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Unified Representation of Curves and Surfaces

Author

Listed:
  • Aizeng Wang

    (School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
    State Key Laboratory of Virtual Reality Technology & System, Beijing 100191, China)

  • Gang Zhao

    (School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
    State Key Laboratory of Virtual Reality Technology & System, Beijing 100191, China)

  • Chuan He

    (School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
    State Key Laboratory of Virtual Reality Technology & System, Beijing 100191, China)

Abstract

In conventional modeling, shared control points can be employed to realize a unified representation for an object consisting of only curves or only surfaces touching one another. However, this method fails in treating the following two cases: (a) a system consisting of detached curves or surfaces; (b) a system having both curves and surfaces. The purpose of the present paper is to develop a new theoretical tool to solve such problems. By introducing the definitions of naked knot and I-mesh, the concept of I-spline is put forth, which is, in essence, an expanded B-spline or T-spline. It is verified by examples that the naked knots make I-splines flexible and effective in transforming different surfaces and/or curves into a unified one, especially in the above two cases.

Suggested Citation

  • Aizeng Wang & Gang Zhao & Chuan He, 2021. "Unified Representation of Curves and Surfaces," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1019-:d:547095
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