椭圆-椭圆不适合边界的解析方程及其干涉判断

No Fit Boundary Analytic Equation and Interference Detection for Ellipse-ellipse

在医疗内外科手术,虚拟装配等计算机可视化领域中,经常需检测椭圆-椭圆的干涉性。为了更好地进行干涉判断,根据椭圆-椭圆外切的代数条件——广义特征多项式具有正的重根,以及进一步证明出的该正重根的唯一性结论,利用仿射变换和逆变换方法,推导出了椭圆-椭圆的不适合边界(NFB)解析方程。根据该解析方程不仅可以直接对任意两个椭圆之间的干涉性做出精确判断,并且可由此绘出NFB的轨迹图,同时使用可视化方法给出了快速粗略的判断。在医学影像诊断上这两种方法可结合应用。

In many computer visualized fields such as medical and surgical operations and virtual assembly, it is of ten neecessary to detect the interference between ellipses. The No Fit Boundary（NFB） of ellipse-ellipse is obtained according to the algebraic condition of exterior contact of ellipse-ellipse. To be specific, its generalized characteristic polynomial has positive double roots, which we proved further has only a double, root by using the affine transformation and inverse affine transformation, his easy to detect interference accurately between two ellipses using NFB analytic equation. The trajectory mapped by NFB can also detect the interfer ence quickly and visually. The above two methods can be used together in medicine.