Automated Synthesis of Numerical Programs for Simulation of Rigid Mechanical Systems in Physics-Based Animation

Physics-based animation programs are important in a variety of contexts, including science, engineering, education and entertainment among others. Manual construction of such programs is expensive, time-consuming and prone to error. We have developed a system for automatically synthesizing physics-based animation programs for a significant class of problems: constrained systems of rigid bodies, subject to driving and dissipative forces, under the control of an interactive user. Our system includes a graphical interface for specifying a physical scenario, including objects, geometry and coordinate systems, along with a symbolic interface for specifying dynamical variables, forces and constraints operating in the scenario. The entities defined in the graphical interface serve as the underlying vocabulary for specifications entered in the symbolic interface. Our system partitions the constraints and dynamical variables into classes and assigns each class to be implemented in a different component of a general simulation program scheme. It generates a numerical C++ simulation program that drives a real-time animation of the specified scenario. Our system is implemented as a collection of rewrite rules in the Mathematica programming language. Our approach provides some of the benefits of formal deductive program synthesis, while keeping the computational costs of program synthesis more in line with conventional program generator technology. We have successfully tested our system on numerous examples.

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