ARAP

As Rigid As Possible (ARAP) constitution

#9 ARAP

Dynamic Deformables: Implementation and Production Practicalities (Now With Code!)

As Rigid As Possible (ARAP) deformation energy density per tetrahedron is defined as:

\[ V = \kappa \|\mathbf{F}-\mathbf{R}\|_F^2 = \kappa \|\mathbf{S}-\mathbf{I}\|_F^2 \]

where \(\kappa\) is the stiffness parameter, \(\mathbf{R}\mathbf{S}\) is the polar decomposition of deformation gradient \(\mathbf{F}\). \(\kappa\) could be \(1 kPa\) ~ \(10 MPa\) depending on the material. If you want a material with \(\kappa\) larger than \(10MPa\), consider directly using Affine Body for better performance.