Combining the advantages of a low-degree polynomial surface representation with Gauss' divergence theorem allows efficient and exact calculation of the moments of objects enclosed by a free-form surface. Volume, center of mass and the inertia tensor can be computed in seconds even for complex objects with 10 5 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 modelling to match prescribed moments. 1 Introduction Realistic animation and geometric design must both pay close attention to the physics implied by the first few moments, the volume, center of mass and inertia frame, of the objects they manipulate. A jug whose fill level is inconsistent with the amount of water filled into it, or one that does not topple over when the projection of the center of mass moves outside the support, puzzles and distracts the viewer and c...