Skeleton-based three-dimensional geometric morphing

Abstract

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 feature sets and different topology. The essential concept that enables the morphing method is utilization of the trimmed skeleton of the symmetric difference as an intermediate shape. The intermediate shape is a valid solid model whose boundary does not self-intersect and is everywhere equidistant from the boundaries of the source shapes. We apply the skeleton-based intermediate shape generation procedure recursively to produce a sequence of shapes, referred to as a morph history, that gradually transform between the initial and target shapes. The method is sufficiently robust to handle significant changes in geometry and topology, such as the creation and annihilation of protrusions, indentations, internal holes and handles, and produces intuitive morph histories. The skeleton also establishes a correspondence between points on the boundaries 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 comparable 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., color, texture, surface roughness, and transparency). The skeleton-based procedure also allows for morphing between open curves or surfaces. A modification of the basic procedure allows the user to control the morph by specifying corresponding feature sets on the initial and final objects. Examples are presented to demonstrate the capabilities of the methods described.