Rotating a Document using Equations in Photo

[John Rostron]

Many options for rotation in Affinity Photo are constrained to simple fractions of a circle, with 15 degrees being the smallest. It is possible to rotate by an arbitrary angle using the Crop tool. You place the cursor just outside a corner, and rotate by dragging the two-arrowed cursor that appears.

This tutorial explains how you can rotate an image using Filter > Distort > Equations. Before rotation you would normally want to expand the canvas so that you can give the document enough room to rotate. The new canvas width should be at least 150% of the existing diagonal and the Anchor should be in the centre of the array of nine positions. See this image:

q

Now select Filter > Distort > Equations. The top pair of buttons allow you to choose the co-ordinate system. The default is Cartesian (the usual x and y axes). You  need to choose the Polar option. You now have two lines:

r=r
t=t

The r represents the radius (the distance of a point from the centre of the image), and the t (or Theta) is the angle of rotation in radians.Radians are a measure based on pi, You can easily express an angle in radians as a multiple of pi, so 2*pi represents the entire 360 degree rotation, pi represents a half-circle rotation (180 degrees) and pi/4 represents a quarter of a half circle, or  45 degrees. So, writing t=t+pi/2  rotates the image  by a quarter of a circle counter-clockwise. Entering t=t-pi*0.333 rotates it by a sixth of a circle clockwise.

So, given a grid like this (after resizing the canvas):

and  using the equations as above, gives an image like this:

which can then be clipped  (Document > Clip Canvas) to give:

.

I have created a macro with a single parameter a which represents the fraction of pi. The default value of 1 will not rotate the image. Increasing a will give progressively more rotation; a value of 0.5 will rotate by a half-circle. In the example here, I have resized the canvas before applying the macro. The formula used in this macro is: t=t+pi*2*a.

Here is the macro: Rotate.afmacro

John