We present some algorithms which construct a triangular graph given a set of points, where each face of the graph complies with the Delaunay criteria. Then we develop an linear time algorithm to construct the contour of such a triangular graph, where each face is coloured either black or white. Our techniques avoid expensive trigonometric computations. We intoduce our algorithms for the $2$-dimensional case and show how to extend them to the $d$-dimensional case in a straightforward manner.