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q-Bézier Curves


	Visualization of Bézier curve and its generalization in -calculus. The Bézier curve, introduced by Pierre Bézier, is widely used in computer graphics for modelling smooth curves and also in the design of planes, sport cars, etc. This concept is generalized in -calculus to obtain a whole family of curves parametrized by in the unit interval. The original Bézier curve is then obtained in the limit as goes to 1.


	Contributed by: Marko Petkovic After work by: Predrag Rajkovic and Marko Petkovic
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For a given set of control points,

the Bézier curve is defined by the relation P(t)=

p_i B_i,n(t) where B_i,n(t) are Bernstein polynomials. Control points form the so-called control polygon. The

-calculus generalization of a Bézier curve, called the

-Bézier curve, is defined similarly by

, where the

are

-Bernstein polynomials. This concept was first introduced by G. M. Phillips.

Contributed by: Marko Petkovic

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