Degree reduction of interval Bézier curves

Interval Bézier curves are new representation forms of parametric curves 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, we discuss the problem of bounding interval Bézier curves with lower degree interval Bézier curves. We propose two different methods— Linear Programming and Optimal Approximation to solve this problem and provide several examples to demonstrate the algorithms. The examples show that while the Linear Programming method generally gives quite good bound, the Optimal Approximation algorithm provides much tighter approximation interval curves than the previous methods. q 2000 Published by Elsevier Science Ltd. All rights reserved.