Technical Report MSC-2021-15

Title: Heterogeneous Parametric Trivariate Fillets
Authors: Ramy Masalha
Supervisors: Gershon Elber
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Abstract: Given two objects, blending refers to the creation of a transition surface which smoothly connects boundary surfaces. In this work, we extend the problem of constructing a blending surface to its three-dimensional analog. More specifically, we seek to create a volumetric fillet which smoothly fills the space between two intersecting objects. Blending and filleting are used for rounding sharp edges or corners, and they are of high importance in the field of computer-aided design. Due to mechanical, aesthetic or other reasons, it is typically desired to replace sharp edges and corners by smooth faces. While methods for constructing a blending surface have been researched intensively in the last decades, to the extent of our knowledge, virtually no research has been conducted on the construction of volumetric fillets. This work presents several algorithms for the construction of, possibly heterogeneous, intersecting trivariates. The input trivariates are assumed to be in R^k, k>=3, and they can include, in addition to geometric information in R^3, additional (scalar, vector, tensor, etc.) properties, such as material properties. The introduced algorithms operate under different assumptions and support different types of input trivariates. Our proposed filleting methods either employ functional composition or use the least-square-fitting method to fit a (set of) tensor product trivariate(s) to the boundary surfaces of the input. The result blends between the two inputs, both geometrically and material-wise. The application of encoding heterogeneous material information into the constructed fillet is discussed and examples of all proposed algorithms are presented.
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