Morphing many polygons across a change in topology

Many solutions have been proposed for morphing between two polygons. However, there has been little attention directed toward morphing between different numbers of polygons, across a change in topology. In this dissertation, three different algorithms are progressively developed for this problem. The first algorithm is designed for the most fundamental case of the category: morphing two polygons that are convex or have minor concavities into one. The second algorithm; or the recursive canyon algorithm, moves a step further to handle input polygons with deep concavities. Based on these two algorithms, the third algorithm is designed to morph between two groups of arbitrary numbers of polygons. All three algorithms require no user interaction; are inexpensive, use dynamic vertex correspondence; follow nonlinear vertex paths, and are able to generate smooth animation results.

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