Skeleton-based three-dimensional geometric morphing

In this paper, we describe a method for generating geometric morphs between general 3D solid models. The method is based on the Euclidean skeleton and is capable of generating morphs between shapes that possess different feat ure sets and different topology. The essential concept that enables the mor phing method is utilization of the trimmed skeleton of the symmetric differ ence as an intermediate shape. The intermediate shape is a valid solid mode l whose boundary does not self-intersect and is everywhere equidistant from the boundaries of the source shapes. We apply the skeleton-based intermedi ate shape generation procedure recursively to produce a sequence of shapes, referred to as a morph history, that gradually transform between the initi al and target shapes. The method is sufficiently robust to handle significa nt changes in geometry and topology, such as the creation and annihilation of protrusions, indentations, internal holes and handles, and produces intu itive morph histories. The skeleton also establishes a correspondence between points on the bounda ries of the source and target objects. Interpolation between corresponding points is performed to enable fast generation of a morph history consisting of a sequence of valid solid models. For source and target models that are sufficiently close, this interpolative morphing scheme generates results c omparable to those obtained by the recursive skeletonization procedure, but with improved computational efficiency. The boundary point correspondence generated by the skeleton enables morphing with surface attributes (e.g., c olor, texture, surface roughness, and transparency). The skeleton-based pro cedure also allows for morphing between open curves or surfaces. A modifica tion of the basic procedure allows the user to control the morph by specify ing corresponding feature sets on the initial and final objects. Examples a re presented to demonstrate the capabilities of the methods described. (C) 2000 Published by Elsevier Science B.V. All rights reserved.