采用"结式法"的圆环面和球面求交算法

提出了一种不需跟踪的求交算法.通过坐标变换使圆环中心轴与球心共处在XOZ平面内,然后讨论该平面内圆环面小圆和球面截圆的位置关系,给出了圆环面和球面不相交、交线为一个或两个圆、有孤立交点的几何条件以及交线的区间.最后,将圆环面和球面求交转化为平行于XOY面的平面内的两圆交点的问题并利用"结式法"解得交点.

Torus/Sphere Intersection Algorithm Based on Resultant Method

No tracing is required at all in this torus/sphere intersection algorithm. Let the central axis of torus and sphere center lie in XOZ coordinate plane through coordinate transformation. With the position relationship between the little circles of torus and the section circle of sphere, the geometric conditions and the scope of intersection for no intersection, one intersecting circle or two intersecting circles and acnode are figured out. At last, the tours/sphere intersection problem could be converted into the intersection of two circles on the plane parallel to XOZ and the intersection points could be obtained using resultant method.