Page 156 - Geometric Modeling and Algebraic Geometry

8 Ridges and Umbilics of Polynomial Parametric Surfaces 157
Figure 8.6 displays the topology of the ridges. In addition to study points, the
regular points of all fibers are displayed as small black dots.

Fig. 8.6. Bi-quadratic B` ezier example : isotopic approximation of the ridge curve with study
points.

8.5 Conclusion

For parametric algebraic surfaces, we developed an algorithm to report a topolog-
ically certified approximation of the ridges. This algorithm is computationally de-
manding in terms of algebra. It is in a sense complementary to the heuristic one
developed in a companion paper [4], which is working directly on a triangulation of
the surface, and provide a fast way to report non certified results.