BezierCurves - B ezier Curves James Keesling 1 Definition...

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Unformatted text preview: B ezier Curves James Keesling 1 Definition of a B ezier Curve A B ezier curve is a parametric curve that is used widely in computer graphics. They were originally used as an aid in design in the automobile industry. The B ezier curves are based on the Bernstein polynomials. The Bernstein polynomial of degree n is given by the following formula. B n ( t ) = n X i =0 n i t i (1- t ) n- i In themselves the Bernstein polynomials are not very interesting. They are just the binomial expansion of ( t + (1- t )) n 1. However, for B ezier curves we will restrict t to the interval [0 , 1]. Then the individual terms in the expansion will be non-negative and will sum to one. We will use them to produce a convex combination of points in R k . Let { P ,P 1 ,...,P n } be a set of n + 1 points in R k . The B ezier curve with control points { P ,P 1 ,...,P n } is given by the following formula. B ( t ) = n X i =0 n i t i (1- t ) n- i P i The curve begins at the point P and ends at point P n , but will not generally go through the other control points. The curve will lie in the convex hull of determined by the setthe other control points....
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This note was uploaded on 11/12/2011 for the course STA 3032 taught by Professor Kyung during the Summer '08 term at University of Florida.

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BezierCurves - B ezier Curves James Keesling 1 Definition...

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