Problem: It is difficult to create a regular pattern on a hemispherical surface.
Solution: On a special spiral curve, it is easy to create a nearly regularly repeating pattern.
Theoretical background: It is not possible to create a pattern that is regular in all respects on a spherical surface. The problem is caused by the shape of the surface (similar to the projection issues appearing in cartography). Even if the elements of the pattern are regular hexagons, a problem to distribute them evenly due to the distorting effect of the surface will occure. Spherical projection does not solve the problem either. The best approximation is given by a pattern running along a spiral line that follows the spherical surface. The simplest way to define such a curve is in parametric form, in a spherical coordinate system, where:
0<=t<=1
rho=73/2 /* the radius of the hemisphere
phi=12*t*360 /* the number of turns is 12
theta=t*85 /* 85<90 thus the lowest cutout does not run either
The cutout hexagons will be properly oriented if they are drawn from their center along a line drawn to the center of the sphere. When organising the pattern of the cutouts, it may be useful to gather the elements used (point, axis, and the cutout itself) into a common group and perform the command on the group.
