Mixing
How to tile a sphere with points at an even density?
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I'm writing a bit of code to plot twitter usage across the globe. To do this, I'm searching for users within n km of a certain longitude/latitude (a circular area), at many different lat/lon coordinates. The fact that this is lat/lon coordinates is irrelevant, since this portion is done in cartesian coordinates.
I need to tile the earth (a sphere in this model) with m points, which will serve as the centre of a search radius. The location of each point (x y z) is subject to the constraint that it cannot be within m km of any other point (x' y' z'), so that the search radii do not overlap. Any thoughts? It seems like the kind of problem that has a perfect solution.
geometry tiling
asked Jul 2 '12 at 19:05
RyanGrannell
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up vote
4
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I'm writing a bit of code to plot twitter usage across the globe. To do this, I'm searching for users within n km of a certain longitude/latitude (a circular area), at many different lat/lon coordinates. The fact that this is lat/lon coordinates is irrelevant, since this portion is done in cartesian coordinates.
I need to tile the earth (a sphere in this model) with m points, which will serve as the centre of a search radius. The location of each point (x y z) is subject to the constraint that it cannot be within m km of any other point (x' y' z'), so that the search radii do not overlap. Any thoughts? It seems like the kind of problem that has a perfect solution.
geometry tiling
asked Jul 2 '12 at 19:05
RyanGrannell
1214
add a comment |
up vote
4
down vote
favorite
up vote
4
down vote
favorite
I'm writing a bit of code to plot twitter usage across the globe. To do this, I'm searching for users within n km of a certain longitude/latitude (a circular area), at many different lat/lon coordinates. The fact that this is lat/lon coordinates is irrelevant, since this portion is done in cartesian coordinates.
I need to tile the earth (a sphere in this model) with m points, which will serve as the centre of a search radius. The location of each point (x y z) is subject to the constraint that it cannot be within m km of any other point (x' y' z'), so that the search radii do not overlap. Any thoughts? It seems like the kind of problem that has a perfect solution.
geometry tiling
asked Jul 2 '12 at 19:05
RyanGrannell
1214
I'm writing a bit of code to plot twitter usage across the globe. To do this, I'm searching for users within n km of a certain longitude/latitude (a circular area), at many different lat/lon coordinates. The fact that this is lat/lon coordinates is irrelevant, since this portion is done in cartesian coordinates.
I need to tile the earth (a sphere in this model) with m points, which will serve as the centre of a search radius. The location of each point (x y z) is subject to the constraint that it cannot be within m km of any other point (x' y' z'), so that the search radii do not overlap. Any thoughts? It seems like the kind of problem that has a perfect solution.
geometry tiling
geometry tiling
asked Jul 2 '12 at 19:05
RyanGrannell
1214
asked Jul 2 '12 at 19:05
RyanGrannell
1214
asked Jul 2 '12 at 19:05
RyanGrannell
1214
asked Jul 2 '12 at 19:05
RyanGrannell
1214
asked Jul 2 '12 at 19:05
RyanGrannell
1214
1214
add a comment |
add a comment |
2 Answers
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up vote
8
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The problem of distributing points on a sphere (as opposed to a circle) does not have a neat solution. There is a lot of information online, but you'll have to see for yourself what you can use. (There is also a common confusion between uniform random distribution and evenly-spaced distribution, which are very different things).
- Spherical codes
- Tammes problem
- Thomson problem
- nice pictures
- some code
thanks for the answer, the links were really useful. after playing around with a few techniques, the most efficient method seems to be the iterative method in the last link. Thanks again :)
– RyanGrannell
Jul 23 '12 at 18:23
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up vote
2
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Your question is a bit ambiguous. You seem to have the answer for uniform random distribution which are mostly approximations.
But if you want exact, evenly-spaced distributions (without including the malevolent varient of n=1), there are only (and exactly only) 6 solutions for a 3-sphere.
These correspond to the vertices of the 5 Platonic solids + the solution of 2 points on opposite sides of each other.
answered May 12 '16 at 22:37
theDoctor
215213
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
8
down vote
The problem of distributing points on a sphere (as opposed to a circle) does not have a neat solution. There is a lot of information online, but you'll have to see for yourself what you can use. (There is also a common confusion between uniform random distribution and evenly-spaced distribution, which are very different things).
