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Proceedings of CAD'16, 2016, 194-199
T-Spline Local Refinement as a Belief Revision System: A Rule-based Implementation
Abstract. The best known methods (B-Splines, NURBS and recursive subdivision, for examples), for modeling geometric surfaces, start from a so-called control mesh on the basis of which the desired surface may be constructed. In this sense, T-splines are no different, because modeling there starts from an initial control mesh. However, the initial control mesh here is abstracted away through embedding its constituents (i.e., vertices, edges and faces) inside a two-dimensional grid called a T-mesh, presumably considered within the knot domain. By comparison with other modeling schemes, a T-mesh permits fewer connections between pairs of control points. Moreover, the structure of the T-mesh allows for the automatic inference of the knot information associated with its constituent control points. More importantly perhaps, it comes equipped with a refinement routine whose local effects are comparable to the classical curve knot insertion. However, as already published, T-spline local refinement is cast in an algorithmic language lacking the mathematic decisiveness manifested in curve knot insertion, keeping in the shadow many of the details that need to be available for implementation purposes.
Keywords. T-spline surfaces, local refinement, belief-revision systems, rule-based systems