A Rotation-Strain Method to Model Surfaces using Plasticity

TL;DR

This paper introduces a rotation-strain method leveraging plasticity to model large, smooth deformations of surfaces embedded in 3D space, overcoming issues of sharp artifacts and compatibility constraints.

Contribution

It proposes a novel approach that modifies fundamental forms via rotation and strain fields, enabling smooth large deformations while satisfying user-defined constraints.

Findings

Successfully deforms surface meshes to large strains

Maintains smoothness and feasibility of deformations

Handles arbitrary large deformations with compatibility conditions

Abstract

Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference between the current status and the rest configuration to maintain the initial shape, which will lead to sharp spikes or wiggles for large deformations; the co-dimensional nature of the problem makes it more complicated because the deformed surface has to locally satisfy compatibility conditions on fundamental forms to guarantee a feasible solution exists. To address these two challenges, we propose a rotation-strain method to modify the fundamental forms in a compatible way, and model the large deformation of surface meshes smoothly using plasticity. The user prescribes the positions of a few vertices, and our method finds a smooth strain and rotation field under which the surface meets the target positions. We demonstrate several examples whereby triangle meshes are smoothly deformed to large strains while meeting user constraints.