Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
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Procedural Method for Detecting Conic Sections in the Intersection of Two Tori

두 토러스의 교차곡선에서 이차곡선의 발견을 위한 절차적 방법

  • 김구진 (아주대학교 정보통신전문대학원) ;
  • 김명수 (서울대학교 컴퓨터공학부)
  • Published : 2000.12.01
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Abstract

This paper presents a geometric method that can detect and compute all conic sections in the intersection of two tori. Conic sections contained in a torus must be circles. Thus, when two tori intersect in a conic section, the intersection curve must be a circle as well. Circles in a torus are classified into profile circles, cross-sectional circlet, and Yvone-Villarceau circles. Based on a geometric classification of these circles, we present a procedural method that can detect and construct all intersection circles between two tori. All computations can be carried out using simple geometric operations only: e.g., circle-circle intersections, circle-line intersections, vector additions, and inner products. Consequently, this simple structure makes our algorithm robust and efficient, which is an important advantage of our geometric approach over other conventional methods of surface intersection.

Keywords

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