# A Splitting Scheme for Flip-Free Distortion Energies

arXiv: https://arxiv.org/abs/2107.05200 · HTML: https://mlsanity.com/paper/2107.05200/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [Symmetric Volume Maps: Order-Invariant Volumetric Mesh Correspondence with Free Boundary](https://mlsanity.com/paper/2202.02568/) (2022)

## Abstract (arXiv)

We introduce a robust optimization method for flip-free distortion energies used, for example, in parametrization, deformation, and volume correspondence. This method can minimize a variety of distortion energies, such as the symmetric Dirichlet energy and our new symmetric gradient energy. We identify and exploit the special structure of distortion energies to employ an operator splitting technique, leading us to propose a novel Alternating Direction Method of Multipliers (ADMM) algorithm to deal with the non-convex, non-smooth nature of distortion energies. The scheme results in an efficient method where the global step involves a single matrix multiplication and the local steps are closed-form per-triangle/per-tetrahedron expressions that are highly parallelizable. The resulting general-purpose optimization algorithm exhibits robustness to flipped triangles and tetrahedra in initial data as well as during the optimization. We establish the convergence of our proposed algorithm under certain conditions and demonstrate applications to parametrization, deformation, and volume correspondence.