类双曲壳的概念及算法

论文提出类双曲壳的概念，类双曲壳是一类通过射影平面无穷远直线的凸壳。运用拓扑同胚来帮助提出射影凸集和类双曲壳的概念。并借助于有向射影几何的正平面上可定向的优势，分析了从经典凸壳到类双曲壳的射影变换。构造出一个在欧氏平面上的实时凸壳算法，用于两个区域中间寻找直线簇。

Notion and Algorithm of Pseudo Hyperbolic Hull

The notion of pseudo hyperbolic hull is posed which is the convex hull passing through the ideal line (infinite line). The topological homeomorphism is used to definite the notion of the projective convex hull and the pseudo hyperbolic hull. And the projective transformation from the classical convex hull to the pseudo hyperbolic hull is analyzed with the orientable advantage of the positive plane in the oriented projective geometry. A real-time algorithm of constructing the pseudo hyperbolic hull in Euclidean plane is made to find the straight-line cluster between two regions.