The Equations filter allows you to apply transform filters through mathematical expressions.

This filter allows you to apply a transform to a pixel layer using mathematical expression. You can achieve a number of distortion-type effects through the use of predetermined variables, trigonometry, exponentiation, etc. Additionally, you can use custom variables a, b and c in the equations and control their values through sliders on the filter dialog.

The following settings can be adjusted in the filter dialog:

- Coordinate System—choose from Cartesian or Polar coordinates.
- Cartesian
- x = —enter expressions for the X-axis.
- y = —enter expressions for the Y-axis.

- Polar
- r = —enter expressions for the radius.
- t = —enter expressions for the polar angle (theta).

- Parameter A (a)—controls the value of custom variable a.
- Parameter B (b)—controls the value of custom variable b.
- Parameter C (c)—controls the value of custom variable c.
- Extend Mode—chooses how to treat pixels outside of the image bounds:
- Zero—fills pixels outside the image bounds with zeros (alpha values).
- Full—fills pixels outside the image bounds with constant values (pure white).
- Repeat—fills pixels outside the image bounds with repetitions of the image's edge pixels.
- Wrap—fills pixels outside the image bounds with copies of the image; useful for positional offset filters and seamless texture authoring.
- Mirror—fills pixels outside the image bounds with mirrored (reflected) copies of the image.