Creating Initial Triangulations

 

The Dual project defines methods for class Geom2d (for single geometries) and Surface (for parameter-dependent sequences of geometries) therefore it adds the Surface project. Initial surfaces for the Dual minimization methods can for example be created with project Explicit (see 8.2.5) or Build (see 8.2.4 and the example in section 8.2.9).

The Build project allows to create topological surfaces of arbitrary type and genus, it especially allows to control the boundary restrictions. To simplify the creation of surfaces with boundary restrictions the minimization algorithms try to detect the boundary types automatically: if a boundary line is straight or planar it is assumed to be restricted to the straight line or plane, if some other restriction is needed it has to be specified explicitly.

The Dual project provides an interface (see figure 8.20) to some methods for modifying triangulations, together with the methods from the Refine project described in the next section they allow to create very good initial triangulations for the minimization methods (please read section 8.2.9 before you use these methods):

This method implements a Delaunay swap algorithm for triangulations in three-space (compare 6.3.4.5), together with

which smoothes the triangulation by averaging the points it allows to make triangulations more uniform and regular. By using as a display method (i.e. press , to switch back press twice) you can configure how often "mollify-send" should be applied and whether boundary points should be mollified, too.

There is also a method which removes degenerated triangles, this might be necessary if for example an edge of a surface patch created with the surface builder is degenerated or if triangles degenerate during the minimization process. But be careful, the resulting triangulation may be singular and you might not be able to continue working with it, saving the Surface with before applying might be a good idea.