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RogCAD home back to RogCAD history Original notes and derivations for RogCAD, April 1993 pre-CAD planning sketch The first nine images below are of the non- generalized derivation (pre-defined perspective point and focal point) of the floating image plane and projection of a structure. The 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. Points on the structure are projected onto the floating image plane. Vector dot-product is used to test from which side of the z-axis each projected point stems. After the initial vector considerations, it's just algebra. But the magic of algebra fascinates me, especially when it goes on for many pages and it actually works. If you are using a laptop or desktop computer, you might want to magnify this page to 150 percent. Microsoft Edge browser users should click on the three dots ... at the upper right-hand corner, then use the "zoom" feature. Vertical three dots for Chrome browser users. 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: The generalized calculator kernel print-out on the dot-matrix printer: back to RogCAD history RogCAD code -- complete RogCAD home |
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