Peter Alfeld, --- Department of Mathematics, --- College of Science --- University of Utah

Multivariate Splines and the 4 Color Map Problem


The essential idea of reducibility is that any spline in S14 can be extended into the reducible configuration. The total dimension of S14 therefore is the dimension of S14 on the current subtriangulation minus the reducible configuration, plus the number of degrees of freedom available on the reducible configuration. That latter number must be such that the validity of the dimension formula is preserved.

As before we need to deal with subtriangulations rather than just triangulations.