Isometry-Aware Preconditioning for Mesh Parameterization
| dc.contributor.author | Claici, Sebastian | en_US |
| dc.contributor.author | Bessmeltsev, Mikhail | en_US |
| dc.contributor.author | Schaefer, Scott | en_US |
| dc.contributor.author | Solomon, Justin | en_US |
| dc.contributor.editor | Bærentzen, Jakob Andreas and Hildebrandt, Klaus | en_US |
| dc.date.accessioned | 2017-07-02T17:37:44Z | |
| dc.date.available | 2017-07-02T17:37:44Z | |
| dc.date.issued | 2017 | |
| dc.description.abstract | This paper presents a new preconditioning technique for large-scale geometric optimization problems, inspired by applications in mesh parameterization. Our positive (semi-)definite preconditioner acts on the gradients of optimization problems whose variables are positions of the vertices of a triangle mesh in R2 or of a tetrahedral mesh in R3, converting localized distortion gradients into the velocity of a globally near-rigid motion via a linear solve. We pose our preconditioning tool in terms of the Killing energy of a deformation field and provide new efficient formulas for constructing Killing operators on triangle and tetrahedral meshes. We demonstrate that our method is competitive with state-of-the-art algorithms for locally injective parameterization using a variety of optimization objectives and show applications to two- and three-dimensional mesh deformation. | en_US |
| dc.description.number | 5 | |
| dc.description.sectionheaders | Maps and Parametrization | |
| dc.description.seriesinformation | Computer Graphics Forum | |
| dc.description.volume | 36 | |
| dc.identifier.doi | 10.1111/cgf.13243 | |
| dc.identifier.issn | 1467-8659 | |
| dc.identifier.pages | 037-047 | |
| dc.identifier.uri | https://doi.org/10.1111/cgf.13243 | |
| dc.identifier.uri | https://diglib.eg.org:443/handle/10.1111/cgf13243 | |
| dc.publisher | The Eurographics Association and John Wiley & Sons Ltd. | en_US |
| dc.title | Isometry-Aware Preconditioning for Mesh Parameterization | en_US |