Exact and efficient computation of moments of free-form surface and trivariate based geometry

Two schemes for computing moments of free-form objects are developed and analyzed. In the first scheme, we assume that the boundary of the analyzed object is represented using parametric surfaces. In the second scheme, we represent the boundary of the object as a constant set of a trivariate function. These schemes rely on a pre-computation step which allows fast re-evaluation of the moments when the analyzed object is modified. Both schemes take advantage of a representation that is based on the B-spline blending functions.