Non regular Grids / Parametric Surfaces

Until now, we only provided Z coordinates as grid position data. However, surfaces allow the definition of X and Y coordinates for the grid points as well. That way, arbitrary shaped objects and parametric surfaces can be constructed. One rather famous example is a torus:

The Cartesian coordinates of the torus are provided by the SpecialData class. We only have to add it to the surface plot and choose a colormap. In order to visualize some data values as 4th data dimension over the hull of the torus, we choose individual colors for every grid point. Here, we simply fetch the automatically computed data values (which were derived from the Z coordinate of the grid points at construction time) and modify them by some sinc function. A real application would choose its own data values here.