Skeleton-based modeling operations on solids

Abstract

The skeleton is a lower-dimensional geometric abstraction that is useful for performing a number of important geometric operations on solid models. In this paper we develop skeleton-based algorithms that demonstrate the utility of the skeleton in addressing: (1) level-of-detail control, the generation of hierarchical representations that preserve overall shape but blur local boundary features; (2) hexahedral mesh generation, the decomposition of a 3D shape into a collection of block elements suitable for finite element analysis; (3) shape interpolation and morphing, the generation of an `intermediate' shape from two given 3D shapes and the generation of a sequence of shapes that smoothly transform one shape into another; and (4) shape synthesis, the generation of an optimal shape from specifications of functional performance requirements and constraints. Besides our goal of providing novel solutions to these problems of significant practical importance, we seek to illustrate the general usefulness of the skeleton as an intermediate geometric description that should be more widely implemented in commercial CAD systems.