An algorithm to improve parameterizations of rational Bézier surfaces using rational bilinear reparameterization

The parameterization of rational Bezier surfaces greatly affects rendering and tessellation results. The uniformity and orthogonality of iso-parametric curves are two key properties of the optimal parameterization. The only rational Bezier surfaces with uniform iso-parametric curves are bilinear surfaces, and the only rational Bezier surfaces with uniform and orthogonal iso-parametric curves are rectangles. To improve the uniformity and orthogonality of iso-parametric curves for general rational Bezier surfaces, an optimization algorithm using the rational bilinear reparameterizations is presented, which can produce a better parameterization with the cost of degree elevation. Examples are given to show the performance of our algorithm for rendering and tessellation applications.