Bezier curve
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Bézier curves are one type of parametric curves. Each point on a Bézier curve is given by a linear combination of the Bernstein basis polynomials, restricted to the interval [0, 1].
Bernstein Basis Polynomials
The Bernstein basis polynomials are given as :
, where 
is a [binomial coefficient (http://en.wikipedia.org/wiki/Binomial_coefficients)]. The value of a binomial coefficient is given by : 
.
Points on the Bézier Curve
Given n+1 points in an euclidean space, a Bézier curve given as :
is said to have degree n.
See also
TODO : this is just the basic layout... things to do include de Casteljau's algorithm to evaluate a curve, the basis polynomials for cubic curves as well as a few nice graphics showing them and some general explanations about interpolation.
part-II of; BÉZIER CURVES
Overview:
The curve representation that is most frequently used in computer graphics, was independently discovered by Pierre Bézier (pronounced Bez-ye), who was an engineer for Renault and Paul de Casteljau, who was an engineer for Citroën, both working for automobile companies in France. These engineers developed a scheme that has both analytical and geometrical roots:the parameter values are points in three-dimensional space, which are blended together by polynomial functions. Being competitors, both companies were very secretive about their work and although De Casteljau's work was slightly earlier than Bézier's, it was never published; so the field retains Bézier's name. However, the fundamental algorithm which forms the basis for the constructions and calculation for Bézier curves is now credited to de Casteljau.
The design and analysis of curves and surfaces belongs to a field of study called geometric modeling, or computer-aided geometric design. Students of this field use mathematical techniques to design curve and surface representations that can be easily implemented on computer systems. The Bézier curve is the cornerstone of this field. The curve has a simple formulation - either through geometrical or analytical means - and is very useful in modeling and design. In these notes we examine the Bézier curve and the many ways that it can be described.
If you are a novice to this subject, it is suggested that you begin with the section that describes a divide-and-conquer strategy for generating a curve, which gives a simple introduction to the ideas behind this curve. You should then proceed via the discussions of the quadratic Bézier curve and the cubic Bézier curve which introduce the most commonly used Bézier curves and their properties.
[1] (http://graphics.idav.ucdavis.edu/education/CAGDNotes/Bezier-Curves/Bezier-Curves.html) reference has been linked; [ On-Line Geometric Modeling Notes : THE BÉZIER CURVES ]
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