An Optimal Triangle Projector with Prescribed Area and Orientation, Application to Position-Based Dynamics
| Autor: | Adrien Bartoli, Carlos Arango Duque |
|---|---|
| Přispěvatelé: | Institut Pascal (IP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Series (mathematics)
Computer science [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV] Numerical Analysis (math.NA) Topology Computer Graphics and Computer-Aided Design law.invention Constraint (information theory) Projector law Modeling and Simulation Orientation (geometry) Convergence (routing) FOS: Mathematics Polygon mesh Geometry and Topology Mathematics - Numerical Analysis Algebraic number Projection (set theory) Software ComputingMilieux_MISCELLANEOUS |
| Zdroj: | Graphical Models Graphical Models, 2021, 118, pp.101117. ⟨10.1016/j.gmod.2021.101117⟩ |
| ISSN: | 1524-0703 1524-0711 |
| DOI: | 10.1016/j.gmod.2021.101117⟩ |
| Popis: | The vast majority of mesh-based modelling applications iteratively transform the mesh vertices under prescribed geometric conditions. This occurs in particular in methods cycling through the constraint set such as Position-Based Dynamics (PBD). A common case is the approximate local area preservation of triangular 2D meshes under external editing constraints. At the constraint level, this yields the nonconvex optimal triangle projection under prescribed area problem, for which there does not currently exist a direct solution method. In current PBD implementations, the area preservation constraint is linearised. The solution comes out through the iterations, without a guarantee of optimality, and the process may fail for degenerate inputs where the vertices are colinear or colocated. We propose a closed-form solution method and its numerically robust algebraic implementation. Our method handles degenerate inputs through a two-case analysis of the problem’s generic ambiguities. We show in a series of experiments in area-based 2D mesh editing that using optimal projection in place of area constraint linearisation in PBD speeds up and stabilises convergence. |
| Databáze: | OpenAIRE |
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