Wu Yaqiong, Li Xin
School of Mathematical Science, University of Science and Technology of China, Hefei, 200026, Anhui, China.
Vis Comput Ind Biomed Art. 2022 Jun 22;5(1):17. doi: 10.1186/s42492-022-00114-3.
This study presents a novel approach to computing all intersections between two Bézier curves using cubic hybrid clipping. Each intersection is represented by two strip intervals that contain an intersection. In each step, one curve is bounded by two fat lines, and the other is bounded by two cubic Bézier curves, clipping away the domain that does not contain the intersections. By selecting the moving control points of the cubic hybrid curves, better cubic polynomial bounds are obtained to make the proposed method more efficient. It was proved that the two strip intervals have second- and fourth-order convergence rates for transversal intersections. Experimental results show that the new algorithm is the most efficient among all existing curve/curve intersection approaches.
本研究提出了一种使用三次混合裁剪来计算两条贝塞尔曲线之间所有交点的新方法。每个交点由包含一个交点的两个条带区间表示。在每一步中，一条曲线由两条粗线界定，另一条曲线由两条三次贝塞尔曲线界定，裁剪掉不包含交点的区域。通过选择三次混合曲线的移动控制点，可以获得更好的三次多项式边界，从而使所提出的方法更高效。证明了对于横向交点，这两个条带区间具有二阶和四阶收敛速度。实验结果表明，新算法在所有现有的曲线/曲线交点计算方法中是最有效的。
