Function Repository Resource:

# BezierInterpolatingControlPoints

Compute the control points of a Bézier curve that interpolates a given set of points

Contributed by: Jan Mangaldan
 ResourceFunction["BezierInterpolatingControlPoints"][{x1,x2,…},{f1,f2,…}] gives the Bernstein basis coefficients of the interpolating polynomial for the function values fi corresponding to x values xi. ResourceFunction["BezierInterpolatingControlPoints"][{t1,t2,…},{{x1,y1,…},{x2,y2,…},…}] generates the control points for a full-degree interpolating Bézier curve with interpolation nodes ti and points {xi,yi,…}.

## Examples

### Basic Examples (3)

A list of points:

 In[1]:=

Get the coefficients of the Bézier interpolant:

 In[2]:=
 Out[2]=

Plot the Bézier interpolant along with the points:

 In[3]:=
 Out[3]=

### Scope (3)

A set of points to interpolate:

 In[4]:=

Generate the Bézier control points:

 In[5]:=
 Out[5]=

Show the Bézier curve along with the points:

 In[6]:=
 Out[6]=

### Applications (1)

Use BezierInterpolatingControlPoints to generate an interpolating Bézier surface patch:

 In[7]:=
 Out[7]=
 In[8]:=
 Out[8]=

### Properties and Relations (1)

With inexact inputs, the result of BezierInterpolatingControlPoints is usually more accurate than using LinearSolve with BernsteinBasis:

 In[9]:=
 Out[9]=
 In[10]:=
 Out[10]=
 In[11]:=
 Out[11]=
 In[12]:=
 Out[12]=

## Version History

• 1.0.0 – 05 April 2021