGAL {
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
template<class Traits>
|
||||||
|
std::ostream& operator<<(std::ostream& s, const Hyperbolic_fundamental_domain_2<Traits>& domain)
|
||||||
|
{
|
||||||
|
CGAL_precondition(domain.is_valid());
|
||||||
|
return domain.to_stream(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits>
|
||||||
|
std::istream& operator>>(std::istream& s, Hyperbolic_fundamental_domain_2<Traits>& domain)
|
||||||
|
{
|
||||||
|
return domain.from_stream(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
template<class Traits>
|
||||||
|
std::ostream& operator<<(std::ostream& s, const Hyperbolic_isometry_2<Traits>& isometry)
|
||||||
|
{
|
||||||
|
for (int k=0; k<4; ++k) {
|
||||||
|
s << isometry.get_coefficient(k);
|
||||||
|
}
|
||||||
|
return s;
|
||||||
|
}
|
||||||
|
|
||||||
|
////////////////////////////////////////////////////////////////////////////////
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
std::ostream& operator<<(std::ostream& s, const Triangulation_on_hyperbolic_surface_2<Traits, Attributes>& triangulation)
|
||||||
|
{
|
||||||
|
triangulation.to_stream(s);
|
||||||
|
return s;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<class Traits, class Attributes>
|
||||||
|
void operator>>(std::istream& s, Triangulation_on_hyperbolic_surface_2<Traits, Attributes>& triangulation)
|
||||||
|
{
|
||||||
|
triangulation.from_stream(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace CGAL
|
||||||
|
|
||||||
|
#endif // CGAL_TRIANGULATION_ON_HYPERBOLIC_SURFACE_2_IO_H
|
||||||
|
|
@ -0,0 +1,3 @@
|
||||||
|
INRIA Nancy -- France
|
||||||
|
Université de Lorraine -- France
|
||||||
|
Université Gustave Eiffel Marne-la-Vallee -- France
|
||||||
|
|
@ -0,0 +1,26 @@
|
||||||
|
Algebraic_foundations
|
||||||
|
Arithmetic_kernel
|
||||||
|
BGL
|
||||||
|
CGAL_Core
|
||||||
|
Cartesian_kernel
|
||||||
|
Circulator
|
||||||
|
Combinatorial_map
|
||||||
|
Distance_2
|
||||||
|
Distance_3
|
||||||
|
Filtered_kernel
|
||||||
|
Hash_map
|
||||||
|
Homogeneous_kernel
|
||||||
|
Installation
|
||||||
|
Intersections_2
|
||||||
|
Intersections_3
|
||||||
|
Interval_support
|
||||||
|
Kernel_23
|
||||||
|
Kernel_d
|
||||||
|
Modular_arithmetic
|
||||||
|
Number_types
|
||||||
|
Profiling_tools
|
||||||
|
Property_map
|
||||||
|
Random_numbers
|
||||||
|
STL_Extension
|
||||||
|
Stream_support
|
||||||
|
Triangulation_on_hyperbolic_surface_2
|
||||||
|
|
@ -0,0 +1,5 @@
|
||||||
|
Package Triangulation_on_hyperbolic_surface_2 : provides
|
||||||
|
triangulations of closed oriented hyperbolic surfaces,
|
||||||
|
Delaunay flip algorithm on those triangulations,
|
||||||
|
construction of the triangulations from convex geodesic fundamental domains,
|
||||||
|
construction of such domains for genus 2 surfaces
|
||||||
|
|
@ -0,0 +1 @@
|
||||||
|
GPL (v3 or later)
