Non-Uniform Rational B Spline - definition. What is Non-Uniform Rational B Spline
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%ما هو (من)٪ 1 - تعريف

A SPLINE FUNCTION
Basis B-spline; B-Spline; B spline; B splines; B-spline surface; B-splines; P-spline; Bspline
  •  Spline curve drawn as a weighted sum of B-splines with control points/control polygon, and marked component curves
  • Cardinal cubic B-spline with knot vector (−2, −2, −2, −2, −1, 0, 1, 2, 2, 2, 2) and control points (0, 0, 0, 6, 0, 0, 0), and its first derivative
  • Cardinal quadratic B-spline with knot vector (0, 0, 0, 1, 2, 3, 3, 3) and control points (0, 0, 1, 0, 0), and its first derivative
  • Cardinal quartic B-spline with knot vector (0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5) and control points (0, 0, 0, 0, 1, 0, 0, 0, 0), and its first and second derivatives
  • NURBS curve – polynomial curve defined in homogeneous coordinates (blue) and its projection on plane – rational curve (red)

Non-uniform rational B-spline         
  • NURBS have the ability to exactly describe circles. Here, the black triangle is the control polygon of a NURBS curve (shown at w=1). The Blue dotted line shows the corresponding control polygon of a B-spline curve in 3D [[homogeneous coordinates]], formed by multiplying the NURBS by the control points by the corresponding weights. The blue parabolas are the corresponding B-spline curve in 3D, consisting of three parabolas. By choosing the NURBS control points and weights, the parabolas are parallel to the opposite face of the gray cone (with its tip at the 3D origin), so dividing by ''w'' to project the parabolas onto the ''w''=1 plane results in circular arcs (red circle; see [[conic section]]).
  • Three-dimensional NURBS surfaces can have complex, organic shapes. Control points influence the directions the surface takes. A separate square below the control cage delineates the X and Y extents of the surface.
  • animated creation of a NURBS spline]].)
  • spline as a mathematical concept]]
  • right
MATHEMATICAL MODEL
Nurbs; NURBS; NURBS curve; NURBS patch; NURB; NURBS Curve; Nurbs curve; NURBS Surface; Nurbs surface; NURBS surface; Nonuniform rational B-spline
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.
Non-Uniform Rational B Spline      
<graphics, mathematics> (nurbs) A common term in Mechanical CAD. The NURBS has excellent continuity characteristics which make it useful for creating accurate models in 3D geometry generation and computer modelling. [What is a nurbs? an rbs? a bs? a s?] (1996-08-27)
NURB         
  • NURBS have the ability to exactly describe circles. Here, the black triangle is the control polygon of a NURBS curve (shown at w=1). The Blue dotted line shows the corresponding control polygon of a B-spline curve in 3D [[homogeneous coordinates]], formed by multiplying the NURBS by the control points by the corresponding weights. The blue parabolas are the corresponding B-spline curve in 3D, consisting of three parabolas. By choosing the NURBS control points and weights, the parabolas are parallel to the opposite face of the gray cone (with its tip at the 3D origin), so dividing by ''w'' to project the parabolas onto the ''w''=1 plane results in circular arcs (red circle; see [[conic section]]).
  • Three-dimensional NURBS surfaces can have complex, organic shapes. Control points influence the directions the surface takes. A separate square below the control cage delineates the X and Y extents of the surface.
  • animated creation of a NURBS spline]].)
  • spline as a mathematical concept]]
  • right
MATHEMATICAL MODEL
Nurbs; NURBS; NURBS curve; NURBS patch; NURB; NURBS Curve; Nurbs curve; NURBS Surface; Nurbs surface; NURBS surface; Nonuniform rational B-spline
Non Uniform Rational B-spline

ويكيبيديا

B-spline

In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are equidistant from each other. B-splines can be used for curve-fitting and numerical differentiation of experimental data.

In computer-aided design and computer graphics, spline functions are constructed as linear combinations of B-splines with a set of control points.