Given four points that define an arbitraryy rectangle,  but at some unknown
position and rotation,  how can I have a transform that will transform any
given object (say a box which shares the rectangle as one of its sides)  to
that position & rotation?

I've tried for about a full man day of programming and came up to a dead
end....

Restating,  I have a pAf,  pBf,  pAb,  pBb,  which represent the position of
four wheels on a railroad that conforms to a wavy isosurface.     I want to
design a train engine or care that fits within a box of this size but then
is transformed out there.

The problem that I ran into was that I inevitably found unwanted "rolling,"
to use an aeronautical term, in the 30-odd  different algorithms that I
tried.

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