单叶双曲面、二次锥面/球面统一求交算法

Uniparted Hyperboloid and Quadric Cone/Sphere Intersection Algorithm

为讨论方便,我们将单叶双曲面、二次锥面统称为∑*.首先考虑曲面∑*的两种特殊情况,给出了其与球面的交线为圆的条件,还直接给出了圆心、半径和法向量等重要几何参数,确保了交线的准确性.其次,通过求出球心P到曲面∑*的最短距离DMIN,直接判断是否无交,相切.在交线为非平面闭合曲线的情况下,通过巧妙的坐标变换,得到了关键方程,求出关键点,并根据关键点的个数确定交线的拓扑结构并求出交曲线的参数方程,确保了交线拓扑结构的稳定.

In this paper, two special cases are considered first. We gain the condition that the intersection line is a circle and gives out its geometric parameters. Then, in all other cases, by calculating the minimum distance DMIN, nointersection and contact can be judged. If the intersection line is a nonplane closed curve, the key equation is gained by coordinate transformation. We can confirm the topological structure of intersection line with the amount of the key points and establish its parametric equation.