The ultra mysterious perspective transformation

Well friends ...

... for a less mysterious case see this: http://www.grasshopper3d.com/forum/topics/the-mysterious-shear-tran...

And here we go (using a 3d text: "Lord of Darkness" as a [suitable] demo):

1. A transformation Matrix is a 4*4 collection of 16 values that "deform" 3d things according the values in the cells. The orthodox way is to deploy "cells" left to right and top to bottom. Rhino does the opposite (why?) hence we need the transpose method.

2. Since "translate" and "perspective" are "symmetrical" the transpose boolean toggle (within the C#) "flips" rows with columns ... so we get perspective or move.

3. When in perspective "mode" the vanishing points are computed internally within a min/max limit (per X/Y/Z axis) thus avoiding the usual havoc with "extreme" perspective angles (very common "glitz" in pretty much every CAD app - CATIA excluded). Vanishing points (and limits) are oriented with respect the pos/neg value of a given control slider.

Note: slider values are percentages between min/max (mode: perspective) and/or actual values*100 (mode: move). 

4.In order to start mastering the whole thing: don't change anything: just play with these 4 sliders selected:

5. The 123 sardine cans challenge: even with DeusExMachine = true (see inside C#: that one redirects the transformation per BrepFace and then joins the breps instead of applying it on a brep basis)... odd things (and/or invalid breps) occur ... thus what is required in order to make things working 100% ??.

he, he 

best, Lord of Darkness