Hierarchical Error-Driven Approximation of Implicit Surfaces from Polygonal Meshes

Kanai, Takashi; Ohtake, Yutaka; Kase, Kiwamu

Hierarchical Error-Driven Approximation of Implicit Surfaces from Polygonal Meshes

Files

021-030.pdf (338.91 KB)

Date

2006

Authors

Kanai, Takashi
Ohtake, Yutaka
Kase, Kiwamu

Publisher

The Eurographics Association

Abstract

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 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.

        @inproceedings{:10.2312/SGP/SGP06/021-030
,
booktitle = {Symposium on Geometry Processing
},
editor = {Alla Sheffer and Konrad Polthier
},
title = {{Hierarchical Error-Driven Approximation of Implicit Surfaces from Polygonal Meshes
}},
author = {Kanai, Takashi and 
Ohtake, Yutaka and 
Kase, Kiwamu
},
year = {2006
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-24-X
},
DOI = {/10.2312/SGP/SGP06/021-030
}
}