Abstract
This paper presents a new kind of spline surfaces, named non-uniform algebraic-trigonometric T-spline surfaces (NUAT T-splines for short) of odd bi-degree. The NUAT T-spline surfaces are defined by applying the T-spline framework to the non-uniform algebraic-trigonometric 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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Supported by the National Natural Science Foundation of China (60933008 and 61272300).
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Duan, Xj., Wang, Gz. NUAT T-splines of odd bi-degree and local refinement. Appl. Math. J. Chin. Univ. 29, 410–421 (2014). https://doi.org/10.1007/s11766-014-3235-x
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DOI: https://doi.org/10.1007/s11766-014-3235-x