|
||||||
|
|
@ -0,0 +1,3 @@
|
||||||
|
Vincent Despré <vincent.despre@loria.fr>
|
||||||
|
Loïc Dubois <loic.dubois@univ-eiffel.fr>
|
||||||
|
Monique Teillaud <monique.teillaud@inria.fr>
|
||||||
|
|
@ -0,0 +1,16 @@
|
||||||
|
# Created by the script cgal_create_cmake_script
|
||||||
|
# This is the CMake script for compiling a CGAL application.
|
||||||
|
|
||||||
|
cmake_minimum_required(VERSION 3.12...3.31)
|
||||||
|
project(Triangulation_on_hyperbolic_surface_2_Tests)
|
||||||
|
|
||||||
|
find_package(CGAL REQUIRED)
|
||||||
|
|
||||||
|
# create a target per cppfile
|
||||||
|
file(
|
||||||
|
GLOB cppfiles
|
||||||
|
RELATIVE ${CMAKE_CURRENT_SOURCE_DIR}
|
||||||
|
${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
|
||||||
|
foreach(cppfile ${cppfiles})
|
||||||
|
create_single_source_cgal_program("${cppfile}")
|
||||||
|
endforeach()
|
||||||
|
|
@ -0,0 +1,65 @@
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Cartesian.h>
|
||||||
|
|
||||||
|
#include <CGAL/Algebraic_kernel_for_circles_2_2.h>
|
||||||
|
#include <CGAL/Circular_kernel_2/Intersection_traits.h>
|
||||||
|
#include <CGAL/Circular_kernel_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_fundamental_domain_factory_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2_IO.h>
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_CK_traits_2.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
#include <sstream>
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
typedef CGAL::Circular_kernel_2<CGAL::Cartesian<CGAL::Exact_rational>,CGAL::Algebraic_kernel_for_circles_2_2<CGAL::Exact_rational>> Kernel;
|
||||||
|
typedef CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef CGAL::Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_2<Traits> Domain;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_factory_2<Traits> Factory;
|
||||||
|
typedef CGAL::Triangulation_on_hyperbolic_surface_2<Traits> Triangulation;
|
||||||
|
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
|
||||||
|
int main()
|
||||||
|
{
|
||||||
|
Factory factory;
|
||||||
|
Domain domain = factory.make_hyperbolic_fundamental_domain_g2(3459);
|
||||||
|
Triangulation triangulation0 = Triangulation(domain);
|
||||||
|
|
||||||
|
assert(triangulation0.is_valid());
|
||||||
|
|
||||||
|
Triangulation triangulation (triangulation0);
|
||||||
|
assert(triangulation.has_anchor());
|
||||||
|
|
||||||
|
std::stringstream buffer;
|
||||||
|
buffer << triangulation;
|
||||||
|
buffer >> triangulation;
|
||||||
|
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> input_not_centered;
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> input_centered;
|
||||||
|
|
||||||
|
input_not_centered = triangulation.lift(false);
|
||||||
|
input_centered = triangulation.lift();
|
||||||
|
|
||||||
|
triangulation.make_Delaunay();
|
||||||
|
|
||||||
|
assert(triangulation.is_Delaunay());
|
||||||
|
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> output_not_centered;
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> output_centered;
|
||||||
|
|
||||||
|
output_not_centered = triangulation.lift(false);
|
||||||
|
output_centered = triangulation.lift();
|
||||||
|
|
||||||
|
|
||||||
|
Triangulation::Combinatorial_map_with_cross_ratios& cmap = triangulation.combinatorial_map();
|
||||||
|
Triangulation::Anchor& anchor = triangulation.anchor();
|
||||||
|
assert(cmap.is_dart_used(anchor.dart));
|
||||||
|
|
||||||
|
std::cout << "printing triangulation for test purposes: " << std::endl << triangulation;
