Hello, This is my first posting to this list.
The following may well be "old hat" for the subscribers to this list, but I'm posting it in hopes that it may be of interest to someone. I've just posted a couple of technical drawings along with an explanation in the form of a PostScript and PDF file on the following web page: http://www.gnu.org/software/3dldf/sundials.html#Calculating_Dials It's a page for sundials among the webpages for GNU 3DLDF, a software package for three-dimensional drawing, of which I am the author. (More about this below.) I recently borrowed the book _Die Sonnenuhren. Kunstwerke der Zeitmessung und ihre Geheimnissse_ (_Sundials. Works of Art for Measuring Time and Their Secrets_) by Lothar M. Loske from the library. I wanted to find out how to draw the dial of a sundial. I had looked into this subject before, but never gotten so far as to actually follow the explanations. Loske describes how to draw equatorial, horizontal and vertical dials using drafting techniques. He also explains how to draw a vertical dial that doesn't face directly south. However, he doesn't explain how to draw one on a plane whose normal isn't parallel to one of the major planes. It seemed to me that the problem could be greatly simplified by using 3D data and working with projections directly instead of using drafting techniques. My idea was simply to find the lines for the time divisions on a plane not containing the gnomon by finding the intersections of the plane of the dial with the plane through the lines representing the time divisions on the equatorial dial and a point on the gnomon not lying in the plane of the equatorial dial. The sample I've posted shows this for one time division. It took me a bit longer to make the drawings than I expected. I will try to make an example using a larger set of time divisions. I would be grateful for any questions, comments, constructive criticism, or corrections, if I've made any errors, or there's a flaw in my logic. Having considered it, I'm pretty certain that the basic idea is correct. However, many people on this list are probably more knowledgeable on the subject than I am and better mathematicians. I am an artist and computer programmer with an interest in model-building and recreational mathematics. One of the reasons why I wanted to solve this problem was for making (cardboard) polyhedron models with sundails on their faces. GNU 3DLDF, which I used for the samples, is Free Software (free in the sense of the GNU General Public License) and part of the GNU Project of the Free Software Foundation. There's a lot of information about it on the webpages, if anyone's interested: http://www.gnu.org/software/3dldf/LDF.html If you've made it this far, thank you for reading to the end of this overly-long posting. Laurence Finston --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
