Function Repository Resource:

# InversionCurve

Compute the inversion of a curve

Contributed by: Wolfram Staff (original content by Alfred Gray)
 ResourceFunction["InversionCurve"][k,curve,t] computes the inversion of curve with respect to a circle with radius k and parameter t. ResourceFunction["InversionCurve"][o,k,curve,t] computes the inversion of a curve with respect to a circle centered at o.

## Details and Options

For a circle C with center O and radius k, if there is a point P in the curve and a point Q in the inverse, then OP·OQ=k2.

## Examples

### Basic Examples (3)

Inversion curve of a tractrix (orange):

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Inversion curve of an ellipse (follows the point and the circle):

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A clothoid:

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Inversion of a clothoid:

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A helicoid:

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Inversion of a helix:

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### Possible Issues (1)

Avoid division by zero:

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Enrique Zeleny

## Version History

• 2.0.0 – 31 August 2020
• 1.0.0 – 24 February 2020