The entirety of what you need to understand is encapsulated in the two gif's on the page I linked to originally.
Scheimpflug is only half the interesting bit, and his work has little relevance to us, he was only interested in huge J point distances that require very little tilt. His work was for battlefield imagery from balloons in the first world war.
Merklinger, and his J point/hinge line, are the really interesting bits for us and nothing explains this half as well as the gif does.
If you want a deeper understanding of the maths then Merklinger's free ebook, and lets not forget he actually wrote the book on this, is available here http://www.cs.cmu.edu/~ILIM/courses/vision-sensors/readings/FVC16.pdf
His other work, on depth of field for tilted images, is available entirely free too, here, http://www.trenholm.org/hmmerk/TIAOOFe.pdf
You do not need to buy anything to have the deepest understanding of tilt and shift use.