sun - How to create unusual sundial?

I am considering small "artsy" project. I would like to create sundial by placing gnomon on the window and painting hour lines on the window facing wall.

Since this is to be placed in bedroom I am constrained by my geographic location, wall, window placement and orientation. The esthetic and size (I have one wall only) of the project is gating factor (otherwise known as "the wife" factor).

Due to above I am perfectly OK with the fact that this sundial will "work" by limited time of the day and even limited time of the year. However whenever it will work (that is the shadow of the gnomon will be cast on the "said" wall) I would like it to be as accurate as possible.

Also all of the above make the calculations for creating hour lines quite challenging (at least for me) and to be honest I do not know where to start.

Could you point me the resources that would help in calculating hour lines (software, tutorials, books, math equations)?
Could you describe how would you approach the task of calculating hour lines?

(Resources that are little heavy on math side are OK for me. I am also capable of wring software on my own.)

Answer

I believe the easiest way to do this would be empirical, rather than theoretical- Just mark out each hour, all day. It would be especially fascinating if you did this, say, every Saturday, starting with the upcoming Summer Solstice. The artistic possibilities are endless as well... different symbols, colors, outlines, etc., for different times of the year, day, ambient temperature, etc.

But if you really wanted to do a theoretical prediction, here are the steps.

1. 
   

   The Sun is at 0 RA, 0 DEC on the Vernal Equinox. Its DEC increases nearly linearly at 360 degrees/365.25 days. The RA is sinusoidal with an amplitude of 23.5 degrees. 1b. OR just get the Sun's sky position from a table or chart.

   
   


2. 
   

   Use spherical trigonometry to transform the RA and DEC chart you made in step 1 into its ALT and AZ coordinates for your geographic location and particular times of day. 2b. OR skip all previous steps and just get the ALT-AZ coordinates from some planetarium software (Starry Night, with which I taught an astronomy course for six or seven years, will do this, but it's commercial software. There are other, free packages out there.)

   
   


3. 
   

   Use regular trigonometry to figure out where the line from the Sun's predicted positions to the tip of the gnomon will intersect the plane of your wall. This will depend on your room's geometry, of course. Basically, if the Sun were at 29 degrees ALT, you would project a line downwards from the tip at 29 degrees. If its AZ were 1 degree East of the meridian (line from North to South), you would run the projecting line at a heading of 1 degree W of North. Hopefully your projection wall runs due East and West, or this will get really ugly. Definitely need a spreadsheet or algorithm to do this for you, if you had any interest in doing a large number of hour lines.