Geometric multigrid on incomplete linear octrees for simulating deformable animated characters

摘要

A method and system for simulation of deformation of elastic materials are disclosed herein. A matrix-free geometric multigrid method utilizing a direct coarse grid discretization is presented for the solution of linear systems resulting from an octree discretization of the equations of corotational linear elasticity. The diagonal component of the stiffness matrix needed for the multigrid smoother is calculated without generating the stiffness matrix. The use of an incomplete linear octree data structure supports the efficient simulation of objects with complicated boundaries. Furthermore, the method is robust to large deformations, making it suitable for character skinning applications in computer animation.