The following surfaces are generated from a well-known polygonizer by Jules Bloomenthal which has been incorporated into our surface system. These two surfaces are triangulated into a large number of small triangles each of which is colored with a random color. However, it is not necessary to have such a large number of triangles. Singularities A general problem of these polygonizers is that most of them do not deal with singularities very well. A point on a parametric or implicit surface is singular if all partials are zero.
Singular points are part of the self-intersection of the surface or sharp edges on the surface.
The following figures show different types of singularities. This is the indicated point on the surface. While the first two cases have only isolated singular points, singular points can be on a line or even on a curve. If both x and z are zero, the first component will also be zero no matter what values y may have. Therefore, the y -axis contains all singular points.