Abstract: 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.

Key words: computer application, pseudo hyperbolic hull, convex hull, oriented projective geometry