# 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_2024_bezierfunction, author="Wolfram Research", title="{BezierFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/BezierFunction.html}", note=[Accessed: 18-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_bezierfunction, organization={Wolfram Research}, title={BezierFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/BezierFunction.html}, note=[Accessed: 18-June-2024 ]}