An Algorithm with Logarithmic Time Complexity for Interactive Simulation of Hierarchically Articulated Bodies Using a Distributed-memory Architecture

Abstract

The dynamic simulation of large systems of hierarchically articulated bodies is very time-consuming and cannot be done in real time using current one-processor workstations. This paper discusses the parallelization of dynamic simulation algorithms for such systems. First, the methods used in computer animation for solving initial-value problems are compared. Using test suites based on articulated bodies, the Gear method for non-stiff problems is identified as the solver with the least right-hand-side evaluations of the differential equations for the executed tests. On the basis of this method and the articulated-body method, a ‘simulation engine’ for distributed-memory architectures is presented. By reimplementing the Gear method and rearranging its parts, logarithmic time complexity is achieved for hierarchically articulated bodies. By using the simulation engine, interactive, physically based animation of large articulated figures is possible.