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A NURBS curve, which is an acronym for Non-Uniform Rational B-Spline curve, is a generalization of both Bézier and BSpline curves. NURBS are commonly used in computer graphics, computer-aided design (CAD), engineering (CAE), and manufacturing (CAM).
A NURBS curve is a parametric curve defined by its degree, a set of weighted control points, and a knot vector. It is defined as
$$ c(u) = \frac { \sum_{i=0}^{n} N_{i,p}(u) w_i P_i} {\sum_{i=0}^{n} N_{i,p}(u) w_i} \quad\quad 0 \leq u \leq 1 $$
where $u$ is the parameter, $p$ is the degree, $N_{i,p}$ are the B-spline basis functions, $P_i$ are the control points and $w_i$ are the weights.
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Cross-references: weights, B-spline basis functions, parameter, knot vector, control points, design, computer, curves, B-spline curve, rational
This is version 9 of NURBS curve, born on 2007-06-01, modified 2007-07-13.
Object id is 9499, canonical name is NURBS.
Accessed 1868 times total.
Classification:
| AMS MSC: | 51N05 (Geometry :: Analytic and descriptive geometry :: Descriptive geometry) |
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Pending Errata and Addenda
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