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Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae ) and modeled shapes .
A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods. [5]
A NURBS curve represents a 1D perfectly smooth curve in 2D or 3D space. To represent a three-dimensional solid object, or a patch of one, B-Spline or NURBS curves are extended to surfaces. These surfaces consist of a rectangular grid of control points, called a control grid or control net, and two knot vectors, commonly called U and V.
The staff also developed an internal NURBS class taught to about 75 Boeing engineers. The class covered Bezier curves, Bezier to B-spline, and surfaces. The first public presentation of our NURBS work was at a Seattle CASA/SME seminar in March 1982. The staff had progressed quite far by then.
Spline/Bézier Surface Voxel, Volume Metaball Point Clouds Particles Triangles Quads N-gons Torus, Donut NURBS regular patch NURBS trimmed surface Bicubic Bézier patch Blender Yes Yes Yes Yes Yes soc-2014-nurbs branch No 2.83 and later Yes 3.1 and later Yes Maya Yes Yes Yes Yes Yes Yes No 3D Texture Yes No Yes 3ds Max Yes Yes Yes ? Yes Yes
In the mathematical subfield of numerical analysis, de Boor's algorithm [1] is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves. The algorithm was devised by German-American mathematician Carl R. de Boor. Simplified ...
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The next most simple spline has degree 1. It is also called a linear spline. A closed linear spline (i.e, the first knot and the last are the same) in the plane is just a polygon. A common spline is the natural cubic spline. A cubic spline has degree 3 with continuity C 2, i.e. the values and first and second derivatives are continuous. Natural ...