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Biconic subdivision of surfaces of revolution and its applications in intersection problems

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Abstract

This paper presents a novel method for the subdivision of surfaces of revolution. We develop a new technique for approximating the genertrix by a series of pairs of conic sections. By using an error estimate based on convex combination, an efficient least-squares approach is proposed that yields near-optimal fitting. The resulting surface approximation is shown to be more efficient than other tessellation methods in terms of the number of fitting segments. This in turn allows us to implement efficient and robust algorithms for such surfaces. In particular, novel intersection techniques based on the proposed subdivision method are introduced for the two most fundamental types of intersections – line/surface and surface/surface intersections. The experimental results show that our method outperforms conventional methods significantly in both computing time and memory cost.

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Authors and Affiliations

  1. Department of Computer Science, Hong Kong University of Science & Technology, Kowloon, Hong Kong

    Jinyuan Jia

  2. Department of Mechanical Engineering, Hong Kong University of Science & Technology, Kowloon, Hong Kong

    Kai Tang

  3. Department of IEEM, Hong Kong University of Science & Technology, Kowloon, Hong Kong

    Ajay Joneja

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  1. Jinyuan Jia
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  2. Kai Tang
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  3. Ajay Joneja
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Correspondence to Kai Tang.

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Jia, J., Tang, K. & Joneja, A. Biconic subdivision of surfaces of revolution and its applications in intersection problems. Visual Comp 20, 457–478 (2004). https://doi.org/10.1007/s00371-004-0252-4

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