Solving Variational Problems Using Nonlinear Rotation-invariant Coordinates

Abstract

We consider Nonlinear Rotation-Invariant Coordinates (NRIC) representing triangle meshes with fixed combinatorics as a vector stacking all edge lengths and dihedral angles. Previously, conditions for the existence of vertex positions matching given NRIC have been established. We develop the machinery needed to use NRIC for solving geometric optimization problems. Moreover, we introduce a fast and robust algorithm that reconstructs vertex positions from close-to integrable NRIC. Our experiments underline that NRIC-based optimization is especially effective for near-isometric problems.