A Method to Triangulate a Set of Points in the Plane (original) (raw)

Given a set of points S in the plane, we propose a triangulation process to construct a triangulation for the set S. Triangulating scattered point-sets is a a very important problem in computational geometry; hence the importance to develop new efficient algorithms and models to triangulate point-sets. This process presents two well distinguished phases; Phase 1 begins with the construction of an auxiliar triangular grid containing all the points. This auxiliar mesh will help us in the triangulation process, since we take this mesh as a reference to determine the points that may be joined by edges to construct triangles that will constitute the triangulation. Phase 2 takes as a starting point the auxiliar triangular mesh obtained in Phase 1. The objective now is to determine which of the vertices of the initial set S must be joined to form the triangles that will constitute the triangulation of the points. Some examples are shown in detail to understand the behaviour of the triangulation process.