Lab on Perspective Boxes

\begin{document} \maketitle Earlier, we determined that it would be nice to have the same cube appear in all three perspectives (right) so that corresponding elements of its perspective frame can be compared. \section{Introduction} In this lab we reverted to a paper, pencil and gnomon solution to measuring two boxes, the second of which crosses the horizon. The gnomon in this case was a file card. All circular arcs needed were supplied as part of the given figure. \subsection{Measure the box below the horizon} Many in the class had trouble finding the perspective frame for this figure. Review perspective framings, location of Thales triangles, eye point etc. Many in the class started by putting in a grid of squares into the Thales triangles. This is inefficient until after you have found the lines to the diagonal points whose "slope" you're trying to measure. Review the relation between the diagonal lines and the proportions of the orthographic rectangles they diagonalize. Finally, the mystery of what to do with two rectangles, their proportions and a common side. If one face of the box comes out in the ratio of 7:2 for example, and the other comes out in the ration of 5:3, AND the common side is the "2" in the first, but the "3" in the second, then the common factore is 6=2*3, and the common proportion is 21:6:10. \subsection{Measure the box crossing the horizon} Do the "same" as before, but with some extra ingenuity. In addition, you should use a perspective ruler to estimate from what level you're looking at the "building". Since you're measuring a vertical lenghth, and verticals vanish at the zenith, you'll need a ruler adapted to that vanishing point. Since no dimensions in feet are given, you can only estimate the ratio of the height relative to the height of the "building". \end{document}