Abstract:

Determining the lowest degree, dimensions and basis functions of btp (bivariate truncated power(s)) spaces with given smoothness requirements and establishing the calculation formulae of btp on a three-and four-direction mesh, we give the necessary and sufficient condition for the existence of the bivariate BM-spline in S₄²,△₂ and the bivariate BM-spline in S₂¹, △₂, in terms of linear combinations of btp. The so-called "revolving around" technique is mentioned.