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Generating Symbolic Interpolants for Scattered Data with Normal Vectors

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Abstract

Algorithms to generate a triangular or a quadrilateral interpolant with G1-continuity are given in this paper for arbitrary scattered data with associated normal vectors over a prescribed triangular or quadrilateral decomposition. The interpolants are constructed with a general method to generate surfaces from moving Bézier curves under geometric constraints. With the algorithm, we may obtain interpolants in complete symbolic parametric forms, leading to a fast computation of the interpolant. A dynamic interpolation solid modelling software package DISM is implemented based on the algorithm which can be used to generate and manipulate solid objects in an interactive way.

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Authors and Affiliations

  1. School of Computer Science, Cardiff University, Cardiff, CF24 3AA, U.K.

    Ming Li

  2. Key Lab of Mathematics Mechamization, AMSS, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Xiao-Shan Gao & Jin-San Cheng

Authors
  1. Ming Li
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  2. Xiao-Shan Gao
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  3. Jin-San Cheng
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Corresponding author

Correspondence to Ming Li.

Additional information

Partially supported by the National Basic Research 973 Program of China (Grant No. G1998030600) and by the US NSF under Grant No. CCR-0201253.

Ming Li was born in 1977. He received his M.sc. degree in 2001 from Jilin University, China and Ph.D. degree in mathematics in 2004 from Chinese Academy Sciences 2004. He is currently a research associate at the School of Computer Sciences, Cardiff University, U.K. His research interests include curve/surface approximation in CAGD, reverse engineering and algebraic geometry.

Xiao-Shan Gao received his Ph.D. degree from Chinese Academy of Sciences in 1988. He is a professor in the Institute of Systems Science, Chinese Academy of Sciences. His research interests include geometric computation and reasoning, symbolic computation, robotics, CAD and CAGD. He has published over 100 research papers, two monographs and edited four books or conference proceedings.

Jin-San Cheng was born in 1976. He received his M.sc. degree in computer mathematics from Jilin University, China in 2003. He is currently a Ph.D. candidate in AMSS, Chinese Academy of Sciences. His research interests include topology of curve/surface in CAGD, CG and algebraic geometry.

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Li, M., Gao, XS. & Cheng, JS. Generating Symbolic Interpolants for Scattered Data with Normal Vectors. J Comput Sci Technol 20, 861–874 (2005). https://doi.org/10.1007/s11390-005-0861-z

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  • DOI: https://doi.org/10.1007/s11390-005-0861-z

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