Some smoothness conditions and conformality conditions for bivariate quartic and quintic splines (Q1294072)

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of \(B\)-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar simplex is introduced, new formulations of smoothness conditions of bivariate quartic \(C^1\) splines and quintic \(C^2\) splines are given, and the conformality conditions of bivariate quartic \(C^1\) splines are simplified.