Planar interpolation with extreme deformation, topology change and dynamics

We present a mesh-based, interpolatory method for interactively creating artist-directed inbetweens from arbitrary sets of 2D drawing shapes without rigging. To enable artistic freedom of expression we remove prior restrictions on the range of possible changes between shapes; we support interpolation with extreme deformation and unrestricted topology change. To do this, we extend discrete variational interpolation by introducing a consistent multimesh structure over drawings, a Comesh Optimization algorithm that optimizes our multimesh for both intra- and inter-mesh quality, and a new shape-space energy that efficiently supports arbitrary changes and can prevent artwork overlap when desired. Our multimesh encodes specified correspondences that guide interpolation paths between shapes. With these correspondences, an efficient local-global minimization of our energy interpolates n-way between drawing shapes to create inbetweens. Our Comesh Optimization enables artifact-free minimization by building consistent meshes across drawings that improve both the quality of per-mesh energy discretization and inter-mesh mapping distortions, while guaranteeing a single, compatible triangulation. We implement our method in a test-bed interpolation system that allows interactive creation and editing of animations from sparse key drawings with arbitrary topology and shape change.