Computing the Union of 3-Colored Triangles

Jean-Daniel Boissonnat (1) , Olivier Devillers (1) , Franco P. Preparata (2)

1 PRISME - Geometry, Algorithms and Robotics
2 Brown University - Department of Computer Science

Given is a set \s\ of $n$ points, each colored with one of $k \geq 3$ colours. We say that a triangle defined by three points of \s\ is 3-colored if its vertices have distinct colours. We prove in this paper that the problem of constructing the boundary of the union \ts\ of all such 3-colored triangles can be done in optimal $O(n \log n)$ time.

Domaines: Géométrie algorithmique [cs.CG]

Jean-Daniel Boissonnat, Olivier Devillers, Franco P. Preparata. Computing the Union of 3-Colored Triangles. International Journal of Computational Geometry and Applications, 1991, 1 (2), pp.187-196. ⟨10.1142/S021819599100013X⟩. ⟨inria-00167176⟩