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,51 @@
|
||||||
|
#include <CGAL/Complex_number.h>
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Interval_nt.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
#include <sstream>
|
||||||
|
|
||||||
|
typedef CGAL::Exact_rational Exact_rational;
|
||||||
|
typedef CGAL::Interval_nt<> Interval;
|
||||||
|
typedef CGAL::Complex_number<Exact_rational> Complex_rational;
|
||||||
|
typedef CGAL::Complex_number<Interval> Complex_interval;
|
||||||
|
|
||||||
|
int main()
|
||||||
|
{
|
||||||
|
// Complex_rational tests :
|
||||||
|
Complex_rational zero_rational = Complex_rational ();
|
||||||
|
assert(zero_rational == Complex_rational(Exact_rational(0), Exact_rational(0)));
|
||||||
|
|
||||||
|
Complex_rational one_rational (Exact_rational(1));
|
||||||
|
assert(one_rational == Complex_rational(Exact_rational(1), Exact_rational(0)));
|
||||||
|
|
||||||
|
Complex_rational z1_rational (Exact_rational(1,2), Exact_rational(-3));
|
||||||
|
z1_rational = - z1_rational;
|
||||||
|
|
||||||
|
Complex_rational z2_rational;
|
||||||
|
z2_rational.real(Exact_rational(-5,7));
|
||||||
|
z2_rational.imag(Exact_rational(11,13));
|
||||||
|
z2_rational = conj(z2_rational) + z1_rational - one_rational;
|
||||||
|
|
||||||
|
assert(- z1_rational * z1_rational / z2_rational == -Complex_rational(Exact_rational(855491,632146), Exact_rational(844298,316073)));
|
||||||
|
assert(z1_rational.real() == Exact_rational(-1,2));
|
||||||
|
assert(z1_rational.imag() == Exact_rational(3));
|
||||||
|
assert(norm(z1_rational) == Exact_rational(37,4));
|
||||||
|
assert(z1_rational != z2_rational);
|
||||||
|
assert(z2_rational == z2_rational);
|
||||||
|
assert(z2_rational == Complex_rational(Exact_rational(-31,14), Exact_rational(28,13)));
|
||||||
|
|
||||||
|
std::cout << "printing a complex for test purposes : " << std::endl << z2_rational << std::endl;
|
||||||
|
|
||||||
|
Complex_rational z3_rational;
|
||||||
|
std::stringstream buffer;
|
||||||
|
buffer << z2_rational;
|
||||||
|
buffer >> z3_rational;
|
||||||
|
assert(z3_rational == z2_rational);
|
||||||
|
|
||||||
|
// Complex_interval test :
|
||||||
|
Complex_interval z_interval (Interval(1, 2), Interval(1, 2));
|
||||||
|
assert(norm(z_interval * z_interval / Complex_interval(Interval(5, 6))) < Interval(10,20));
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,81 @@
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Cartesian.h>
|
||||||
|
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_fundamental_domain_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2_IO.h>
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
typedef CGAL::Cartesian<CGAL::Exact_rational> Kernel;
|
||||||
|
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef CGAL::Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_2<Traits> Domain;
|
||||||
|
|
||||||
|
typedef typename Traits::FT FT;
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
typedef typename Traits::Complex Complex;
|
||||||
|
|
||||||
|
|
||||||
|
int main()
|
||||||
|
{
|
||||||
|
std::vector<Point> vertices;
|
||||||
|
Point z0 = Point(FT("4881/5000"),FT("0"));
|
||||||
|
Point z1 = Point(FT("9211/10000"),FT("2733/10000"));
|
||||||
|
Point z2 = Point(FT("1709/5000"),FT("7253/10000"));
|
||||||
|
Point z3 = Point(FT("-427262704257582473474868322141310044732400799603/1267155016747148041260345910894159385550919570000"),FT("582571804584198065321856347012850217722442509611/1267155016747148041260345910894159385550919570000"));
