Constructive theory and algorithm for blending several implicit algebraic surfaces

Authors:
Yurong Li;Na Lei;Shugong Zhang;Guochen Feng
Affiliations:
The Information Electronic Engineering School, Shandong Institute of Business and Technology, Yantai, China;Key Laboratory of Symbolic Computation and Knowledge Engineering in JLU Ministry of Education, Changchun, China;,Key Laboratory of Symbolic Computation and Knowledge Engineering in JLU Ministry of Education, Changchun, China;,Key Laboratory of Symbolic Computation and Knowledge Engineering in JLU Ministry of Education, Changchun, China
Venue:
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Year:
2004

Citing 5
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Abstract

Blending implicit algebraic surfaces has long been a hard work due to the complex calculations and the lack of effective algorithms. In this paper, we present a recursive method to derive the existence conditions and expressions of the blending surface for an arbitrary number of quadratic surfaces based on the blending surface for few quadratic surfaces. The existence conditions can be described in terms of geometric parameters of the given quadratic surfaces, which makes them easy to check. This greatly simplifies the calculations. Finally, some examples are presented.