I know what you mean about not being a fan of your own voice!
OK just so we get definitions right, a chaser describes the effect of displaying something across each mapped surface in turn. If you can imagine 3 sides of a cube being viewed from a corner and the projection shows content on each side in turn. With many surfaces it looks like the images is chasing across the set. I guess easy enough with a Input Selector.
By other (potentially cliche) effects I am referring to edge and face effects on mapped surfaces like edge marquees or depth effects on faces.
Regarding accurate and predictable foreshortening (perhaps that not the right word) - when an image is mapped to an oblique surface not only does the vertical height get squashed as it recedes but the horizontal distance continuously decreases (see the grid in the image).

- 71J1NlCkdkL._AC_SY355_.jpg (46.96 KiB) Viewed 3173 times
It isn't too challenging to to jockey vertices into place to the corner points pushing receding points closer together thereby scaling the image vertically. Moving corner points only scales between vertices though, so while an image in perspective might be vertically smaller at the back, it should also squash continuously horizontally. This horizontal squashing is done automatically when rotating images in 3d space but not necessarily when moving the corner vertices of an image.
Obviously, rotating planes is easy enough but not always convenient for projection mapping where planes might not be square or are at an odd angle. So for point pushing you need to guess the vanishing point and then scale continuously smaller
horizontally.