Abstract
The polygonal approximation problem is a primary problem in computer graphics, pattern recognition, CAD/CAM, etc. InR 2, the cone intersection method (CIM) is one of the most efficient algorithms for approximating polygonal curves. With CIM Eu and Toussaint, by imposing an additional constraint and changing the given error criteria, resolve the three-dimensional weighted minimum number polygonal approximation problem with the parallel-strip error criterion (PS-WMN) underL 2 norm. In this paper, without any additional constraint and change of the error criteria, a CIM solution to the same problem with the line segment error criterion (LS-WMN) is presented, which is more frequently encountered than the PS-WMN is. Its time complexity isO(n 3), and the space complexity isO(n 2). An approximation algorithm is also presented, which takesO(n 2) time andO(n) space. Results of some examples are given to illustrate the efficiency of these algorithms.
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This research was supported by the National Natural Science Foundation of China (No69902004) and NKBRSF (No.G1998030600).
YONG Junhai received his Ph.D. degree from the Department of Computer Science and Technology, Tsinghua University, Beijing, P.R. China in 2000. He received the B.S. degree from the Department of Computer Science and Technology, Tsinghua University, in 1996. From March to June in 2000, he was a visiting researcher in the Hong Kong University of Science and Technology. His research interests are computer aided design, computer graphics and standardization of product data.
HU Shimin is an associate professor in the Department of Computer Science and Technology, Tsinghua University, Beijing, P.R China. He received the Ph.D. degree in 1996 from Zhejiang University, P. R. China, and finished postdoctoral research work in 1998 at Tsinghua University. His research interests are computer aided design, computer graphics, fractal geometry and its applications.
SUN Jiaguang is a professor in the Department of Computer Science and Technology, Tsinghua University, Beijing, P.R. China. His research interests are computer graphics, computer aided design, computer aided manufacturing, product data management and software engineering.
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Yong, J., Hu, S. & Sun, J. CIM algorithm for approximating three-dimensional polygonal curves. J. Comput. Sci. & Technol. 16, 552–559 (2001). https://doi.org/10.1007/BF02943239
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DOI: https://doi.org/10.1007/BF02943239