The book "Digital Image Warping" by George Wolberg[0] goes into these tricks in great detail, as well as choices for the resampling filter.

The world is very different today, bilinear texture sampling is built into GPU hardware and is lightning fast. The idea that a sequence of skews might be more efficient is a curious relic of when CPU was considered a reasonable place to do image transformation.

[0]: https://www.amazon.com/Digital-Image-Warping-George-Wolberg/...