Enumerating trichromatic triangles containing the origin in linear time

Consider a set P of n points in the plane, where each point is associated with one of three colours. We give an output-sensitive algorithm that enumerates a set of triangles T, where each triangle in T contains the origin and its three vertices are points in P   with distinct colours. Our algorithm requires O(n+|T|)O(n+|T|) time, and hence it is asymptotically optimal in terms of n   and |T||T|.