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Journal of Computer Science and Technology

, Volume 16, Issue 6, pp 552–559 | Cite as

CIM algorithm for approximating three-dimensional polygonal curves

  • Yong Junhai 
  • Hu Shimin 
  • Sun Jiaguang 
Correspondence

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.

Keywords

polygonal curve CIM LS-WMN approximation optimization 

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References

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Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2001

Authors and Affiliations

  • Yong Junhai 
    • 1
    • 2
  • Hu Shimin 
    • 1
    • 2
  • Sun Jiaguang 
    • 1
    • 2
  1. 1.National CAD Engineering CenterTsinghua UniversityBeijingP.R. China
  2. 2.Department of Computer Science and TechnologyTsinghua UniversityBeijingP.R. China

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