Physical Sciences and Mathematics Commons^™

Estimating Tessellation Parameter Intervals For Rational Curves And Surfaces, Thomas W. Sederberg, Jianmin Zheng

Faculty Publications

This paper presents a method for determining a priori a constant parameter interval with which a rational curve or surface can be tessellated such that the deviation of the curve or surface from its piecewise linear approximation is within a specified tolerance. The parameter interval is estimated based on information about the second order derivatives in the homogeneous coordinates, instead of using affine coordinates directly. This new step size can be found with roughly the same amount of computation as the step size presented in [Cheng 1992], though it can be proven to always be larger than Cheng's step size. …