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NURBS Curve


A nonuniform rational B-spline curve defined by

 C(t)=(sum_(i=0)^(n)N_(i,p)(t)w_iP_i)/(sum_(i=0)^(n)N_(i,p)(t)w_i),

where p is the order, N_(i,p) are the B-spline basis functions, P_i are control points, and the weight w_i of P_i is the last ordinate of the homogeneous point P_i^w. These curves are closed under perspective transformations and can represent conic sections exactly.


See also

B-Spline, Bézier Curve, NURBS Surface

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References

Piegl, L. and Tiller, W. The NURBS Book, 2nd ed. New York: Springer-Verlag, 1997.

Referenced on Wolfram|Alpha

NURBS Curve

Cite this as:

Weisstein, Eric W. "NURBS Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NURBSCurve.html

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