Abstract
At the start of this paper, a recurrence formula for calculating the Bézier functions of any order is proved. Based on this formula, the Bézier functions are written in matrix form which enables us to develop the Bézier technique in a concise way. There are some new identities of the Bézier functions which are potentially useful in CAGD. Surprisingly a matrix involving the Bézier functions has been shown to be a doubly-stochastic matrix and the convergence behaviour of its powers is determined. Based upon these facts, the Kelisky — Rivlin theorem for the Bernstein polynomials has been extended to the Bézier curves.
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