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Bernstein Polynomial and Bezier Curves

Defining and Evaluating a One-Dimensional Evaluator Bezier curves are base on Bernstein Polynomials. The Bernstein polynomial of degree n (or order n+1) is given by

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If Pi represents a set of control points (one-, two-, three-, or even four- dimensional), then the equation

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represents a Bezier curve as u varies from 0 to 1. To represent the same curve but allowing u to vary between u1 and u2 instead of 0 and 1, evaluate

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The command glMap1() defines a one-dimensional evaluator that uses these equations.