We consider the spaces of bivariate C-splines of degree k deened over arbitrary triangulations of a polygonal domain. We get an explicit formula for the dimension of such spaces when k 3 + 2 and construct a local supported basis for them. The dimension formula is valid for any polygonal domain even it is complex connected , and the formula is sharp since it arrives at the lower-bound which is g...

Bivariate Gončarov polynomials are a basis of the solutions of the bivariate Gončarov Interpolation Problem in numerical analysis. A sequence of bivariate Gončarov polynomials is determined by a set of nodes Z = {(xi,j, yi,j) ∈ R2} and is an affine sequence if Z is an affine transformation of the lattice grid N2, i.e., (xi,j, yi,j) = A(i, j)T + (c1, c2) for some 2 × 2 matrix A and constants c1,...