| _version_ | 1867014769147379712 |
|---|---|
| author | Koray Akalin Ugo Finnendahl Olga Sorkine‐Hornung Marc Alexa |
| author_facet | Koray Akalin Ugo Finnendahl Olga Sorkine‐Hornung Marc Alexa Koray Akalin Ugo Finnendahl Olga Sorkine‐Hornung Marc Alexa |
| collection | Wiley Open Access |
| contents | Mesh Parameterization Meets Intrinsic Triangulations Koray Akalin Ugo Finnendahl Olga Sorkine‐Hornung Marc Alexa Computer Graphics Forum AbstractA parameterization of a triangle mesh is a realization in the plane so that all triangles have positive signed area. Triangle mesh parameterizations are commonly computed by minimizing a distortion energy, measuring the distortions of the triangles as they are mapped into the parameter domain. It is assumed that the triangulation is fixed and the triangles are mapped affinely. We consider a more general setup and additionally optimize among the intrinsic triangulations of the piecewise linear input geometry. This means the distortion energy is computed for the same geometry, yet the space of possible parameterizations is enlarged. For minimizing the distortion energy, we suggest alternating between varying the parameter locations of the vertices and intrinsic flipping. We show that this process improves the mapping for different distortion energies at moderate additional cost. We also find intrinsic triangulations that are better starting points for the optimization of positions, offering a compromise between the full optimization approach and exploiting the additional freedom of intrinsic triangulations. 10.1111/cgf.15134 http://creativecommons.org/licenses/by/4.0/ |
| doi_str_mv | 10.1111/cgf.15134 |
| format | Artículo Open Access |
| id | wiley_oa_10_1111_cgf_15134 |
| institution | Wiley Open Access |
| license_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| publishDate | 2024 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | Mesh Parameterization Meets Intrinsic Triangulations Koray Akalin Ugo Finnendahl Olga Sorkine‐Hornung Marc Alexa Computer Graphics Forum Mesh Parameterization Meets Intrinsic Triangulations Koray Akalin Ugo Finnendahl Olga Sorkine‐Hornung Marc Alexa Computer Graphics Forum AbstractA parameterization of a triangle mesh is a realization in the plane so that all triangles have positive signed area. Triangle mesh parameterizations are commonly computed by minimizing a distortion energy, measuring the distortions of the triangles as they are mapped into the parameter domain. It is assumed that the triangulation is fixed and the triangles are mapped affinely. We consider a more general setup and additionally optimize among the intrinsic triangulations of the piecewise linear input geometry. This means the distortion energy is computed for the same geometry, yet the space of possible parameterizations is enlarged. For minimizing the distortion energy, we suggest alternating between varying the parameter locations of the vertices and intrinsic flipping. We show that this process improves the mapping for different distortion energies at moderate additional cost. We also find intrinsic triangulations that are better starting points for the optimization of positions, offering a compromise between the full optimization approach and exploiting the additional freedom of intrinsic triangulations. 10.1111/cgf.15134 http://creativecommons.org/licenses/by/4.0/ |
| title | Mesh Parameterization Meets Intrinsic Triangulations |
| topic | Computer Graphics Forum |
| url | https://onlinelibrary.wiley.com/doi/10.1111/cgf.15134 |