区间Bézier曲面的降阶

Degree Reduction of Interval Bézier Surfaces

论文讨论了用低阶的区间Bzier曲面来界定高阶的区间Bzier曲面的问题 ,提出了两种不同的解决方法———线性规划及最佳一致逼近 ,最后提供的实例结果表明线性规划方法能得到一个界 。

Interval Bzier surfaces are new representation forms of parametric surfaces that can embody a complete description of coefficient errors. Using this new representation, the problem of lack of robustness in all state-of-the-art CAD systems can be largely overcome. In this paper, the problem of bounding degree interval Bzier surfaces with degree interval Bzier surfaces are discussed. Two different methods--Linear Programming and Optimal Uniform Approximation are proposed to solve this problem and provide an example to demonstrate the algorithms. The example show that while the Linear Programming method generally gives good bound, the Optimal Uniform Approximation algorithm provides better approximation.