mirror of https://github.com/CGAL/cgal
moved bib to cgal_manual.bib & restored geom.bib
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@ -1331,6 +1331,29 @@ Teillaud"
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address = {Girona, Spain}
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}
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@article{cgal:lrtc-iccmps-20,
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author = {Jacques-Olivier Lachaud and Pascal Romon and Boris Thibert and David Coeurjolly},
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journal = {Computer Graphics Forum (Proceedings of Symposium on Geometry Processing)},
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number = {5},
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title = {Interpolated Corrected Curvature Measures for Polygonal Surfaces},
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volume = {39},
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month = aug,
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year = {2020},
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url = {https://doi.org/10.1111/cgf.14067},
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doi = {10.1111/cgf.14067}
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}
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@article{cgal:lrt-ccm-22,
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author = {Jacques-Olivier Lachaud and Pascal Romon and Boris Thibert},
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journal = {Discrete & Computational Geometry},
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title = {Corrected Curvature Measures},
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volume = {68},
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pages = {477-524},
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month = jul,
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year = {2022},
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url = {https://doi.org/10.1007/s00454-022-00399-4}
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}
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@article{cgal:lm-clscm-12,
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author = {Lafarge, Florent and Mallet, Clement},
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title = {{Creating large-scale city models from 3D-point clouds: a robust approach with hybrid representation}},
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@ -152043,7 +152043,6 @@ pages = {179--189}
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Pages = {215--224},
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Year = {2012},
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Url = {https://monge.univ-mlv.fr/~colinde/pub/09edgewidth.pdf}
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}
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@inproceedings{tang2009interactive,
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title={Interactive Hausdorff distance computation for general polygonal models},
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@ -152054,26 +152053,4 @@ pages = {179--189}
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pages={74},
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year={2009},
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organization={ACM}
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}
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@article{lachaud2020,
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author = {Jacques-Olivier Lachaud and Pascal Romon and Boris Thibert and David Coeurjolly},
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journal = {Computer Graphics Forum (Proceedings of Symposium on Geometry Processing)},
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number = {5},
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title = {Interpolated corrected curvature measures for polygonal surfaces},
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volume = {39},
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month = jul,
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year = {2020}
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}
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@article{lachaud2022
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author = {Jacques-Olivier Lachaud and Pascal Romon and Boris Thibert},
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journal = {Discrete & Computational Geometry},
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title = {Corrected Curvature Measures},
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volume = {68},
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pages = {477-524},
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month = jul,
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year = {2022},
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url = {https://doi.org/10.1007/s00454-022-00399-4}
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}
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}
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@ -940,7 +940,7 @@ not provide storage for the normals.
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\section PMPICC Computing Curvatures
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This package provides methods to compute curvatures on polygonal meshes based on Interpolated
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Corrected Curvatures on Polyhedral Surfaces \cgalCite{lachaud2020}. This includes mean curvature,
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Corrected Curvatures on Polyhedral Surfaces \cgalCite{cgal:lrtc-iccmps-20}. This includes mean curvature,
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Gaussian curvature, principal curvatures and directions. These can be computed on triangle meshes,
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quad meshes, and meshes with n-gon faces (for n-gons, the centroid must be inside the n-gon face).
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The algorithms used prove to work well in general. Also, on meshes with noise on vertex positions,
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@ -955,10 +955,10 @@ in each direction is called the principal curvature: \f$ k_1 \f$ and \f$ k_2 \f$
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curvatures). Curvature is usually expressed as scalar quantities like the mean curvature \f$ H \f$ and
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the Gaussian curvature \f$ K \f$ which are defined in terms of the principal curvatures.
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The algorithms are based on the two papers \cgalCite{lachaud2022} and \cgalCite{lachaud2020}. They
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introduce a new way to compute curvatures on polygonal meshes. The main idea in \cgalCite{lachaud2022} is
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The algorithms are based on the two papers \cgalCite{cgal:lrt-ccm-22} and \cgalCite{cgal:lrtc-iccmps-20}. They
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introduce a new way to compute curvatures on polygonal meshes. The main idea in \cgalCite{cgal:lrt-ccm-22} is
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based on decoupling the normal information from the position information, which is useful for dealing with
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digital surfaces, or meshes with noise on vertex positions. \cgalCite{lachaud2020} introduces some
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digital surfaces, or meshes with noise on vertex positions. \cgalCite{cgal:lrtc-iccmps-20} introduces some
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extensions to this framework. As it uses linear interpolation on the corrected normal vector field
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to derive new closed form equations for the corrected curvature measures. These <b>interpolated</b>
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curvature measures are the first step for computing the curvatures. For a triangle \f$ \tau_{ijk} \f$,
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@ -1285,7 +1285,7 @@ is covered by a set of prisms, where each prism is an offset for an input triang
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That is, the implementation in \cgal does not use indirect predicates.
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The interpolated corrected curvatures were implemented during GSoC 2022. This was implemented by Hossam Saeed and under
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supervision of David Coeurjolly, Jaques-Olivier Lachaud, and Sébastien Loriot. The implementation is based on \cgalCite{lachaud2020}.
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supervision of David Coeurjolly, Jaques-Olivier Lachaud, and Sébastien Loriot. The implementation is based on \cgalCite{cgal:lrtc-iccmps-20}.
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<a href="https://dgtal-team.github.io/doc-nightly/moduleCurvatureMeasures.html">DGtal's implementation</a> was also
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used as a reference during the project.
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