Problem statement

Suppose we wish to visualize

Recall that a function is not just a formula which yields values for given values of x,y; it is also the domain of definition, here

To represent the domain we will use an approximation, which is the union of triangles numbered over a set of integers I.

A triangulation is such a covering with the following properties (cf figure 1):

• The union of all triangles is an approximation of the domain
• Two distinct elements (triangles) can intersect only as a FULL edge or a vertex.
• Corners and other singular points of the continuous domain must be vertices of the approximate domain.
• Vertices of the approximate boundary must be on the continuous boundary.

Note that the continuous domain and the approximate domain are equal if and only if the first one is polygonal.