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
Wu Wen-tsun. On surface-fitting problem in CAGD.MM Research Preprints, 1993, (10): 1–10.
Becker T, Weispfenning V. Gorebner Basis, A Computational Approach to Commutative Algebra.Graduate Texts in Mathematics, Springer-Verlag, 1993, Vol.141.
Warren J. Blending algebraic surfaces.ACM Transactions on Graphics, 1989, 8(4): 263–278.
Wu Tie-ru, Gao Wei-guo, Feng Guo-chen. Blending of implicit algebraic surfaces. InProceedings of the ASIAN Symp. on Computer Math., 1995, 125–131,Tokyo:Scientists Incorporated.
Wu Tie-ru. Blending of implicit algebraic surfaces.Master’s Thesis of Jilin University, 1995.
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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