L2 degree reduction of interval Bézier curves using Chebyshev-Bernstein basis transformations [articol]

Abstract

This paper presents an algorithmic approach to degree reduction of interval Bézier curves. The four fixed Kharitonov’s polynomials (four fixed Bézier curves) associated with the original interval Bézier curve are obtained. The four fixed Kharitonov’s polynomials (four fixed Bézier curves) associated with the approximate interval Bézier curve are also found. The algorithm is based on the matrix representations of the degree elevation and degree reduction processes. The computations are carried out by minimizing the L₂ distance between the four fixed Bézier curves Pi n of degree n and the four fixed approximate Bézier curves Qi m degree m.