Good Degree Reduction of Rational Bezie Curves in L=Norm

Based on homogeneous coordinates, an algorithm for degree reduction of rational Bézier curves with C¹-continuity constraints at the boundaries in L_∞ norm was presented by extending the degree reduction of polynomial Bézier curves. We firstly reparameterized the rational curves to make the weights more uniform. Then in the space of homogeneous coordinates, we did degree reduction for each component of the polynomial Bézier curves corresponding to rational curves by the constrained Jacobi polynomial. Finally converted the polynomial Bézier curves after degree reduction to the rational Bézier curves. The results of example show that the algorithm is effective and runs simply and rapidly.