NUAT T-splines of odd bi-degree and local refinement |
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Authors: | DUAN Xiao-juan WANG Guo-zhao |
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Institution: | Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
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Abstract: | This paper presents a new kind of spline surfaces, named non-uniform algebraictrigonometric T-spline surfaces(NUAT T-splines for short) of odd bi-degree. The NUAT Tspline surfaces are defined by applying the T-spline framework to the non-uniform algebraictrigonometric B-spline surfaces(NUAT B-spline surfaces). Based on the knot insertion algorithm of the NUAT B-splines, a local refinement algorithm for the NUAT T-splines is given. This algorithm guarantees that the resulting control grid is a T-mesh as the original one. Finally,we prove that, for any NUAT T-spline of odd bi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAT T-spline-to-NUAT B-spline transformation matrix. |
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Keywords: | odd bi-degree non-uniform algebraic-trigonometric T-spline local refinement blending function linear independence |
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