Journal
ACM TRANSACTIONS ON GRAPHICS
Volume 38, Issue 2, Pages -Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3209887
Keywords
Collision response; conjugate residual
Categories
Funding
- European Research Council (ERC Consolidator Grant TouchDesign) [772738]
- European Research Council (ERC) [772738] Funding Source: European Research Council (ERC)
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Simulating (elastically) deformable models that can collide with each other and with the environment remains a challenging task. The resulting contact problems can be elegantly approached using Lagrange multipliers to represent the unknown magnitude of the response forces. Typical methods construct and solve a Linear Complementarity Problem (LCP) to obtain the response forces. This requires the inverse of the generalized mass matrix, which is generally hard to obtain for deformable-body problems. In this article, we tackle such contact problems by directly solving the Mixed Linear Complementarity Problem (MLCP) and omitting the construction of an LCP matrix. Since a convex quadratic program with linear constraints is equivalent to an MLCP, we propose to use a Conjugate Residual (CR) solver as the backbone of our collision response system. By dynamically updating the set of active constraints, the MLCP with inequality constraints can be solved efficiently. We also propose a simple yet efficient preconditioner that ensures faster convergence. Finally, our approach is faster than existing methods (at the same accuracy), and it allows accurate treatment of friction.
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