An Improved Algorithm of the Gauss Map Computation for Free-form Surface with Nested Case

The Gauss map is a fundamental concept in surface differential geometry. Although the algorithm of the Gauss map for free-form surface is current more matures, it often can not be used when encountered with nested case. In this paper, a calculation algorithm for the Gauss map is designed in a nested case through which the global Gauss map can be drawn when mapping the Gauss map for free-form surface to the parameters domain. We discuss its decomposition, and inverse mapping back to the surface and get all of its smallest closed area boundary. Finally, we improve the algorithm and validate it with a numerical example.