## Exercise on Completing a Cube, given an Edge.

28jun10

\begin{document} \maketitle \section{Introduction} This exercise is nothing more than actually carrying out the recipe for drawing a cube in perspective, given one edge (and a 3-pt perspective frame), as in Lessons P4. The figures in this lesson are correct but not very useful for physical experimentation, as described in Lesson P5 on building a peeping house. They were drawn compactly, with the vertical vanishing point much too close to the horizon. This was done so that all construction could be fitted on one page. This exercise calls for a construction in KSEG which can be wiggled into one position for easy construction, as in the lesson, and again into a more realistic position, suitable for building a peeping house. The figure at the right shows the construction lines in orange that the lesson text describes, but which are not drawn into to original figure. \section{Exercise} Based on an arbitrary triangle $V_1 V_2 V_3$ whose vertices become the three vanishing points, complete the Thales triangles on all three sides and determine the three diagonal vanishing points. This is your perspective frame. (You might save this much of the construction as a separate file in order to use it later.) Now choose an arbitrary point $P$, and second arbitrary point $Q$ on the construction line $PV_2$. Now construct a cube based on this edge as described in the lesson. \section{Discussion} Since you will need to understand this construction for the take home examination for this section of the course you should repeat this construction for an initial edge \textbf{not} lying inside the perspective triangle. You can drag your pont $P$ outside the triangle, but certain constructions will not be drawn by KSEG. You'll have to redo those in order to draw all visible sides of the cube. \end{document}