Least Squares Subdivision Surfaces

Simon Boyé (1, 2) , Gael Guennebaud (1, 2) , Christophe Schlick (1, 2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 IPARLA - Visualization and manipulation of complex data on wireless mobile devices

The usual approach to design subdivision schemes for curves and surfaces basically consists in combining proper rules for regular configurations, with some specific heuristics to handle extraordinary vertices. In this paper, we introduce an alternative approach, called Least Squares Subdivision Surfaces (LS^3), where the key idea is to iteratively project each vertex onto a local approximation of the current polygonal mesh. While the resulting procedure have the same complexity as simpler subdivision schemes, our method offers much higher visual quality, especially in the vicinity of extraordinary vertices. Moreover, we show it can be easily generalized to support boundaries and creases. The fitting procedure allows for a local control of the surface from the normals, making LS^3 very well suited for interactive freeform modeling applications. We demonstrate our approach on diadic triangular and quadrangular refinement schemes, though it can be applied to any splitting strategies.

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Simon Boyé, Gael Guennebaud, Christophe Schlick. Least Squares Subdivision Surfaces. Computer Graphics Forum, 2010, 29 (7). ⟨inria-00524555⟩