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Proceedings of CAD'16, 2016, 131-136
Bivariate Splines over Triangular Meshes for Freeform Surface Modeling with Sharp Feature
Juan Cao, Xiamen University
Abstract. Generalizing univariate B-splines to bivariate splines is a basic strategy to construct spline surfaces in freeform surface modeling. A popular approach is to use tensor-product. A typical example is NURBS which has been an industry standard in CAD/CAE. NURBS has many good properties such as clear geometric intuition, compact representation, automatic maintenance of smoothness, analytic formula, local control, and many nice algorithms. However, due to inherent tensor-product structure, NURBS has two serious limitations: (1) NURBS does not support local refinement which is often demanded in interactive modeling and engineering simulation; and (2) NURBS has difficulty in modeling shapes of arbitrary topology. To solve the first limitation, T-splines were proposed, which allow the existence of T-junctions in the control grid of the surface definition and thus enable local refinement. To solve the second limitation, subdivision surfaces were developed, which generalize B-spline surfaces to arbitrary topology. Due to the nature of recursive subdivision process, subdivision surfaces are not widely used in CAD/CAE than in animation and game industry.
Keywords. Freeform Surface Modeling, Bivariate Splines, Triangular Meshes, Sharp Feature