A geometric characterization of Powell-Sabin triangulations allowing the construction of C2 quartic splines

The paper deals with the characterization of Powell-Sabin triangulations allowing the construction of bivariate quartic splines of class C-2. The result is established by relating the triangle and edge split points provided by the refinement of each triangle. For a triangulation fulfilling the characterization obtained, a normalized representation of the splines in the C-2 space is given.

Automated summary

This paper investigates the characterization of Powell-Sabin triangulations for constructing bivariate quartic splines of class C-2. The relationship between the triangle and edge split points obtained through refinement of each triangle is used to establish the result. A normalized representation of the splines in the C-2 space is provided for triangulations that meet the established characterization.