Abstract: For solving least squares approximation problem of Bézier surface effectively and
simply on triangular domains in CAGD, we present a polynomial representation, bivariate
Chebyshev polynomials, adapted to a triangular domain, with properties similar to the univariate
Chebyshev form．We convert and compare this representation to the Bernstein-Bézier and Jacobi
representations．We also give some examples to illustrate that the deviation of the bivariate
Chebyshev polynomials compared with zero is the least than of the bivariate Bernstein
polynomials and bivariate Jacobi polynomials.

Key words: triangular domains, Bernstein basis, Chebyshev polynomial