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Topic: globe distribution (Read 1675 times) |
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5cameron
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globe distribution
« on: Feb 25th, 2005, 1:26am » |
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Hi,
so I'm trying to wrap my mind around how to distribute a number of elements evenly over a globe.
I understand how to do it in 2d, over a circle its as simple as dividing 360 into the number of elements, and defining X, Y using COS and SIN.
but how would I do it in 3d??
thanks muchly in advance,
-cameron
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fjen
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Re: globe distribution
« Reply #1 on: Feb 25th, 2005, 9:55am » |
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see:
http://www.math.niu.edu/~rusin/known-math/95/sphere.faq
Quote:
Q1. What does it mean to place N points "evenly" on a sphere?
Well, what do you want it to mean? Several valid interpretations exist;
they lead to slightly different distributions of points.
...
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some sources are here:
http://www.math.niu.edu/~rusin/known-math/index/spheres.html
i ported one of the sources from there before ... here it is:
Code:
/*
note: this will give you an exact amount of points (46) on the sphere,
if you need more then just subdevide the triangles it creates.
*/
// ported from basic code (sphere.bas).
// see the sphere-faq: http://www.math.niu.edu/~rusin/known-math/index/spheres.html
//
float K=6;
float eps = 0.01;
int N = 0;
Point3D[] sp = new Point3D[46];
sp[N] = new Point3D(100.0, 0.0, 0.0);
for (int i=1; i<K; i++)
{
float M = round(2.0*K*sin(PI*(i/K)));
for (int j=1; j<=M; j++)
{
N++; sp[N] = new Point3D(100.0, PI*(i/K), TWO_PI*(j/M));
}
}
N++; sp[N] = new Point3D(100.0, PI, 0.0);
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Code:
// POINT3D
class Point3D
{
public float x; public float y; public float z;
public Point3D (float _x, float _y, float _z)
{
this.x = _x; this.y = _y; this.z = _z;
}
}
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i more or less "handcoded" the triangles .. like this:
triangles = new Triangle3D[] {
// upper cap
new Triangle3D( sp[0], sp[1], sp[6] ),
new Triangle3D( sp[0], sp[2], sp[1] ),
new Triangle3D( sp[0], sp[3], sp[2] ),
new Triangle3D( sp[0], sp[4], sp[3] ),
new Triangle3D( sp[0], sp[5], sp[4] ),
new Triangle3D( sp[0], sp[6], sp[5] ),
// row 1
...
// row 2
...
}
i'm sure there is a better way to do it though ...
i recommend looking into spherical coordinates which would give you a 2D + radius description of every point. then repel them until a certain distance-threshold is reached ...
/F
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5cameron
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Re: globe distribution
« Reply #2 on: Mar 4th, 2005, 2:21am » |
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wow, that stuff is intense! Still trying to soak it in.
I also found this which seems to be something:
http://mathworld.wolfram.com/SpherePointPicking.html
I wonder if there is a babelfish to convert mathmatician-speak into layman's terms?
THANKS!
-5
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fjen
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Re: globe distribution
« Reply #3 on: Mar 4th, 2005, 10:49am » |
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mathelfish ... i was hoping someone would come up with that!
/F
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