Institute for Data Analysis and Visualization

B-Spline curves and surfaces can be de(r)ned by a set of control points and a set of refinement rules. These rules act on the defining mesh of control points to create a new refined mesh. Repeated application of the rules generates a sequence of meshes that converge to the curve or surface. In the surface case, Catmull and Clark extended the refinement rules for the rectangular topological meshes of the B-spline form to meshes that have an arbitrary topological structure. In much the same way, the refinement rules for a trivariate B-spline solid can be extended from those that apply to the regular hexahedral topological lattices of the B-spline form to lattices that have an arbitrary topological structure. We present a uniform development of the refinement rules for trivariate B-spline solids and extend the rules to apply to solid lattices of arbitrary topology.