There is an article in Graphics Gems 1 which gives an algorithm for applying a rotation-only transformation matrix to an image, using an algorithm that is not only the fastest possible, but also provides anti-aliasing in a natural efficient manner that leverages the algorithm.
The article is in Graphics Gems I, here’s the bibliographical entry:
Paeth, Alan W., A Fast Algorithm for General Raster Rotation, Graphics Gems, p. 179-195.
Unfortunately, the source code is missing, but if you can implement a simple function to apply a fractional shear to a single row or column of pixels, you can make this work.
If the Juce GraphicsSoftwareRenderer is not already using this technique for applying rotation-only transforms to images, it will get a very nice performance boost from using it!
This is particularly handy for those people who want to have animated rotating objects in their interface.