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A new representation and algorithm for constructing convex hulls in higher dimensional spaces

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Abstract

This paper presents a new and simple scheme to describe the convex hull in Rd, which only uses three kinds of the faces of the convex hull, i. e., thed-1-faces,d-2-faces and 0-faces. Thus, we develop an efficient new algorithm for constructing the convex hull of a finite set of points incrementally. This algorithm employs much less storage and time than that of the previously existing approaches. The analysis of the running time as well as the storage for the new algorithm is also theoretically made. The algorithm is optimal in the worst case for evend.

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Authors and Affiliations

  1. CAD/CAM Research Center, Zhejiang University, 310027, Hanzhou

    Wei Lü & Youdong Liang

Authors
  1. Wei Lü
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  2. Youdong Liang
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Additional information

This work is supported by the National Natural Science Foundation of China.

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Lü, W., Liang, Y. A new representation and algorithm for constructing convex hulls in higher dimensional spaces. J. of Comput. Sci. & Technol. 7, 1–5 (1992). https://doi.org/10.1007/BF02946159

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  • DOI: https://doi.org/10.1007/BF02946159

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