Transformation between Bivariate Jacobi and Bernstein Basis on Triangular Domain and its Application

For solving least squares approximation problem simply and effectively on triangular domains in CAGD,this paper derives the matrices of transformation of the bivariate Bernstein basis form into the Jacobi basis of the same degree and vice versa.A method for constructing bivariate Jacobi-weighted orthogonal polynomials in the Bernstein form on triangular domains is formulated firstly.And then,by using connection coefficients between the univariate Bernstein and Jacobi basis,the transformation matrices between bivariate Jacobi and Bernstein basis are presented.Finally,by using the matrices,an explicit form of the multi-degree reduction matrix for Bézier surface on triangular domains with respect to Jacobi weighted L₂ norm is proposed,and the error of the degree reduction is given.