L-2 DEGREE REDUCTION OF TRIANGULAR BÉZIER SURFACES WITH COMMON TANGENT PLANES AT VERTICES

In this paper, we present a method of degree reduction for triangular Bézier surfaces. The approximate and the original triangular Bézier surfaces have common tangent planes at the vertices. We use the least squares method with the L 2 and l2 norms to get a closed form for the reduction of the degree and show that both solutions are the same. This scheme uses the matrix representations of the degree raising and the Bézier control vertices. The computational cost of the method is evaluated. The error term is derived and a numerical example is given.