mirror of https://github.com/CGAL/cgal
pass on code and doc following reviews
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Sven Oesau
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@ -7,13 +7,8 @@
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// $Id$
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Stéphane Tayeb, Aymeric PELLE
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//
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//******************************************************************************
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// File Description :
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// class Labeled_mesh_domain_3. See class description.
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//******************************************************************************
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#ifndef CGAL_LABELED_MESH_DOMAIN_3_H
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#define CGAL_LABELED_MESH_DOMAIN_3_H
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@ -875,17 +870,15 @@ public:
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* function. The domain to be discretized is assumed to be the domain where
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* the function has negative values.
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*
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* The method takes as argument a bounding sphere which is required to
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* circumscribe the surface and to have its center inside the domain.
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*
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* \tparam Function a type compatible with the signature `FT(Point_3)`: it takes a point as argument,
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* and returns a scalar value. That object must be model of `CopyConstructible`
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* \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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* \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
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* or a bounding `Iso_cuboid_3`
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* or a bounding `Iso_cuboid_3` which is required to circumscribe
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* the surface and to have its center inside the domain.
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*
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* \param function the implicit function
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* \param bounding_object object boundint the meshable domain and its center is inside the domain.
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* \param bounding_object object bounding the meshable domain and its center is inside the domain.
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* \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
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*
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* \cgalNamedParamsBegin
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@ -1196,7 +1189,7 @@ public:
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// If both extremities are in the same subdomain,
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// there is no intersection.
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// Should only happen during initial point generation.
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// Should only be able to happen during initial point generation.
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if( value_at_p1 == value_at_p2 )
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{
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return Intersection();
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@ -13,8 +13,7 @@ This \cgal component implements a surface reconstruction method which
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takes as input point sets with oriented normals and computes an
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implicit function. We assume that the input points contain no outliers
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and little noise. The output surface mesh is generated by extracting
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an isosurface of this function with the \ref Chapter_3D_Mesh_Generation or \cgal Surface Mesh Generator
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\cgalCite{cgal:ry-gsddrm-06} or potentially with any other surface
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an isosurface of this function with the \ref 3D Mesh Generator or potentially with any other surface
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contouring algorithm.
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\cgalFigureBegin{Poisson_surface_reconstruction_3figintroduction,introduction.jpg}
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@ -76,7 +75,7 @@ indicator function \f$ f\f$ represented as a piecewise linear function
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over the refined triangulation. More specifically, it solves for the
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Poisson equation \f$ \Delta f = div(\mathbf{n})\f$ at each vertex of
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the triangulation using a sparse linear solver. Eventually, the \cgal
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surface mesh generator extracts an isosurface with function value set
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3D mesh generator extracts an isosurface with function value set
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by default to be the median value of \f$ f\f$ at all input points.
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\section Poisson_surface_reconstruction_3Function Reconstruction Function
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@ -86,9 +85,7 @@ provided. It takes points with normals as input and handles the whole
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reconstruction pipeline :
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- it computes the implicit function
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- it reconstructs the surface with a given precision using the \cgal
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surface mesh generator based on Delaunay refinement
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\cgalCite{cgal:ry-gsddrm-06} \cgalCite{cgal:bo-pgsms-05}
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- it reconstructs the surface with a given precision using the \cgal 3D mesh generator
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- it outputs the result in a polygon mesh.
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This function aims at providing a quick and user-friendly API for
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@ -120,14 +117,11 @@ The following example reads a point set, creates a Poisson implicit function and
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The computed implicit functions can be iso-contoured to reconstruct a
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surface by using the \ref Chapter_3D_Mesh_Generation or the \cgal surface mesh generator
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\cgalCite{cgal:ry-gsddrm-06} \cgalCite{cgal:bo-pgsms-05} :
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surface by using the \cgal 3D mesh generator :
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`make_mesh_3()` for using parallel Mesh_3
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`make_mesh_3()` with the `surface_only()` parameter for using parallel Mesh_3
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`make_surface_mesh()` of using the deprecated 3D Surface Mesh Generation
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The parameter `Tag` affects the behavior of `make_surface_mesh()`:
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The parameter `Tag` affects the behavior of `make_mesh_3()`:
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- `Manifold_tag`: the output mesh is guaranteed to be a manifold surface without boundary.
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- `Manifold_with_boundary_tag`: the output mesh is guaranteed to be manifold and may have boundaries.
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- `Non_manifold_tag`: the output mesh has no guarantee and hence is outputted as a polygon soup.
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@ -137,13 +131,6 @@ The parameter `Tag` affects the behavior of `make_surface_mesh()`:
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The surface reconstructed by `make_mesh_3()` is required to be a model of the concept
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`MeshComplex_3InTriangulation_3`, a data structure devised to represent a three dimensional complex embedded into a three dimensional triangulation. The surface facets can then be extracted into a face graph by `facets_in_complex_3_to_triangle_mesh()`.
