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


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.


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:

Introduced in 2008