Abstract

Morphing is a tough problem. Almost all of the literature has dealt with transitions between surfaces with one-to-one vertex correspondences, or at least introduce methods to remesh surfaces to have these contrived relationships. These methods cannot deal with topological alteration.

I’ll bypass this minefield of geometric constraints by stepping boldly into the 4th dimension. We consider our input geometry as planar cross sections at different time instances, connect them up and extract the boundary. Isosurfaces extracted from this boundary manifold at various time instances yield a morph sequence.

Sadly, given time constraints, I will almost certainly only be able to present a subset of the full morphing pipeline.

Expect formulae, theorems, pretty animations and demonstrations of my software crashing.