Function Repository Resource:

# AberrancyCurve

Compute the curve of aberrancy of a plane curve

Contributed by: Jan Mangaldan
 ResourceFunction["AberrancyCurve"][c,t] computes the curve of aberrancy of the plane curve c parametrized by variable t.

## Details

The curve of aberrancy is also known as the affine evolute.
The curve of aberrancy is the envelope of the lines that are parallel to the axes of a plane curve's osculating parabolas and pass through their point of contact with the plane curve.
The curve of aberrancy is the locus of the centers of aberrancy of a plane curve.

## Examples

### Basic Examples (2)

Define the parametric equations for an astroid:

 In[1]:=

Compute its curve of aberrancy:

 In[2]:=
 Out[2]=

Plot the astroid and its curve of aberrancy:

 In[3]:=
 Out[3]=

Compute the implicit equation for the curve of aberrancy of a quartic:

 In[4]:=
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### Properties and Relations (1)

The curve of aberrancy of a plane curve involves third and fourth derivatives:

 In[5]:=
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## Version History

• 1.0.0 – 04 March 2021