The MinMax-angle triangulation is the triangulation for the sites which minmizes (lexicographically) the sorted vector of all the angles of triangles in the triangulation. The MaxMin-height and MinMax-slope triangulations are similar. The algorithms used for the computations are not heuristics, they actually achieve the optimum.
The regular triangulation is the weighted version of the delaunay triangulation (weights are assigned to the sites, the delaunay triangulation corresponds to the regular triangulation where all the sites have identical weights).
The output is saved in vector file format.
The computation times for the various operations depends strongly on the algorithm used.
The plansweep triangulation and convex hull computation require O(n log n) operations in the worst case [Ed]. The Delaunay heuristic needs O(n^2) time in the worst case, however it performs much faster in practice. The MinMax-angle and MaxMin-height triangulations need O(n^2 log n) operations [BeEd, EdTa], and the MinMax-slope triangulation needs O(n^3) operations [BeEd].
Internally, the coordinates of the sites are stored in fix-point format. Therefore, the number of decimal digits cannot exceed 64 bit (or apprx. 16 decimal digits).
[Ed] H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Heidelberg, Germany, 1987.
[EdSh] H. Edelsbrunner, N. R. Shah. Incremental Flipping Works for Regular Triangulations. In Proc. 8th Ann. Sympos. Comput. Geom. 1992, 43-52.
[EdTa] H. Edelsbrunner, T.S. Tan and R. Waupotitsch. An O(n^2 log n) Time Algorithm for the MinMax Angle Triangulation. SIAM J. Sci. Statist. Comput. 13 1992, 994-1008.