Mapping problem ( sphere to rectangle )

This may be the wrong group for this problem,.. POLITE suggestions as to where I should go gratefully received :-)
Here is the problem :
If I have a sphere of radius R, with a band drawn on it of width W the edges of the band are circles.
If the sphere is centered on the origin, it's surface can be mapped to a square of 180 x 360 units with the unit being a degree of latitude or longitude. ( origin at centre ).
With a horizontal band the two edges are just horizontal lines at Y = ( + - ) SIN^-1 ( R / ( W / 2 )).
For a vertical band the plot of the edges is a pair of sort of " squared of " circles. Can someone please tell me how to calculate the shape of these "circles".
If I can plot a set of points around the shape, I can use AutoCAD to draw a spline curve to plot the shape with reasonable accuracy.
( the idea is to use the plot to print a series of colour bands on the " quarters " of a sphere )
Ideally I want a formula of the form Y = f ( X, (W/R)) with Y being latitude and X longitude and W/R the relative width of the strip on the sphere.
--
Regards Jonathan

remove AT to reply
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Dear Jonathan Barnes:

You are attempting to create a printable surface that you can "roll up" into a sphere?
Not made like you asked: http://www.bfi.org/?q=taxonomy/term/40
Sounds like what you asked for: http://www.vendian.org/mncharity/dir3/planet_globes / "Icosahedron" will get you other good hits, perhaps with algorithms.
You do understand that a flat surface cannot be "rolled up" into a true sphere, unless you make an infinte number or "points", right? It'll just be close...
David A. Smith
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
message

Not quite rolling up.
I have software that wraps a rectangular bit map onto a virtual sphere using this mapping. I can export suitable bitmaps from AutoCAD if I can draw them.
In the real world it can be used like this :
Put a sphere on a stick ( Z axis ), with a rotary driver on the stick, Have a printing head on a rotary frame rotating it about the X axes.
trace the shape on a flat bed to get your shape on the sphere... direct control two stepper motors on the sphere and printer frame from linear motions of the plotter ( or programmed motions ).
--
Regards Jonathan

remove AT to reply
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Dear Jonathan Barnes:
...

...
If you still have difficulty getting the algorithm from the keyword above, let us know.
David A. Smith
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.