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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Blending and filleting operations in solid modeling and computer-aided geometric design have been extensively studied. This work introduces algorithms for constructing trivariate fillets between heterogeneous inputs, supporting smooth transitions geometrically and in terms of material properties. The algorithms fit tensor product trivariates to boundary surfaces and encode heterogeneous material information for a seamless transition.