Computing Delaunay Triangulation with Imprecise Input Data

The key step in the construction of the Delaunay triangulation of a finite set of planar points is to establish correctly whether a given point of this set is inside or outside the circle determined by any other three points. We address the problem of formulating the in-circle test when the coordinates of the planar points are given only up to a given precision, which is usually the case in practice. By modelling imprecise points as rectangles, and using the idea of partial disc, we construct a reliable in-circle test that provides the best possible Delaunay triangulation with the imprecise input data given by rectangles.