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

Multivariate Splines and the 4 Color Map Problem


The Morgan-Scott split is a tessellation of a triangle by seven small triangles, as indicated in the figure above (which also shows the cubic domain point). It has been used as the basis for the construction of finite elements. It also serves as a well known example for a geometric degeneracy. The dimension of S12 is 6 generically, but 7 if the split is symmetric in the sense that the three green lines as indicated in the small figure to the left all intersect in one point. Note that the green lines are not part of the triangulation. The picture to the right shows a generic Morgan-Scott split.