  We present MeshODE, a scalable and robust framework for pairwise CAD model
deformation without prespecified correspondences. Given a pair of shapes, our
framework provides a novel shape feature-preserving mapping function that
continuously deforms one model to the other by minimizing fitting and rigidity
losses based on the non-rigid iterative-closest-point (ICP) algorithm. We
address two challenges in this problem, namely the design of a powerful
deformation function and obtaining a feature-preserving CAD deformation. While
traditional deformation directly optimizes for the coordinates of the mesh
vertices or the vertices of a control cage, we introduce a deep bijective
mapping that utilizes a flow model parameterized as a neural network. Our
function has the capacity to handle complex deformations, produces deformations
that are guaranteed free of self-intersections, and requires low rigidity
constraining for geometry preservation, which leads to a better fitting quality
compared with existing methods. It additionally enables continuous deformation
between two arbitrary shapes without supervision for intermediate shapes.
Furthermore, we propose a robust preprocessing pipeline for raw CAD meshes
using feature-aware subdivision and a uniform graph template representation to
address artifacts in raw CAD models including self-intersections, irregular
triangles, topologically disconnected components, non-manifold edges, and
nonuniformly distributed vertices. This facilitates a fast deformation
optimization process that preserves global and local details. Our code is
publicly available.
