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NURBS Surface


A nonuniform rational B-spline surface of degree (p,q) is defined by

 S(u,v)=(sum_(i=0)^(m)sum_(j=0)^(n)N_(i,p)(u)N_(j,q)(v)w_(i,j)P_(i,j))/(sum_(i=0)^(m)sum_(j=0)^(n)N_(i,p)(u)N_(j,q)(v)w_(i,j)),

where N_(i,p) and N_(j,q) are the B-spline basis functions, P_(i,j) are control points, and the weight w_(i,j) of P_(i,j) is the last ordinate of the homogeneous point P_(i,j)^w.

NURBS surfaces are implemented in the Wolfram Language as BSplineSurface[array].


See also

B-Spline, Bézier Curve, NURBS Curve

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Cite this as:

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

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