Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
440784 | Computer-Aided Design | 2013 | 11 Pages |
The parameterization of rational Bézier 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 Bézier surfaces with uniform iso-parametric curves are bilinear surfaces, and the only rational Bézier surfaces with uniform and orthogonal iso-parametric curves are rectangles. To improve the uniformity and orthogonality of iso-parametric curves for general rational Bézier 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.
► Only bilinear surfaces have uniform iso-parametric curves. ► Only rectangles have both uniform and orthogonal iso-parametric curves. ► We give the bilinear reparameterizations of rational Bezier surfaces. ► We present an optimization algorithm to improve surface parameterizations. ► Our optimization algorithm is based on the bilinear reparameterization.