Assigned paper
1. Sentence: We propose a solution to the vertex interpolation problem that starts from interpolating the local metric (edge lengths) and mean curvature (dihedral angles) and makes consistent choices of local affine transformations using shape matching applied to successively larger parts of the mesh. (Abstract, 5th sentence)
2. Problem: The fundamental problem is commonly known as the “vertex path problem”: interpolating vertex positions among triangle meshes with identical vertex-edge graphs.
3. Key Idea: 1) Interpolate the local intrinsic properties of the mesh (edge length and dihedral angles) and 2) use hierarchical shape matching to derive a globally coherent solution.
4a. What the paper does: The authors demonstrate multiple interpolations (and some extrapolations) between a source mesh and a target mesh, and also within a space of more than two input meshes. The best example comes from interpolations between a cylinder and a cylinder which has been deformed into a tight helix.
4b. What it could be used for: Their approach can be used for exploring the natural space shape spanned by a set of key poses. They can express animations as a simple 2D path inside a reference polygon (defined by the key poses), which can be a good tool for character animation or even crowd generation.
5. Resources: Here is a video.