On intrinsic representations of 3D polygons for shape blending

Abstract

An intrinsic representation of a geometric object comprises a set of parameters that are invariant under Euclidean transformations and determine the shape and size of the object uniquely. Unlike the case of a two-dimensional polygon which has essentially only one intrinsic representation, a three-dimensional (3D) polygon allows several variations. We study three different intrinsic representations of a 3D polygon, focusing on properties regarding their applications in shape blending. We show that only one of these representations, which is a natural extension to the intrinsic functions of a 3D differentiable curve, is suitable for shape blending, while the others lead to discontinuous shape transformation. Detailed discussions about the evaluation criteria, numerical sensitivity, and an inherent difficulty in shape blending of 3D polygons are also presented. © 2002 Elsevier Science Ltd. All rights reserved.