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The surface reconstructed by `make_surface_mesh()` instead is required to be a
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model of the concept `SurfaceMeshComplex_2InTriangulation_3`, a data
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structure devised to represent a two dimensional complex embedded into
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a three dimensional triangulation.
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`SurfaceMeshComplex_2InTriangulation_3` defines the methods to traverse the reconstructed surface, and e.g. convert it to a triangle soup.
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Other \cgal components provide functions to write the reconstructed
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surface mesh to the %Object File Format (OFF) \cgalCite{cgal:p-gmgv16-96}
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and to convert it to a polyhedron (when it is manifold):
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@ -223,7 +210,7 @@ function over the tetrahedra of a 3D Delaunay triangulation
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constructed from the input points then refined through Delaunay
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refinement. For this reason, any iso-surface is also piecewise linear
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and hence may contain sharp creases. As the contouring algorithm
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`make_surface_mesh()` expects a smooth implicit function these
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`make_mesh_3()` expects a smooth implicit function these
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sharp creases may create spurious clusters of vertices in the final
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reconstructed surface mesh when setting a small mesh sizing or surface
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approximation error parameter (see
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@ -352,12 +339,13 @@ with the 03 option which maximizes speed. All measurements were done using the
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The point set chosen for benchmarking the Poisson implicit function is the Lucy statue point set from the
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<a href="https://graphics.stanford.edu/data/3Dscanrep/">The Stanford 3D Scanning Repository</a>
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(originally 14 million points, here downscaled to 2.9 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-simplification_bench}.
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(originally 14 million points, here downsampled to 2.9 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-contouring_bench}.
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We measure the Poisson implicit function computation (i.e., the call to
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`Poisson_reconstruction_function::compute_implicit_function()` denoted by Poisson solve hereafter)
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for this point set as well as for simplified versions obtained through random simplification.
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The following table provides Poisson solve computation times in seconds for an increasing number of points.
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<CENTER>
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<TABLE CELLSPACING=5 >
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<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
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<TR>
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@ -408,19 +396,20 @@ Poisson solve duration (in s)
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2,900
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<TD class="math" ALIGN=CENTER NOWRAP>
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486
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<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
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<TR><TD ALIGN=CENTER NOWRAP COLSPAN=2><HR>
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</TABLE>
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</CENTER>
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\subsection SurfReconstPerfCont Contouring
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The point set chosen for benchmarking the contouring stage is the Lucy point
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set simplified to 2.9M points. We measure the contouring (i.e.\ the calls to `make_mesh_3()` and `facets_in_complex_3_to_triangle_mesh()`)
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set simplified to 2.9M points. We measure the contouring (i.e., the calls to `make_mesh_3()` and `facets_in_complex_3_to_triangle_mesh()`)
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duration and the reconstruction error for a range of approximation distances.
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The reconstruction error is expressed as the average distance from input points to the reconstructed surface in mm (the Lucy statue is 1597 mm tall).
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<CENTER>
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<TABLE CELLSPACING=5 >
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<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
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<TR><TD ALIGN=CENTER NOWRAP COLSPAN=4><HR>
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<TR>
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<TD class="math" ALIGN=CENTER NOWRAP>
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Approx. distance (*average spacing)
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@ -430,7 +419,7 @@ Contouring duration single-thread (in s)
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Contouring duration parallel (in s)
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<TD class="math" ALIGN=CENTER NOWRAP>
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Reconstruction error (mm)
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<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
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<TR><TD ALIGN=CENTER NOWRAP COLSPAN=4><HR>
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<TR>
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<TD class="math" ALIGN=CENTER NOWRAP>
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@ -552,8 +541,9 @@ Reconstruction error (mm)
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<TD class="math" ALIGN=CENTER NOWRAP>
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1.50
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<TR>
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<TD ALIGN=LEFT NOWRAP COLSPAN=3><HR>
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<TD ALIGN=CENTER NOWRAP COLSPAN=4><HR>
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</TABLE>
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</CENTER>
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\cgalFigureAnchor{Poisson_surface_reconstruction_3-fig-contouring_bench}
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<center>
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@ -572,6 +562,7 @@ set (2.9 millions points) as well as for further simplified versions.\n
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The Poisson implicit function computation has a memory peak when solving the Poisson linear
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system using the sparse linear solver.
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<CENTER>
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<TABLE CELLSPACING=5 >
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<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
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<TR>
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@ -622,6 +613,7 @@ Memory occupancy (MBytes)
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6,868
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<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
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</TABLE>
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</CENTER>
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\subsection SurfReconstPerfPSS Point Set Simplification
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@ -633,6 +625,7 @@ simplified versions. All reconstructions use the recommended contouring paramete
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The reconstruction error is expressed as the average distance from input points to the reconstructed surface in mm
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(the Lucy statue is 1597 mm tall).
