Heterogeneous Parametric Trivariate Fillets

Blending and filleting are well established operations in solid modeling and computer-aided geometric design. The creation of a transition surface which smoothly connects the boundary surfaces of two (or more) objects has been extensively investigated. In this work, we introduce several algorithms for the construction of, possibly heterogeneous, trivariate fillets, that support smooth filleting operations between pairs of, possibly heterogeneous, input trivariates. Several construction methods are introduced that employ functional composition algorithms as well as introduce a half Volumetric Boolean sum operation. A volumetric fillet, consisting of one or more tensor product trivariate(s), is fitted to the boundary surfaces of the input. The result smoothly blends between the two inputs, both geometrically and material-wise (properties of arbitrary dimension). The application of encoding heterogeneous material information into the constructed fillet is discussed and examples of all proposed algorithms are presented