Every smooth surface you have ever seen in CAD is a lie told with astonishing precision. NURBS stands for Non-Uniform Rational B-Splines. It is the mathematical backbone of nearly every serious CAD system on Earth. Aircraft fuselages, turbine blades, car bonnets, hull forms. None of them are stored as triangles or pixels. They are stored as a handful of control points and a set of weighting functions. Break the name apart and the whole thing falls open: - Spline: a smooth curve built from piecewise polynomials, named after the flexible wooden battens draughtsmen once bent through fixed pins in shipyards - B-spline: basis spline, where each control point influences only a local region of the curve rather than the entire shape - Rational: every control point carries a weight, allowing exact representation of conics such as circles, ellipses and parabolas - Non-uniform: the knot vector spacing can vary, letting the designer cluster resolution where curvature demands it That third term...