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Built-in Mathematica Symbol

BezierFunction

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

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

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 pt_i.

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 TensorRank[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.

degree of polynomials

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:

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: