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Hyperfinite interpolation, Wu’s Method and blending of implicit algebraic surfaces

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Abstract

One of the central questions in CAGD[1] is blending surfaces which provides the theoretical basis for the design technology of space surfaces. We will discuss the general theories and algorithms for multivariate hyperfinite interpolation and their application to the blending of implicit algebraic surfaces, and investigate the existence conditions of hyperfinite interpolation. Based on Wu’s theory on blending implicit algebraic surfaces, the problem of blending two quadric surfaces is studied. The conditions for the coefficient ofg i under which there exists the cubic blending surfaceS(f) (the lowest degree) are obtained and the concrete expressions off are presented if they exist. These results can be applied directly to CAGD.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Jilin University, 130023, Changchun, P.R. China

    Zhang Shugong & Ren Hongju

Authors
  1. Zhang Shugong
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  2. Ren Hongju
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Correspondence to Zhang Shugong.

Additional information

For the biography ofZHANG Shugong, please refer to p.517 of this issue.

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Zhang, S., Ren, H. Hyperfinite interpolation, Wu’s Method and blending of implicit algebraic surfaces. J. Comput. Sci. & Technol. 14, 518–529 (1999). https://doi.org/10.1007/BF02948793

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  • DOI: https://doi.org/10.1007/BF02948793

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