This paper describes an efficient method for the hierarchical approximation of implicit surfaces from polygonal meshes. A novel error function between a polygonal mesh and an implicit surface is proposed. This error function is defined so as to be scale-independent on its global behavior as well as to be area-dependent on local regions. An implicit surface tightly-fitted to polygons can be computed by the least-squares fitting method. Furthermore, this function can be represented as the quadric form, which realizes a compact representation of such an error metric. Our novel algorithm rapidly constructs a SLIM (Sparse Low-degree IMplicit) surface which is recently developed non-conforming hierarchical implicit surface representation. Users can quickly obtain a set of implicit surfaces with arbitrary resolution according to errors from a SLIM surface.
Papers
- Takashi Kanai, Yutaka Ohtake, Kiwamu Kase: “Hierarchical Error-Driven Approximation of Implicit Surfaces from Polygonal Meshes” Proc. 4th Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (Cagliari, Italy, 26-28 June 2006), pp.21-30, Eurographics Association, Aire-la-Ville, Switzerland, 2006. [paper (Adobe PDF) (5.4MB)] [Presentation Slide (Microsoft Powerpoint) (8.5MB)]