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<CENTER>
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<TABLE CELLSPACING=5 >
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<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
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<TR>
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@ -698,6 +691,7 @@ Reconstruction error (mm)
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0.150947
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<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
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</TABLE>
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</CENTER>
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\cgalFigureBegin{Poisson_surface_reconstruction_3-fig-simplification_bench,simplification_bench.jpg}
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@ -7,13 +7,7 @@
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// $Id$
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Sven Oesau
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//
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//******************************************************************************
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// File Description :
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// class Poisson_mesh_domain_3. See class description.
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//******************************************************************************
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#ifndef CGAL_POISSON_MESH_DOMAIN_3_H
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#define CGAL_POISSON_MESH_DOMAIN_3_H
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@ -38,7 +32,6 @@ namespace CGAL {
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the basic operations to implement intersection tests and intersection computations through a bisection
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method.This parameter must be instantiated with a model of the concept `BisectionGeometricTraits_3`.
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This class is a model of concept `MeshDomain_3`.
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\cgalModels{MeshDomain_3}
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\sa `CGAL::Labeled_mesh_domain_3`
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@ -111,16 +104,15 @@ public:
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typedef CGAL::Poisson_reconstruction_function<BGT> Function;
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#endif
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Function poisson_function;
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/// \name Creation
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/// @{
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/*! \brief Construction from a function, a bounding object and a relative error bound.
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*
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* \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
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* or a bounding `Iso_cuboid_3`
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* \tparam NamedParameters
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* a sequence of \ref bgl_namedparameters "Named Parameters"
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* \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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*
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* \param function the Poisson reconstruction function
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* \param bounding_object the bounding object bounding the meshable space.
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@ -205,12 +197,10 @@ public:
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* function. The domain to be discretized is assumed to be the domain where
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* the function has negative values.
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*
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* The method takes as argument a bounding sphere which is required to
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* circumscribe the surface and to have its center inside the domain.
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*
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* \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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* \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
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* or a bounding `Iso_cuboid_3`
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* or a bounding `Iso_cuboid_3` which is required to circumscribe
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* the surface and to have its center inside the domain.
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*
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* \param function the Poisson reconstruction function
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* \param bounding_object object bounding the meshable domain and its center is inside the domain.
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@ -236,14 +226,13 @@ public:
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{
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using parameters::get_parameter;
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using parameters::choose_parameter;
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FT relative_error_bound_ = choose_parameter(get_parameter(np, internal_np::error_bound), FT(1e-3));
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CGAL::Random* p_rng_ = choose_parameter(get_parameter(np, internal_np::rng), nullptr);
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auto null_subdomain_index_ = choose_parameter(get_parameter(np, internal_np::null_subdomain_index_param),
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Null_functor()); auto construct_surface_patch_index_ = choose_parameter(get_parameter(np,
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internal_np::surface_patch_index), Null_functor());
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namespace p = CGAL::parameters;
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return Poisson_mesh_domain_3
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(function,
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auto null_subdomain_index_ = choose_parameter(get_parameter(np, internal_np::null_subdomain_index_param), Null_functor());
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auto construct_surface_patch_index_ = choose_parameter(get_parameter(np, internal_np::surface_patch_index), Null_functor());
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return Poisson_mesh_domain_3(function,
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bounding_object,
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CGAL::parameters::relative_error_bound(relative_error_bound_)
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.function(make_implicit_to_labeling_function_wrapper<BGT>(function))
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@ -256,13 +245,13 @@ internal_np::surface_patch_index), Null_functor());
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template<typename CGAL_NP_TEMPLATE_PARAMETERS>
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static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS& np = parameters::default_values())
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{
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static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::function_param_t>::value,
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"Value for required parameter not found"); static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS,
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internal_np::bounding_object_param_t>::value, "Value for required parameter not found");
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using parameters::get_parameter;
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return create_Poisson_mesh_domain(parameters::get_parameter(np, internal_np::function_param),
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parameters::get_parameter(np, internal_np::bounding_object_param),
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static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::function_param_t>::value, "Value for required parameter not found");
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static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::bounding_object_param_t>::value, "Value for required parameter not found");
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return create_Poisson_mesh_domain(get_parameter(np, internal_np::function_param),
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get_parameter(np, internal_np::bounding_object_param),
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np);
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}
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// If both extremities are in the same subdomain,
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// there is no intersection.
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// Should only happen during initial point generation.
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// Should only be able to happen during initial point generation.
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if(label_at_p1 == label_at_p2)
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return Intersection();
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// Else lets find a point (by bisection)
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// Bisection ends when the point is near than error bound from surface
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// Bisection ends when the point is nearer from surface than the error bound
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while(true) {
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if(c1 == c2) {
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if(c1_is_inf) {
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