Excellent! We now have two elegant solutions proposed: Tony Moss's orthographic projection and Fear de Varies's mathematics. I need to study both to understand and use them.
Tony, your sketch is worth 10,000 words. I see from the sketch how things are laid out and points projected to different planes. But I am having some trouble with the words as you seem to be starting at the solution (P1) and working back to find the location of the sun. I would thing you need to start with the time and time angle and work towards the point on the cylinder from there. I have modified you sketch to try to do that. I hope this file is small enough to get through the filter. The explanation of this sketch is as follows. Define a new plane perpendicular to the style. On this equatorial plane, the style which is parallel to the earths axis, projects as a point and the trig on as a circle. The sun moves around this plane as the time angle (t), 15 degrees per hour. For any time angle, project the intersection with the circle back to the edge view and down to the plan view to establish time angles on the elliptical projection of the trigon. As you have done, project the sun's ray through the axis and onto the cylinder at (P1) and then up to establish (P2). As you proposed then move the trigon along the axis of the style to (Pn) to repeat for other points on the hour line. From this point of view shouldn't the trigon touch the edge of the cylinder so the various projections for (Pn) form a cone around the style axis? You are correct, the orthographic projection technique works but it is a tedious procedure to establish sufficient points to fix the hour lines. Maybe I should have another look at the mathematical solution. Roger Bailey Walking Shadow Designs N 51 At 07:49 PM 3/4/00 +0000, Tony Moss wrote: >Roger Bailey Contributed >> >SNIP > >>....Calculate the lines for each >>face the usual way as a series of vertical declining dials. Lay out the >>design for each facet and draw a smooth curve through the mid points for >>each face to approximate the hour angles. >> >>I am sure there are more elegant solutions but the mathematics is beyond >>me. Your challenge remains. >> >I couldn't begin to contemplate a numerical approach to laying out such a >dial but to do so by simple orthographic projection is fairly >straightforward, though perhaps somewhat tedious. > >One picture is worth 10 000 words so I'm taking the liberty of including >a small GIF (43k) showing how this can be achieved. > >Tony Moss > >Attachment Converted: "c:\eudora\attach\PlotCylr.gif" Attachment converted: Macintosh HD:Cyl-RTB.gif (GIFf/JVWR) (00010117)
