Geometry-aware bases for shape approximation
We introduce a new class of shape approximation techniques for irregular triangular meshes. Our method approximates the geometry of the mesh using a linear combination of a small number of basis vectors. The basis vectors are functions of the mesh connectivity and of the mesh indices of a number of...
| Veröffentlicht in: | IEEE transactions on visualization and computer graphics. - 1996. - 11(2005), 2 vom: 12. März, Seite 171-80 |
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| Weitere Verfasser: | , , |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2005
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on visualization and computer graphics |
| Schlagworte: | Evaluation Study Journal Article Research Support, Non-U.S. Gov't Research Support, U.S. Gov't, Non-P.H.S. |
| Zusammenfassung: | We introduce a new class of shape approximation techniques for irregular triangular meshes. Our method approximates the geometry of the mesh using a linear combination of a small number of basis vectors. The basis vectors are functions of the mesh connectivity and of the mesh indices of a number of anchor vertices. There is a fundamental difference between the bases generated by our method and those generated by geometry-oblivious methods, such as Laplacian-based spectral methods. In the latter methods, the basis vectors are functions of the connectivity alone. The basis vectors of our method, in contrast, are geometry-aware since they depend on both the connectivity and on a binary tagging of vertices that are "geometrically important" in the given mesh (e.g., extrema). We show that, by defining the basis vectors to be the solutions of certain least-squares problems, the reconstruction problem reduces to solving a single sparse linear least-squares problem. We also show that this problem can be solved quickly using a state-of-the-art sparse-matrix factorization algorithm. We show how to select the anchor vertices to define a compact effective basis from which an approximated shape can be reconstructed. Furthermore, we develop an incremental update of the factorization of the least-squares system. This allows a progressive scheme where an initial approximation is incrementally refined by a stream of anchor points. We show that the incremental update and solving the factored system are fast enough to allow an online refinement of the mesh geometry |
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| Beschreibung: | Date Completed 31.03.2005 Date Revised 10.12.2019 published: Print Citation Status MEDLINE |
| ISSN: | 1941-0506 |