|
||||||
|
Point z4 = Point(FT("-4881/5000"),FT("0"));
|
||||||
|
Point z5 = Point(FT("-9211/10000"),FT("-2733/10000"));
|
||||||
|
Point z6 = Point(FT("-1709/5000"),FT("-7253/10000"));
|
||||||
|
Point z7 = Point(FT("427262704257582473474868322141310044732400799603/1267155016747148041260345910894159385550919570000"),FT("-582571804584198065321856347012850217722442509611/1267155016747148041260345910894159385550919570000"));
|
||||||
|
vertices.push_back(z0);
|
||||||
|
vertices.push_back(z1);
|
||||||
|
vertices.push_back(z2);
|
||||||
|
vertices.push_back(z3);
|
||||||
|
vertices.push_back(z4);
|
||||||
|
vertices.push_back(z5);
|
||||||
|
vertices.push_back(z6);
|
||||||
|
vertices.push_back(z7);
|
||||||
|
|
||||||
|
std::vector<std::size_t> pairings;
|
||||||
|
for (std::size_t k=0; k<8; ++k) {
|
||||||
|
pairings.push_back((k+4)%8);
|
||||||
|
}
|
||||||
|
|
||||||
|
Domain domain = Domain(vertices, pairings);
|
||||||
|
assert(domain.size()==8);
|
||||||
|
for (std::size_t k=0; k<8; ++k) {
|
||||||
|
assert(domain.vertex(k)==vertices[k]);
|
||||||
|
assert(domain.paired_side(k)==(k+4)%8);
|
||||||
|
assert(domain.side_pairing(k).evaluate(domain.vertex((k+4)%8))==domain.vertex((k+1)%8));
|
||||||
|
assert(domain.side_pairing(k).evaluate(domain.vertex((k+5)%8))==domain.vertex(k));
|
||||||
|
}
|
||||||
|
|
||||||
|
assert(domain.is_valid());
|
||||||
|
|
||||||
|
Domain domain_prime = Domain(vertices, pairings);
|
||||||
|
assert(domain_prime.size()==8);
|
||||||
|
for (std::size_t k=0; k<8; ++k) {
|
||||||
|
assert(domain_prime.vertex(k)==vertices[k]);
|
||||||
|
assert(domain_prime.paired_side(k)==(k+4)%8);
|
||||||
|
|
||||||
|
assert(domain_prime.side_pairing(k).evaluate(domain_prime.vertex((k+4)%8))==domain_prime.vertex((k+1)%8));
|
||||||
|
assert(domain_prime.side_pairing(k).evaluate(domain_prime.vertex((k+5)%8))==domain_prime.vertex(k));
|
||||||
|
}
|
||||||
|
|
||||||
|
Domain domain_ter = Domain();
|
||||||
|
std::stringstream buffer;
|
||||||
|
buffer << domain;
|
||||||
|
buffer >> domain_ter;
|
||||||
|
assert(domain_ter.size()==8);
|
||||||
|
for (std::size_t k=0; k<8; ++k) {
|
||||||
|
assert(domain_ter.vertex(k)==vertices[k]);
|
||||||
|
assert(domain_ter.paired_side(k)==(k+4)%8);
|
||||||
|
}
|
||||||
|
|
||||||
|
std::cout << "printing a domain for test purposes : " << std::endl << domain << std::endl;
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,31 @@
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Cartesian.h>
|
||||||
|
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_fundamental_domain_factory_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
|
||||||
|
typedef CGAL::Cartesian<CGAL::Exact_rational> Kernel;
|
||||||
|
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef CGAL::Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_2<Traits> Domain;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_factory_2<Traits> Factory;
|
||||||
|
|
||||||
|
typedef typename Traits::FT FT;
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
typedef typename Traits::Complex Complex;
|
||||||
|
|
||||||
|
int main()
|
||||||
|
{
|
||||||
|
Factory factory;
|
||||||
|
Domain domain = factory.make_hyperbolic_fundamental_domain_g2(3459);
|
||||||
|
|
||||||
|
assert(domain.size()==8);
|
||||||
|
for (std::size_t k=0; k<8; ++k) {
|
||||||
|
assert(domain.paired_side(k)==(k+4)%8);
|
||||||
|
}
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,88 @@
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Cartesian.h>
|
||||||
