Interactive Mesh Deformation with Hard Constraints

Abstract

Interactive mesh editing techniques typically encode geometric shapes using discrete differential equations and approximately solve them using the least squares method. However, these techniques fail to precisely preserve user-defined constraints. In our method, user-defined constraints, such as positional constraints, are treated as hard constraints, and then the combination of hard and soft constraints is converted into a typical least-squares system using QR decomposition. Our method stably and efficiently calculates vertex positions that preserve differential properties. A well-known problem with hard constraints is over-constraints. If over-constraints are involved, they may cause the solver to halt the computation. We show how our framework resolves over-constrained situations, which include redundant and conflicting constraints.