What is NURBS?

I had read this term many of times but don't know what it stands for and what is the purpose of it.

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Non-uniform rational basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces which offers great flexibility and precision for handling both analytic (shapes defined by common mathematical formulas) and freeform shapes.

 
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Non Uniform Rational B-Spline curve is a mapping of one variable say "t" from the parametric domain into 3D soace X(t)/W(t),Y(t)/W(t),Z(t)/W(t) where each component is a rational B-Spline.The intervals of parametric domain may be unequal lenth.B-Spline curves are represented by coefficients called control points and rational blending functions.

A rational B-Spline curve is generally defined by order of the curve and number of segments.

This is the technical info I could share with you.

 
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NURB is the way curves are generated by comptuers Non Uniform rational B spline curves. Basically mathematical method of producing a curve with SV points. It goes back to the principles of lofting boats before computer age.

http://web.cs.wpi.edu/~matt/courses/cs563/talks/nurbs.html

http://www.rhino3d.com/nurbs/

 
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NURBS is mathematical model to create free from curves and surfaces in computer graphics. Here is short summary of each letter in NURBS -
NU - non uniform - the knot vector can be non-uniform.
R -Rational - the control points of curve/surface may have weights other than 1.
BS - B-Spline - Defines the mathematical formula for the curve/surface.

I've found a very nice webGL based NURBS evaluator - http://nurbscalculator.in/. It is very helpful in understanding how the curve changes with various parameters

 
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