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Explicit Continuity Conditions for G 1 Connection of S- λ Curves and Surfaces

Author

Listed:
  • Gang Hu

    (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, China)

  • Huinan Li

    (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, China)

  • Muhammad Abbas

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Kenjiro T. Miura

    (Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8011, Japan)

  • Guoling Wei

    (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, China)

Abstract

The S- λ model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S- λ curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G 1 connection of S- λ curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S- λ basis functions, the conditions of G 1 geometric continuity between two adjacent S- λ curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S- λ curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system.

Suggested Citation

  • Gang Hu & Huinan Li & Muhammad Abbas & Kenjiro T. Miura & Guoling Wei, 2020. "Explicit Continuity Conditions for G 1 Connection of S- λ Curves and Surfaces," Mathematics, MDPI, vol. 8(8), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1359-:d:398638
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