Computing moments of objects enclosed by piecewise polynomial surfaces

Abstract

Combining a polynomial free-form surface representation with Gauss' divergence theorem allows efficient and exact calculation of the moments of the enclosed object. For example, for a cubic representation, volume, center of mass, and the inertia tensor can be computed in seconds even for complex objects with several thousand patches while changes due to local modification of the surface geometry can be computed in real-time as feedback for animation or design. Speed and simplicity of the approach allow solving the inverse problem of modeling to match prescribed moments.