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Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance Control

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Abstract

Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling, numerically controlled machining, feature recognition, computer animation, etc. In practical applications, quadric surfaces, which are the most basic type of surfaces, are typically bounded surfaces trimmed by a sequence of planes. In this paper, a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics. The proposed algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance. The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique. Some examples are presented to validate the robustness and effectiveness of the proposed algorithm.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    Wenbing Shao & Falai Chen

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  1. Wenbing Shao
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  2. Falai Chen
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Correspondence to Falai Chen.

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The authors declare no conflict of interest.

Additional information

This research was supported in part by the National Natural Science Foundation of China under Grant No. 61972368.

This paper was recommended for publication by Editor LEI Na.

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Shao, W., Chen, F. Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance Control. J Syst Sci Complex 37, 2207–2239 (2024). https://doi.org/10.1007/s11424-024-2519-3

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  • DOI: https://doi.org/10.1007/s11424-024-2519-3

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