Premium
A Finite Element Formulation of Baraff‐Witkin Cloth
Author(s) -
Kim Theodore
Publication year - 2020
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.14111
Subject(s) - hyperelastic material , isotropy , finite element method , shearing (physics) , strain energy density function , coupling (piping) , anisotropy , classical mechanics , computer science , physics , optics , mechanical engineering , engineering , thermodynamics
The Baraff‐Witkin [BW98] model has been a popular formulation for cloth for 20 years. However, its relationship to the finite element method (FEM) has always been unclear, because the model resists being written as an isotropic, hyperelastic strain energy. In this paper, we show that this is because the Baraff‐Witkin model is actually a coupled anisotropic strain energy. We show that its stretching term approximates the isotropic As‐Rigid‐As‐Possible (ARAP) energy, and its shearing term is a cross‐fiber coupling energy common in biomechanics. While it has been known empirically for some time that the model can produce indefinite force Jacobians, the conditions under which they occur has never been clear. Our formulation enables a complete eigenanalysis that precisely characterizes exactly when indefiniteness occurs, and leads to fast, analytic, semi‐positive‐definite projection methods. Finally, our analysis suggests a generalized Baraff‐Witkin energy with non‐orthogonal warp and weft directions.