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BezierFunction[{pt1,pt2,…}]

represents a Bézier function for a curve defined by the control points pti.

BezierFunction[array]

represents a Bézier function for a surface or high-dimensional manifold.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
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BezierFunction

BezierFunction[{pt1,pt2,…}]

represents a Bézier function for a curve defined by the control points pti.

BezierFunction[array]

represents a Bézier function for a surface or high-dimensional manifold.

Details and Options

  • BezierFunction[…][u] gives the point on a Bézier curve corresponding to parameter u.
  • BezierFunction[…][u,v,…] gives the point on a general Bézier manifold corresponding to the parameters u, v, ….
  • The embedding dimension for the curve represented by BezierFunction[{pt1,pt2,…}] is given by the length of the lists pti.
  • BezierFunction[array] can handle arrays of any depth, representing manifolds of any dimension.
  • The dimension of the manifold represented by BezierFunction[array] is given by ArrayDepth[array]-1. The lengths of the lists that occur at the lowest level in array define the embedding dimension.
  • The parameters u, v, … by default run from 0 to 1 over the domain of the curve or other manifold.
  • The following options can be given:
  • Method{}details of methods to use
    WorkingPrecisionMachinePrecisionprecision to use in internal computations

Examples

Basic Examples  (2)

Construct a Bézier curve using a list of control points:

Wolfram Language code: pts = {{0, 0}, {1, 1}, {2, 0}, {3, 2}};
Wolfram Language code: f = BezierFunction[pts]

Apply the function to find a point on the curve:

Wolfram Language code: f[.5]

Plot the Bézier curve with the control points:

Wolfram Language code: Show[Graphics[{Red, Point[pts], Green, Line[pts]}, Axes -> True], ParametricPlot[f[t], {t, 0, 1}]]

Single cubic Bézier surface patch:

Wolfram Language code: pts = {{{0, 0, 0}, {0, 1, 0}, {0, 2, 0}, {0, 3, 0}}, {{1, 0, 0}, {1, 1, 1}, {1, 2, 1}, {1, 3, 0}}, {{2, 0, 0}, {2, 1, 1}, {2, 2, 1}, {2, 3, 0}}, {{3, 0, 0}, {3, 1, 0}, {3, 2, 0}, {3, 3, 0}}};
Wolfram Language code: f = BezierFunction[pts]
Wolfram Language code: Show[Graphics3D[{PointSize[Medium], Red, Map[Point, pts]}], Graphics3D[{Gray, Line[pts], Line[Transpose[pts]]}], ParametricPlot3D[f[u, v], {u, 0, 1}, {v, 0, 1}, Mesh -> None]]
Wolfram Research (2008), BezierFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/BezierFunction.html.

Text

Wolfram Research (2008), BezierFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/BezierFunction.html.

CMS

Wolfram Language. 2008. "BezierFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BezierFunction.html.

APA

Wolfram Language. (2008). BezierFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BezierFunction.html

BibTeX

@misc{reference.wolfram_2026_bezierfunction, author="Wolfram Research", title="{BezierFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/BezierFunction.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_bezierfunction, organization={Wolfram Research}, title={BezierFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/BezierFunction.html}, note=[Accessed: 13-June-2026]}