Kanai, TakashiOhtake, YutakaKase, KiwamuAlla Sheffer and Konrad Polthier2014-01-292014-01-2920063-905673-24-X1727-8384https://doi.org/10.2312/SGP/SGP06/021-030This 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 from its global behavior as well as to be area-sensitive 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 a 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.Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, Surface, Solid and Object Representations, G.1.2 [Numerical Analysis]: Approximation of Surfaces and Contours