|
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_isometry_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2_IO.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
|
||||||
|
typedef CGAL::Cartesian<CGAL::Exact_rational> Kernel;
|
||||||
|
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef CGAL::Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef CGAL::Hyperbolic_isometry_2<Traits> Isometry;
|
||||||
|
|
||||||
|
typedef typename Traits::FT FT;
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
typedef typename Traits::Complex Complex;
|
||||||
|
|
||||||
|
int main()
|
||||||
|
{
|
||||||
|
Isometry identity_1 = Isometry ();
|
||||||
|
assert(identity_1.get_coefficient(0)==Complex(FT(1)));
|
||||||
|
assert(identity_1.get_coefficient(1)==Complex(FT(0)));
|
||||||
|
assert(identity_1.get_coefficient(2)==Complex(FT(0)));
|
||||||
|
assert(identity_1.get_coefficient(3)==Complex(FT(1)));
|
||||||
|
|
||||||
|
Isometry identity_2;
|
||||||
|
identity_2.set_to_identity();
|
||||||
|
assert(identity_2.get_coefficient(0)==Complex(FT(1)));
|
||||||
|
assert(identity_2.get_coefficient(1)==Complex(FT(0)));
|
||||||
|
assert(identity_2.get_coefficient(2)==Complex(FT(0)));
|
||||||
|
assert(identity_2.get_coefficient(3)==Complex(FT(1)));
|
||||||
|
|
||||||
|
Isometry f;
|
||||||
|
f.set_coefficient(0, Complex(FT(-12,17), FT(1,3)));
|
||||||
|
f.set_coefficient(1, Complex(FT(56,7), FT(21,5)));
|
||||||
|
f.set_coefficient(2, Complex(FT(56,7), FT(-21,5)));
|
||||||
|
f.set_coefficient(3, Complex(FT(-12,17), FT(-1,3)));
|
||||||
|
assert(f.get_coefficient(0)==Complex(FT(-12,17), FT(1,3)));
|
||||||
|
assert(f.get_coefficient(1)==Complex(FT(56,7), FT(21,5)));
|
||||||
|
assert(f.get_coefficient(2)==Complex(FT(56,7), FT(-21,5)));
|
||||||
|
assert(f.get_coefficient(3)==Complex(FT(-12,17), FT(-1,3)));
|
||||||
|
|
||||||
|
Isometry g;
|
||||||
|
g.set_coefficients(Complex(FT(-12,17), FT(1,3)), Complex(FT(56,7), FT(21,5)), Complex(FT(56,7), FT(-21,5)), Complex(FT(-12,17), FT(-1,3)));
|
||||||
|
assert(g.get_coefficient(0)==Complex(FT(-12,17), FT(1,3)));
|
||||||
|
assert(g.get_coefficient(1)==Complex(FT(56,7), FT(21,5)));
|
||||||
|
assert(g.get_coefficient(2)==Complex(FT(56,7), FT(-21,5)));
|
||||||
|
assert(g.get_coefficient(3)==Complex(FT(-12,17), FT(-1,3)));
|
||||||
|
|
||||||
|
Isometry h = f*g;
|
||||||
|
assert(h.get_coefficient(0) == Complex(FT(5333816,65025),FT(-8,17)));
|
||||||
|
assert(h.get_coefficient(1) == Complex(FT(-192,17),FT(-504,85)));
|
||||||
|
assert(h.get_coefficient(2) == Complex(FT(-192,17),FT(504,85)));
|
||||||
|
assert(h.get_coefficient(3) == Complex(FT(5333816,65025),FT(8,17)));
|
||||||
|
|
||||||
|
Point point (FT(3,11),FT(-1,73));
|
||||||
|
Point image_point = h.evaluate(point);
|
||||||
|
assert(image_point==Point(FT("9146011623056232") /
|
||||||
|
FT("66567955527962869"),
|
||||||
|
-FT("12617302915955411") /
|
||||||
|
FT("133135911055925738")));
|
||||||
|
|
||||||
|
std::cout << "printing an isometry for test purposes : " << std::endl << h;
|
||||||
|
|
||||||
|
Isometry tau_1 = CGAL::hyperbolic_translation<Traits>(point);
|
||||||
|
Isometry tau_1_prime = CGAL::hyperbolic_translation<Traits>(Point (FT(-3,11),FT(1,73)), true);
|
||||||
|
Isometry tau_1_inv = CGAL::hyperbolic_translation<Traits>(point, true);
|
||||||
|
assert(tau_1.evaluate(image_point) == tau_1_prime.evaluate(image_point));
|
||||||
|
assert((tau_1*tau_1_inv).evaluate(image_point) == image_point);
|
||||||
|
|
||||||
|
Point p (FT(2,15),FT(0));
|
