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Proceedings of CAD'14, 2014, 109-111
Wavelet-based Surface Decomposition with Boundary Continuity
Abstract. B-spline surfaces are a powerful mathematical representation of freeform surfaces and also play a primary role in computer-aided design (CAD) and computer aided manufacturing (CAM), especially in the area of industrial design such as ships, aircrafts and cars. In addition, surface decomposition operations are often used in CAD systems to get surface simplification and fairing. B-splines that provide a unified geometry representation of conic sections and free-form shapes have been widely used in CAD and CAM. However, for B-spline surfaces, all control points must lie topologically in a rectangular grid, and this makes they do not allow local refinement. To overcome these drawbacks, T-splines that are defined on a T-mesh and allow T-junctions in their control grid were proposed. A T-junction is a control point which terminates a partial row or column in the control grid. Unlike B-spline surfaces, T-splines allow local refinement, and have good properties in surface merging and model simplification. This paper presents a new decomposition algorithm for B-spline surfaces with boundary continuity. First, a B-spline surface is divided into a boundary part and a non-boundary part, and then the non-boundary one is decomposed into a scale part and a wavelet part; finally, the T-spline is utilized to reconstruct the boundary one and the scale one. In the new decomposition approach, the result surface is a T-spline which can preserve the boundary continuity.
Keywords. Wavelet transform, B-spline surface, boundary continuity, CAGD