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.