||||||
|
Point q (FT(0),FT(17,93));
|
||||||
|
Isometry rotation = CGAL::hyperbolic_rotation<Traits>(p, q);
|
||||||
|
Isometry rotation_prime = CGAL::hyperbolic_rotation<Traits>(q, p, true);
|
||||||
|
Isometry rotation_inv = CGAL::hyperbolic_rotation<Traits>(p, q, true);
|
||||||
|
assert(rotation.evaluate(image_point) == rotation_prime.evaluate(image_point));
|
||||||
|
assert((rotation*rotation_inv).evaluate(image_point) == image_point);
|
||||||
|
|
||||||
|
Point p_imag = rotation.evaluate(p);
|
||||||
|
Point q_imag = rotation.evaluate(q);
|
||||||
|
Isometry pairing = CGAL::isometry_pairing_the_sides<Traits>(p, q, p_imag, q_imag);
|
||||||
|
assert(pairing.evaluate(p) == p_imag);
|
||||||
|
assert(pairing.evaluate(q) == q_imag);
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,63 @@
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Hyperbolic_fundamental_domain_factory_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2_IO.h>
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Lazy_exact_nt.h>
|
||||||
|
#include <CGAL/Cartesian.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
#include <sstream>
|
||||||
|
#include <tuple>
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
typedef CGAL::Cartesian<CGAL::Lazy_exact_nt<CGAL::Exact_rational>> Kernel;
|
||||||
|
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef CGAL::Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_2<Traits> Domain;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_factory_2<Traits> Factory;
|
||||||
|
typedef CGAL::Triangulation_on_hyperbolic_surface_2<Traits> Triangulation;
|
||||||
|
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
|
||||||
|
int main()
|
||||||
|
{
|
||||||
|
Factory factory;
|
||||||
|
Domain domain = factory.make_hyperbolic_fundamental_domain_g2(3459);
|
||||||
|
Triangulation triangulation0 = Triangulation(domain);
|
||||||
|
|
||||||
|
assert(triangulation0.is_valid());
|
||||||
|
|
||||||
|
Triangulation triangulation (triangulation0);
|
||||||
|
assert(triangulation.has_anchor());
|
||||||
|
|
||||||
|
std::stringstream buffer;
|
||||||
|
buffer << triangulation;
|
||||||
|
buffer >> triangulation;
|
||||||
|
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> input_not_centered;
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> input_centered;
|
||||||
|
|
||||||
|
input_not_centered = triangulation.lift(false);
|
||||||
|
input_centered = triangulation.lift();
|
||||||
|
|
||||||
|
triangulation.make_Delaunay();
|
||||||
|
|
||||||
|
assert(triangulation.is_Delaunay());
|
||||||
|
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> output_not_centered;
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> output_centered;
|
||||||
|
|
||||||
|
output_not_centered = triangulation.lift(false);
|
||||||
|
output_centered = triangulation.lift();
|
||||||
|
|
||||||
|
Triangulation::Combinatorial_map_with_cross_ratios& cmap = triangulation.combinatorial_map();
|
||||||
|
Triangulation::Anchor& anchor = triangulation.anchor();
|
||||||
|
assert(cmap.is_dart_used(anchor.dart));
|
||||||
|
|
||||||
|
std::cout << "printing triangulation for test purposes: " << std::endl << triangulation;
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,80 @@
|
||||||
|
#include <CGAL/Hyperbolic_surface_traits_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2.h>
|
||||||
|
#include <CGAL/Triangulation_on_hyperbolic_surface_2_IO.h>
|
||||||
|
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||||
|
|
||||||
|
#include <CGAL/Exact_rational.h>
