Anisotropic Strain Limiting for Quadrilateral and Triangular Cloth Meshes

The cloth simulation systems often suffer from excessive extension on the polygonal mesh, so an additional strain-limiting process is typically used as a remedy in the simulation pipeline. A cloth model can be discretized as either a quadrilateral mesh or a triangular mesh, and their strains are measured differently. The edge-based strain-limiting method for a quadrilateral mesh creates anisotropic behaviour by nature, as discretization usually aligns the edges along the warp and weft directions. We improve this anisotropic technique by replacing the traditionally used equality constraints with inequality ones in the mathematical optimization, and achieve faster convergence. For a triangular mesh, the state-of-the-art technique measures and constrains the strains along the two principal (and constantly changing) directions in a triangle, resulting in an isotropic behaviour which prohibits shearing. Based on the framework of inequality-constrained optimization, we propose a warp and weft strain-limiting formulation. This anisotropic model is more appropriate for textile materials that do not exhibit isotropic strain behaviour.