Le 26/10/2010 05:09, Steve Martell a écrit :
> So...
> 
> All I want to do is start out at <1,0,0> and spiral up to the top of a
> hemisphere.  I want to be able to vary the vertical step up (via angle, of
> course) and the horizontal step.  I can make plain old vertical columnar spirals
> all day long, but I'm just not getting the translation for the hemisphere.  The
> eqs I have found online aren't quite doing what I want - I get fancy loxo
> things, but not just a nice spiral.

loxodrom is the spiral on a sphere when driven by only the spiral
constant angle.
So if your only constant parameter is the angle, you would get a
loxodrom (which also mean it never reach the pole exactly)

> If I leave the Phi out of it all, just using the X and Z, I get my nice columnar
> spirals.  Nice if I want to make car springs, that is!  I am going to use this
> to make indents on a golfball, but it is really just a concept struggle at this
> point.  I just want a nice, adjustable, hemispherical spiral!  Argh!

Indents on golf-ball are subject to patents (sad, but true).
Usual approach is to use a icosahedron, each vertex is a 5 neighbors
circle. Then you subdivide each triangle (equilateral) with 6 neighbors
circles (up to you for the number of circles in each triangle (including
the 3 of the vertices), their number can be 3,6,10,15,21,28,...
(traditional triangular number)
Then you project each triangle on the sphere in respect to the sphere's
center (the icosahedron's center and sphere's center are at the same
point), and that generate the centers of all your indents (as the
projection of the center of each circle).
To make indent with CSG, add a bit on the length from the center of the
indent to the center of the sphere (that bit being smaller than the
radius of the spherical indent)

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