Constant-time triangulation problems on reconfigurable meshes

Triangulating a set of points in the plane is a central theme in computer-aided manufacturing, robotics, CAD, VLSI design, geographic data processing, and computer graphics. Even more challenging are constrained triangulations, where a triangulation is sought in the presence of a number of constraints such as prescribed edges and/or forbidden areas. In this paper, we show that the flexibility of the reconfigurable mesh architecture can be exploited to obtain constant-time algorithms for a number of triangulation problems. These include triangulating an arbitrary set of points in the plane, a convex planar region with a convex hole, and a convex planar region in the presence of rectangular holes. Specifically, with a collection of O(n) such constraints as input, our algorithms run in O(1) time on a reconfigurable mesh of size n×n. To the best of our knowledge, these are the first constant time solutions to constrained triangulations reported on this architecture