Distance for degree raising and reduction of triangular Bézier surfaces (Q1410863)

Given a triangular Bézier surface of degree \(n\) with specific Bézier points, two other sets of Bézier points are determined: the first set defines the same surface using a basis of degree \(n+1\) (degree raising), while the second set defines the approximative surface of degree \(n-1\) which minimizes the least-squares distances between the old and the new set of points (degree reduction). The formulas for these sets are obtained using the least-squares method, generalized Bernstein polynomials, \(L_2\) and \(l_2\) measures of distance.