BUILT-IN MATHEMATICA SYMBOL

# BezierFunction

BezierFunction[{pt1, pt2, ...}]
represents a Bézier function for a curve defined by the control points .

BezierFunction[array]
represents a Bézier function for a surface or high-dimensional manifold.

## Details and OptionsDetails 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 .
• 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:
•  SplineDegree Automatic degree of polynomials

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Construct a Bézier curve using a list of control points:

 Out[2]=

Apply the function to find a point on the curve:

 Out[3]=

Plot the Bézier curve with the control points:

 Out[4]=

Single cubic Bézier surface patch:

 Out[2]=
 Out[3]=

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