OOPS, sorry for the earlier empty post caused by finger trouble caused by brain trouble caused by ...
A good approach, Ron, but the complexity lies in: " Of course the computer would have to calculate all of the points for you." The complexity can be reduced by following your suggestions for selecting Point A at the centre of the dial face and Point B at the North intersection of the meridian and the dial circle. Then all your fractional and whole hour lines can be easily set by keeping the AC distance constant ( = to the radius of the dial circle or the"construction layout" dial circle) and varying your BC distance to obtain your points, and therefore lines, in either one of two ways: 1) straight line distance from B to C, which requires a complex calculation or, 2) arc length distance from B to C which is simply calculated but is a little more difficult to measure since you are measuring along a curve. (This is an "R - THETA", or polar coordinate system, where THETA is determined by arc length rather than by angle directly.) I should have pointed out in my earlier post that this is really easy if you make a template by cutting an arc from a piece of plywood. For Celeste, referred to in my posting, "Subject: Re: plotting timelines for giant sundials Date: Mon, 24 May 1999 00:52:52 -0400 To: John Carmichael <[EMAIL PROTECTED]> CC: Sundial List <sundial@rrz.uni-koeln.de>", I got over 20 degrees of arc length along the circumference of the dial using an arc cut from an eight foot piece of plywood. And I easily marked it to pencil line width transferring a mark precision of better than a minute (of angle, not time!) to the dial plate. I had four templates from one cut: two concave and two convex, enough to do 45 degrees using the two pieces at once. After reading your post I think that it would also be easier to locate even non-radial figures and lines using polar coordinates than to use rectangular coordinates with the continual right angle problem at layout time. Simply establish "Theta" using arc length on the template and measure "R" out on the established line, which could be a surveyors tape. ( I have a thin, <1/4", one, 50m long which would work beautifully.) The computer calculation of R-Theta points is straightforward or automatic in most graphics or CAD programs. It would be a simple matter to square off a rectangle on top of the polar plot, if that is what the shape of the perimeter is to be. Now, if we could just come up with a way to generate ASCII graphics so simply! Or better yet if we could just use FranÁois BLATEYRON's Shadows version 1.5.3 (18 April 1999) program on my iMac! : ^ ( Good stuff, Ron. Cheers, Tom Ron Anthony wrote: > All, > > I'm sorry I was only half awake when this thread started so forgive me if > I'm off course. If I had to lay out a large dial (say 100 ft) to a high > degree of accuracy (say .1 of an inch) I would plot all the points not as > x,y co-ordinates. I would plot them all out as the intersection of two > lines from two fixed points. > > To see what I mean pick 2 points that are well established, e.g., point A > where the gnomom meets the dial face, and point B some number of feet due > north (in line with the gnomon base) of point A. Every point on the dial > face is now at the intersection of two tape measures that start at points A > and B. Assuming that the dial face is flat the accuracy would be good as > the tape measures used. For the points that are almost inline with the AB > line, a third point C could be used as one of the points. Point C could be > calculated from points A and B. Of course the computer would have to > calculate all of the points for you. > > As a crude ASCII art: Point X is 30" 1 1/4" from point A, and 22" 3 7/8" > from point B. (A metric tape measure would be a lot handier) > > B > \ > \ > \ > \ > \ > / X > / C > / > / > / > / > / > / > A > > -----Original Message----- > From: John Carmichael <[EMAIL PROTECTED]> > To: François BLATEYRON <[EMAIL PROTECTED]> > Cc: sundial@rrz.uni-koeln.de <sundial@rrz.uni-koeln.de> > Date: Tuesday, May 25, 1999 9:45 AM > Subject: frame & grid method > > > > > > >>Perhaps a precise solution would be to calculate the intersection of the > >>hour line with the enclosing frame of your sundial. It must be done by a > >>computer but its easy to give a very good precision. > >> > >>The result would be given as a length and a direction (north, east, south, > >>west side of the sundial), the origin could be one of the two opposite > >>corners. > >> > >>The only problem then is to precisely draw your frame, with parallel sides > >>and a good perpendicularity. > >> > >>With one intersection point you can draw the line by joining it to the > >>gnomon foot. > >> > >>I plan to include such kind of data in my Shadows program in a futur > >>version. > > > >Bonjour Francois and everyone else: > > > >Your frame method for plotting would be a good practical way to implement > >John Pickard's (x,y) coordinate method. With a squared frame around the > >sundial work area, one could use it as a reference to easily measure the > >horizontal and vertical distances to the x,y coordinates. > > > >Let us know when you get your new shadows program up and running. Do you > >think I'd understand it or would I have to get someone to help me? > > > >merci Francois, > > > >John Carmichael > > > > -- Tom Semadeni O [EMAIL PROTECTED] o aka I (Ned) Ames . Britthome Bounty ><<((((*> Box 176 Britt ON P0G 1A0 'Phone 705 383 0195 fax 2920 45.768* North 80.600* West
