采用“结式法”的圆环面和球面求交算法  

Torus/Sphere Intersection Algorithm Based on Resultant Method

作　　者：谌炎辉[1] 徐武彬[1] 

机构地区：[1]广西工学院机械系,广西柳州545006

出　　处：《工程图学学报》2007年第3期61-66,共6页Journal of Engineering Graphics

基　　金：广西自然科学基金资助项目(0481015);广西工学院科研基金资助项目(061626)

摘　　要：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。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.

关 键 词：工程图学 求交算法 结式法 坐标变换 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]