Towards the multivariate simplotope spline: continuity conditions in a   class of mixed simplotopic grids
  Smooth joins of simplex Bernstein-B\'ezier polynomials have been studied extensively in the past. In this paper a new method is proposed to define continuity conditions for tensor-product Bernstein polynomials on a class of mixed grids that meets certain out-of-facet parallelism criteria. The conditions are derived by first defining a simplex around the simplotopic bases of the tensor-product polynomials. Then the continuity conditions in the multivariate simplex spline defined on the resulting simplices, are adapted to hold for the tensor-product polynomials. The two- and three-dimensional results agree with the results found in the literature. It is expected that the method can be employed in more general grids. 
Tim Visser, Cornelis C. de Visser and Erik-Jan van Kampen
math.NA