Dual Domain Extrapolation

Bruno Lévy (1)

1 ISA - Models, algorithms and geometry for computer graphics and vision

Shape optimization and surface fairing for polygon meshes have been active research areas for the last few years. Existing approaches either require the border of the surface to be fixed, or are only applicable to closed surfaces. In this paper, we propose a new approach, that computes natural boundaries. This makes it possible not only to smooth an existing geometry, but also to extrapolate its shape beyond the existing border. Our approach is based on a global parameterization of the surface and on a minimization of the squared curvatures, discretized on the edges of the surface. The so-constructed surface is an approximation of a minimal energy surface (MES). Using a global parameterization makes it possible to completely decouple the outer fairness (surface smoothness) from the inner fairness (mesh quality). In addition, the parameter space provides the user with a new means of controlling the shape of the surface. When used as a geometry filter, our approach computes a smoothed mesh that is discrete conformal to the original one. This allows smoothing textured meshes without introducing distortions.

Mots clés: polygon meshes; differential geometry; minimal energy surfaces; shape optimization; polygonal meshes; minimum energy surfaces; maillages polygonaux; geometrie differentielle; surfaces d'energie minimum; frontieres naturelles; natural boundaries; optimisation de formes

Domaines: Autre [cs.OH]

Bruno Lévy. Dual Domain Extrapolation. ACM Transactions on Graphics, 2003, 22 (3), pp.364-369. ⟨10.1145/882262.882277⟩. ⟨inria-00099625⟩