An Algorithm for the Intersection Problem of Planar Parametric Curves.

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.