multi-scale geometry interpolation
interpolating vertex positions among triangle meshes with identical
vertex-edge graphs is a fundamental part of many geometric modelling
systems. linear vertex interpolation is robust but fails to preserve
local shape. most recent approaches identify local affine transformations
for parts of the mesh, model desired interpolations of the affine
transformations, and then optimize vertex positions to conform with
the desired transformations. however, the local interpolation of the
rotational part is non-trivial for more than two input configurations
and ambiguous if the meshes are deformed significantly. 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. the local interpolation can be applied to any number
of input vertex configurations and due to the hierarchical scheme for
generating consolidated vertex positions, the approach is fast and
can be applied to very large meshes.