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Original notes and derivations for RogCAD, April 1993





pre-CAD planning sketch



The first nine images below are of the non-
generalized derivation of the floating image 
plane and projection of a structure.

Then second batch of nine images is of the
generalized derivation (variable perspective point
and focal point) which is much more complicated.

Vector cross-product is used to create a floating 
image plane with a normal vector that passes 
through the origin of the xyz axes.

Vector dot-product is used to test which side of 
the z-axis each projected point which intersects
with the image plane stems from.

After the initial vector considerations, it's just
algebra -- nothing we didn't do in high school.
But the magic of algebra fascinates me, especially
when it goes on for many pages and the darn thing
actually works.



















Those derivations produced the original 
program code for a specific
perspective point and focal point:





The program print-out on 
the dot-matrix printer:





The first RogCAD output.
The points had to be plotted on paper:





Derivation of floating image plane and 
projection of structure, generalized,
next nine images:





















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