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Issue No.02  Feb. (2014 vol.20)
pp: 172181
Hongwei Lin , Dept. of Math., Zhejiang Univ., Hangzhou, China
Yang Qin , Dept. of Math., Zhejiang Univ., Hangzhou, China
Hongwei Liao , Dept. of Math., Zhejiang Univ., Hangzhou, China
Yunyang Xiong , Dept. of Math., Zhejiang Univ., Hangzhou, China
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2013.237
ABSTRACT
Because the Bspline surface intersection is a fundamental operation in geometric design software, it is important to make the surface intersection operation robust and efficient. As is well known, affine arithmetic is robust for calculating the surface intersection because it is able to not only find every branch of the intersection, but also deal with some singular cases, such as surface tangency. However, the classical affine arithmetic is defined only for the globally supported polynomials, and its computation is very time consuming, thus hampering its usefulness in practical applications, especially in geometric design. In this paper, we extend affine arithmetic to calculate the range of recursively and locally defined Bspline basis functions, and we accelerate the affine arithmeticbased surface intersection algorithm by using a GPU. Moreover, we develop efficient methods to thin the stripshaped intersection regions produced by the affine arithmeticbased intersection algorithm, calculate the intersection points, and further improve their accuracy. The many examples presented in this paper demonstrate the robustness and efficiency of this method.
INDEX TERMS
Graphics processing units, Splines (mathematics), Strips, Robustness, Accuracy, Threedimensional displays, Acceleration,GPU acceleration, Graphics processing units, Splines (mathematics), Strips, Robustness, Accuracy, Threedimensional displays, Acceleration, geometric design, Surfacesurface intersection, affine arithmetic
CITATION
Hongwei Lin, Yang Qin, Hongwei Liao, Yunyang Xiong, "Affine ArithmeticBased BSpline Surface Intersection with GPU Acceleration", IEEE Transactions on Visualization & Computer Graphics, vol.20, no. 2, pp. 172181, Feb. 2014, doi:10.1109/TVCG.2013.237
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