- Spherical codes
- Tammes problem
- Thomson problem
- nice pictures
- some code
thanks for the answer, the links were really useful. after playing around with a few techniques, the most efficient method seems to be the iterative method in the last link. Thanks again :)
– RyanGrannell
Jul 23 '12 at 18:23
add a comment |
up vote
8
down vote
The problem of distributing points on a sphere (as opposed to a circle) does not have a neat solution. There is a lot of information online, but you'll have to see for yourself what you can use. (There is also a common confusion between uniform random distribution and evenly-spaced distribution, which are very different things).
- Spherical codes
- Tammes problem
- Thomson problem
- nice pictures
- some code
thanks for the answer, the links were really useful. after playing around with a few techniques, the most efficient method seems to be the iterative method in the last link. Thanks again :)
– RyanGrannell
Jul 23 '12 at 18:23
add a comment |
up vote
8
down vote
up vote
8
down vote
The problem of distributing points on a sphere (as opposed to a circle) does not have a neat solution. There is a lot of information online, but you'll have to see for yourself what you can use. (There is also a common confusion between uniform random distribution and evenly-spaced distribution, which are very different things).
- Spherical codes
- Tammes problem
- Thomson problem
- nice pictures
- some code
The problem of distributing points on a sphere (as opposed to a circle) does not have a neat solution. There is a lot of information online, but you'll have to see for yourself what you can use. (There is also a common confusion between uniform random distribution and evenly-spaced distribution, which are very different things).
- Spherical codes
- Tammes problem
- Thomson problem
- nice pictures
- some code
answered Jul 2 '12 at 20:49
user31373
thanks for the answer, the links were really useful. after playing around with a few techniques, the most efficient method seems to be the iterative method in the last link. Thanks again :)
– RyanGrannell
Jul 23 '12 at 18:23
add a comment |
thanks for the answer, the links were really useful. after playing around with a few techniques, the most efficient method seems to be the iterative method in the last link. Thanks again :)
– RyanGrannell
Jul 23 '12 at 18:23
thanks for the answer, the links were really useful. after playing around with a few techniques, the most efficient method seems to be the iterative method in the last link. Thanks again :)
– RyanGrannell
Jul 23 '12 at 18:23
thanks for the answer, the links were really useful. after playing around with a few techniques, the most efficient method seems to be the iterative method in the last link. Thanks again :)
– RyanGrannell
Jul 23 '12 at 18:23
add a comment |
up vote
2
down vote
Your question is a bit ambiguous. You seem to have the answer for uniform random distribution which are mostly approximations.
But if you want exact, evenly-spaced distributions (without including the malevolent varient of n=1), there are only (and exactly only) 6 solutions for a 3-sphere.
These correspond to the vertices of the 5 Platonic solids + the solution of 2 points on opposite sides of each other.
answered May 12 '16 at 22:37
theDoctor
215213
add a comment |
up vote
2
down vote
Your question is a bit ambiguous. You seem to have the answer for uniform random distribution which are mostly approximations.
But if you want exact, evenly-spaced distributions (without including the malevolent varient of n=1), there are only (and exactly only) 6 solutions for a 3-sphere.
These correspond to the vertices of the 5 Platonic solids + the solution of 2 points on opposite sides of each other.
answered May 12 '16 at 22:37
theDoctor
215213
add a comment |
up vote
2
down vote
up vote
2
down vote
Your question is a bit ambiguous. You seem to have the answer for uniform random distribution which are mostly approximations.
But if you want exact, evenly-spaced distributions (without including the malevolent varient of n=1), there are only (and exactly only) 6 solutions for a 3-sphere.
These correspond to the vertices of the 5 Platonic solids + the solution of 2 points on opposite sides of each other.
answered May 12 '16 at 22:37
theDoctor
215213
Your question is a bit ambiguous. You seem to have the answer for uniform random distribution which are mostly approximations.
But if you want exact, evenly-spaced distributions (without including the malevolent varient of n=1), there are only (and exactly only) 6 solutions for a 3-sphere.
These correspond to the vertices of the 5 Platonic solids + the solution of 2 points on opposite sides of each other.
answered May 12 '16 at 22:37
theDoctor
215213
edited 2 days ago
answered May 12 '16 at 22:37
theDoctor
215213
answered May 12 '16 at 22:37
theDoctor
215213
answered May 12 '16 at 22:37
theDoctor
215213
215213
add a comment |
add a comment |
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