The previously defined mapping from a triangulation around a candidate vertex to a retriangulation permits us to compute errors introduced over the surface. The mutual projection segments the triangulation into pieces within which the functions and the geometry all vary linearly, as shown in figure 6. Thus, it suffices to compute errors at the intersections of the projected edges in order to compute an upper bound on the error in each triangle of the new mesh.
Figure 6: Segmentation of mutual projection