Bézier Curves
The Renault automotive engineer Pierre Bézier publicized the Bézier curve vector functions in 1962. These are defined by vector sums with coefficients corresponding to the Binomial Theorem expansion terms for t and t - 1. For example, for vectors P1 and P2 we have tP1 + (1 - t)P2. For vectors P1, P2 and P3 we have t2P1 + 2t(1 - t)P2 + (1 - t)2P3:
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