|
||||||
|
#include <CGAL/Cartesian.h>
|
||||||
|
|
||||||
|
#include <iostream>
|
||||||
|
#include <sstream>
|
||||||
|
#include <vector>
|
||||||
|
|
||||||
|
typedef CGAL::Cartesian<CGAL::Exact_rational> Kernel;
|
||||||
|
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<Kernel> ParentTraits;
|
||||||
|
typedef CGAL::Hyperbolic_surface_traits_2<ParentTraits> Traits;
|
||||||
|
typedef CGAL::Hyperbolic_fundamental_domain_2<Traits> Domain;
|
||||||
|
typedef CGAL::Triangulation_on_hyperbolic_surface_2<Traits> Triangulation;
|
||||||
|
|
||||||
|
typedef typename Traits::FT FT;
|
||||||
|
typedef typename Traits::Hyperbolic_point_2 Point;
|
||||||
|
typedef typename Traits::Complex Complex;
|
||||||
|
|
||||||
|
Domain build_domain()
|
||||||
|
{
|
||||||
|
std::vector<Point> vertices;
|
||||||
|
vertices.push_back( Point(FT(809,10000),FT(0)));
|
||||||
|
vertices.push_back( Point(FT(7359,10000),FT(1877,10000)));
|
||||||
|
vertices.push_back( Point(FT(-999,2500),FT(881,1000)));
|
||||||
|
vertices.push_back( Point(FT("-22088524601252853411192791001942853611410938513/24711029456888649611435724068315791591836010000"),FT("9482675065452890527617859332378101016513362487/24711029456888649611435724068315791591836010000")));
|
||||||
|
vertices.push_back( Point(FT(-809,10000),FT(0)));
|
||||||
|
vertices.push_back( Point(FT(-7359,10000),FT(-1877,10000)));
|
||||||
|
vertices.push_back( Point(FT(999,2500),FT(-881,1000)));
|
||||||
|
vertices.push_back( Point(FT("22088524601252853411192791001942853611410938513/24711029456888649611435724068315791591836010000"),FT("-9482675065452890527617859332378101016513362487/24711029456888649611435724068315791591836010000")));
|
||||||
|
|
||||||
|
std::vector<int> pairings;
|
||||||
|
for (int k=0; k<8; ++k) {
|
||||||
|
pairings.push_back((k+4)%8);
|
||||||
|
}
|
||||||
|
|
||||||
|
return Domain(vertices, pairings);
|
||||||
|
}
|
||||||
|
|
||||||
|
int main()
|
||||||
|
{
|
||||||
|
Domain domain = build_domain();
|
||||||
|
Triangulation triangulation0 = Triangulation(domain);
|
||||||
|
|
||||||
|
assert(triangulation0.is_valid());
|
||||||
|
|
||||||
|
Triangulation triangulation (triangulation0);
|
||||||
|
assert(triangulation.has_anchor());
|
||||||
|
|
||||||
|
std::stringstream buffer;
|
||||||
|
buffer << triangulation;
|
||||||
|
buffer >> triangulation;
|
||||||
|
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> input_not_centered;
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> input_centered;
|
||||||
|
|
||||||
|
input_not_centered = triangulation.lift(false);
|
||||||
|
input_centered = triangulation.lift();
|
||||||
|
|
||||||
|
triangulation.make_Delaunay();
|
||||||
|
|
||||||
|
assert(triangulation.is_Delaunay());
|
||||||
|
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> output_not_centered;
|
||||||
|
std::vector<std::tuple<typename Triangulation::Combinatorial_map_with_cross_ratios::Dart_const_handle,Point,Point,Point>> output_centered;
|
||||||
|
|
||||||
|
output_not_centered = triangulation.lift(false);
|
||||||
|
output_centered = triangulation.lift();
|
||||||
|
|
||||||
|
Triangulation::Combinatorial_map_with_cross_ratios& cmap = triangulation.combinatorial_map();
|
||||||
|
Triangulation::Anchor& anchor = triangulation.anchor();
|
||||||
|
assert(cmap.is_dart_used(anchor.dart));
|
||||||
|
|
||||||
|
std::cout << "printing triangulation for test purposes: " << std::endl << triangulation;
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
Loading…
Reference in New Issue