An Algorithm for the Intersection Problem of Planar Parametric Curves.
CASC(2023)
摘要
This study presents a novel approach for handling the intersection of planar parametric curves. By leveraging the inherent properties of parametric curves, our technique simplifies the process by reducing and comparing the ranges of x and y coordinates. The essential advantage of this technique lies in its simplicity, achieved through the reduction and comparison of the x and y coordinates ranges of the two curves. The monotonicity of curves is used during the reduction strategy. We utilize the opposite monotone system within a box to determine the uniqueness and existence of a simple intersection point. Moreover, we comprehensively analyzed singular cases like cusps, self-intersections, and tangents. Examples and comparisons with other methods showcase the algorithm’s robustness and efficiency, particularly for high-degree systems.
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关键词
planar parametric curves,intersection problem,algorithm
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