Generating the Envelope of a Swept Trivariate Solid

We present a method for calculating the envelope of the swept surface of a solid along a path in three-dimensional space. The generator of the swept surface is a trivariate tensorproduct Bèzier solid and the path is a non-uniform rational B-spline curve. The boundary surface of the solid is the combination of parametric surfaces and an implicit surface where the determinant of the Jacobian of the defining function is zero. We define methods to calculate the envelope for each type of boundary surface, defining characteristic curves on the envelope and connecting them with triangle strips. The envelope of the swept solid is then calculated by taking the union of the envelopes of the family of boundary surfaces, defined by the surface of the solid in motion along the path.