A Non-Uniform Rational B-Spline (NURBS) is a mathematical model used in computer graphics and computer-aided design (CAD) to represent curves and surfaces. NURBS are powerful because they can accurately represent both standard shapes (like conic sections: circles, ellipses, parabolas, etc.) and freeform shapes.
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A non-uniform rational B-spline surface isHere the and are B-spline basis functions for possibly nonuniform spline knot sequences, and the are weights. Positive weights make each evaluated point a convex combination of the active control points, supplying bounding volumes for geometric searches. The denominator must remain nonzero for the parametrization to be defined.