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Fast ray tracing NURBS surfaces

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Abstract

In this paper, a new algorithm with extrapolation process for computing the ray/surface intersection is presented. Also, a ray is defined to be the intersection of two planes, which are non-orthogonal in general, in such a way that the number of multiplication operations is reduced. In the preprocessing step, NURBS surfaces are subdivided adaptively into rational Bézier patches. Parallelepipeds are used to enclose the respective patches as tightly as possible. Therefore, for each ray that hits the enclosure (i.e., parallelepiped) of a patch the intersection points with the parallelepiped's faces can be used to yield a good starting point for the following iteration. The improved Newton iteration with extrapolation process saves CPU time by reducing the number of iteration steps. The intersection scheme is faster than previous methods for which published performance data allow reliable comparison. The method may also be used to speed up tracing the intersection of two parametric surfaces and other operations that need Newton iteration.

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, 100084, Beijing

    Qin Kaihuai, Gong Minglun & Tong Geliang

Authors
  1. Qin Kaihuai
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  2. Gong Minglun
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  3. Tong Geliang
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Additional information

Project supported by the National Natural Science Foundation of China under grant number 69473010.

Qin Kaihuai obtained his Ph.D. degree in computer-aided manufacturing from Tsinghua University in 1990. He is now an Associate Professor in computer science and technology at Tsinghua University. His research areas include computer graphics, geometric modeling, spline curves and surfaces (epsecially NURBS surfaces), nueral network, scientific visualization, virtual reality, CAD/CAM.

Gong Minglun is a graduate student of Department of Computer Science and Technology, Tsinghua University.

Tong Geliang is a graduate student of Department of Computer Science and Technology, Tsinghua University.

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Qin, K., Gong, M. & Tong, G. Fast ray tracing NURBS surfaces. J. of Compt. Sci. & Technol. 11, 17–29 (1996). https://doi.org/10.1007/BF02943518

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  • DOI: https://doi.org/10.1007/BF02943518

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