Improve Derivative Bounds of Rational Parametric Curves and Surfaces Using Reparameterization

In this paper,to improve derivative bounds of rational parametric curves and surfaces,a linear fractional transformation is used to reparameterize the curves and surfaces.Due to the fact that derivative bounds are determined by the ratio of weights,two weight optimization methods are presented.One is to minimize the maximal ratio of weights in the reparameterized representation,which is solved by a linear programming method.The other is to minimize the variance of the log weights,which is solved explicitly.Numerical experiments show that these two methods can obtain tighter derivative bounds than the other methods,which significantly improve the efficiency of rendering and intersection detection for curves and surfaces.