Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
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A Planar Curve Intersection Algorithm : The Mix-and-Match of Curve Characterization, Subdivision , Approximation, Implicitization, and Newton iteration

평면 곡선의 교점 계산에 있어 곡선 특성화, 분할, 근사, 음함수화 및 뉴턴 방법을 이용한 Mix-and-Mntch알고리즘

  • Published : 1998.09.01
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Abstract

There are many available algorithms based on the different approaches to solve the intersection problems between two curves. Among them, the implicitization method is frequently used since it computes precise solutions fast and is robust in lower degrees. However, once the degrees of curves to be intersected are higher than cubics, its computation time increases rapidly and the numerical stability gets worse. From this observation, it is natural to transform the original problem into a set of easier ones. Therefore, curves are subdivided appropriately depending on their geometric behavior and approximated by a set of rational quadratic Bezier cures. Then, the implicitization method is applied to compute the intersections between approximated ones. Since the solutions of the implicitization method are intersections between approximated curves, a numerical process such as Newton-Raphson iteration should be employed to find true intersection points. As the seeds of numerical process are close to a true solution through the mix-and-match process, the experimental results illustrates that the proposed algorithm is superior to other algorithms.

Keywords

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