Linear-Time Dynamics Using Lagrange Multipliers

Current linear-time simulation methods for articulated figures are based exclusively on reduced-coordinate formulations. This paper describes a general, non-iterative linear-time simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics applications because they bypass the difficult (and often intractable) problem of parameterizing a system's degrees of freedom. Given a loop-free set of n equality constraints acting between pairs of bodies, the method takes O(n) time to compute the system's dynamics. The method does not rely on matrix bandwidth, so no assumptions about the constraints' topology are needed. Bodies need not be rigid, constraints can be of various dimensions, and unlike reduced-coordinate approaches, nonholonomic (e.g. velocity-dependent) constraints are allowed. An additional set of k one-dimensional constraints which induce loops and/or handle inequalities can be accommodated with cost O(kn)....

• Type: Conference
• Year: 1996
• Where: SIGGRAPH
• Authors: David Baraff
• Keywords: Articulated Figures, Computer Graphics, Lagrange Multiplier, Linear-time Simulation Method, SIGGRAPH 1996