Estimating tessellation parameter intervals for rational curves and surfaces

This paper presents a method for determining a priori a constant parameter interval for tessellating a rational curve or surface such that the deviati on of the curve or surface from its piecewise linear approximation is withi n a specified tolerance. The parameter interval is estimated based on infor mation about second-order derivatives in the homogeneous coordinates, inste ad of using affine coordinates directly. This new step size can be found wi th roughly the same amount of computation as the step size in Cheng [1992], though it can be proven to always be larger than Cheng's step size. In fac t, numerical experiments show the new step is typically orders of magnitude larger than the step size in Cheng [1992]. Furthermore, for rational cubic and quartie curves, the new step size is generally twice as large as the s tep size found by computing bounds on the Bernstein polynomial coefficients of the second derivatives function.