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.

Examples

Basic Examples  (2)

Construct a Bézier curve using a list of control points:

Apply the function to find a point on the curve:

Plot the Bézier curve with the control points:

Single cubic Bézier surface patch:

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_2025_bezierfunction, author="Wolfram Research", title="{BezierFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/BezierFunction.html}", note=[Accessed: 29-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_bezierfunction, organization={Wolfram Research}, title={BezierFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/BezierFunction.html}, note=[Accessed: 29-January-2025 ]}