Geosphere?

thomthom

How do you calculate a set of points on a sphere which is evenly distributed from each other?

thomthom

Best I can find is: http://en.nicoptere.net/?p=12 - actionscript based on this: http://www.math.niu.edu/~rusin/known-math/96/repulsion
But I'm not making a whole lot sense out of it. The code doesn't have much commenting...

pilou

A sphere with a center (x0,y0,z0) with diameter r
has all points x,y,z like

$http://upload.wikimedia.org/math/3/3/0/33031c82e871501422b05455c81d2680.png$

with

$http://upload.wikimedia.org/math/e/b/9/eb91f8174391d023015dedf9beb94e5d.png$

$http://upload.wikimedia.org/math/9/0/1/9011474548ae3216019a280ff95d25a3.png$
= Latitude

$http://upload.wikimedia.org/math/1/9/6/1964adc54d7dc608fd9f63a46cae422b.png$
= longitude

thomthom

Isn't that a sphere with poles? The points would not be evenly spaced.

I'm looking to generate the points for the sphere on the right.

tml

@thomthom said:

I'm looking to generate the points for the sphere on the right.

Start with a octahedron, divide each edge into half and thus each face into four equal smaller triangles, move the new vertices to the desired radius, repeat.

tml

Note that the above results in just a fairly nice approximation, though. (And I don't know if it matches the subdivision used in your example image.) Only for the (not really sphere-like, as they have so few faces) Platonic solids are the vertices in a strict sense evenly distributed, though. See http://www.cgafaq.info/wiki/Evenly_distributed_points_on_sphere and especially http://www.math.niu.edu/~rusin/known-math/95/sphere.faq .

thomthom

Approximation is ok. Just just want to take a fixed number of points and distribute them approximately evenly. Doesn't matter if they need to be rounded to a number that fit some geometric restriction.

Thanks for the links - I'll look into them.