Mixing
A Suitable Function for Terrain, Mountain Modeling
$begingroup$
On Google Maps and various other mapping programs, one can see contour lines that correspond to elevation. Sometimes these contour lines are concentric corresponding to a mountain.
My question is what would be the most suitable function to represent such data? I thought the simplest choice would be multiple Gaussian "bumps" placed additively on a map; whose composition would define a certain map? Are there any other functional representation methods that could give this output?
My next goal would be fitting such function to a set of elevation data collected on a grid.
functions contour-integration 3d surfaces
asked Feb 1 at 16:02
BB_MLBB_ML
6,07652644
$endgroup$
add a comment |
$begingroup$
On Google Maps and various other mapping programs, one can see contour lines that correspond to elevation. Sometimes these contour lines are concentric corresponding to a mountain.
My question is what would be the most suitable function to represent such data? I thought the simplest choice would be multiple Gaussian "bumps" placed additively on a map; whose composition would define a certain map? Are there any other functional representation methods that could give this output?
My next goal would be fitting such function to a set of elevation data collected on a grid.
functions contour-integration 3d surfaces
asked Feb 1 at 16:02
BB_MLBB_ML
6,07652644
$endgroup$
1
$begingroup$
The answer probably depends on what you are going to use it for. My starting point would be 2-d interpolation of which there are many methods. en.wikipedia.org/wiki/Multivariate_interpolation
$endgroup$
– user121049
Feb 1 at 16:09
$begingroup$
Thanks for the share. I will be going over the links referenced in the article. My goal: is finding a "flattest path" from source to a destination. That would probably trigger another question here! But if you've heard of any approaches, please do share. I worked with discretized PDEs, ODEs, and level sets before.
$endgroup$
– BB_ML
Feb 1 at 16:17
add a comment |
$begingroup$
On Google Maps and various other mapping programs, one can see contour lines that correspond to elevation. Sometimes these contour lines are concentric corresponding to a mountain.
My question is what would be the most suitable function to represent such data? I thought the simplest choice would be multiple Gaussian "bumps" placed additively on a map; whose composition would define a certain map? Are there any other functional representation methods that could give this output?
My next goal would be fitting such function to a set of elevation data collected on a grid.
functions contour-integration 3d surfaces
asked Feb 1 at 16:02
BB_MLBB_ML
6,07652644
$endgroup$
On Google Maps and various other mapping programs, one can see contour lines that correspond to elevation. Sometimes these contour lines are concentric corresponding to a mountain.
My question is what would be the most suitable function to represent such data? I thought the simplest choice would be multiple Gaussian "bumps" placed additively on a map; whose composition would define a certain map? Are there any other functional representation methods that could give this output?
My next goal would be fitting such function to a set of elevation data collected on a grid.
functions contour-integration 3d surfaces
functions contour-integration 3d surfaces
asked Feb 1 at 16:02
BB_MLBB_ML
6,07652644
asked Feb 1 at 16:02
BB_MLBB_ML
6,07652644
asked Feb 1 at 16:02
BB_MLBB_ML
6,07652644
asked Feb 1 at 16:02
BB_MLBB_ML
6,07652644
asked Feb 1 at 16:02
BB_MLBB_ML
6,07652644
6,07652644
1
$begingroup$
The answer probably depends on what you are going to use it for. My starting point would be 2-d interpolation of which there are many methods. en.wikipedia.org/wiki/Multivariate_interpolation
$endgroup$
– user121049
Feb 1 at 16:09
$begingroup$
Thanks for the share. I will be going over the links referenced in the article. My goal: is finding a "flattest path" from source to a destination. That would probably trigger another question here! But if you've heard of any approaches, please do share. I worked with discretized PDEs, ODEs, and level sets before.
$endgroup$
– BB_ML
Feb 1 at 16:17
add a comment |
1
$begingroup$
The answer probably depends on what you are going to use it for. My starting point would be 2-d interpolation of which there are many methods. en.wikipedia.org/wiki/Multivariate_interpolation
$endgroup$
– user121049
Feb 1 at 16:09
$begingroup$
Thanks for the share. I will be going over the links referenced in the article. My goal: is finding a "flattest path" from source to a destination. That would probably trigger another question here! But if you've heard of any approaches, please do share. I worked with discretized PDEs, ODEs, and level sets before.
$endgroup$
– BB_ML
Feb 1 at 16:17
1
1
$begingroup$
The answer probably depends on what you are going to use it for. My starting point would be 2-d interpolation of which there are many methods. en.wikipedia.org/wiki/Multivariate_interpolation
$endgroup$
– user121049
Feb 1 at 16:09
$begingroup$
The answer probably depends on what you are going to use it for. My starting point would be 2-d interpolation of which there are many methods. en.wikipedia.org/wiki/Multivariate_interpolation
$endgroup$
– user121049
Feb 1 at 16:09
$begingroup$
Thanks for the share. I will be going over the links referenced in the article. My goal: is finding a "flattest path" from source to a destination. That would probably trigger another question here! But if you've heard of any approaches, please do share. I worked with discretized PDEs, ODEs, and level sets before.
$endgroup$
– BB_ML
Feb 1 at 16:17
$begingroup$
Thanks for the share. I will be going over the links referenced in the article. My goal: is finding a "flattest path" from source to a destination. That would probably trigger another question here! But if you've heard of any approaches, please do share. I worked with discretized PDEs, ODEs, and level sets before.
$endgroup$
– BB_ML
Feb 1 at 16:17
add a comment |
2 Answers
2
active
oldest
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$begingroup$
This is a huge question...
It depends on the precision you'd like and on the kind of input data you have.
For discrete methods, you can use Delaunay triangulation. See for example Delaunay Triangulation Algorithm and Application to Terrain Generation. You have commercial packages like https://www.geo-media.com/solutions/logiciel-covadis/modele-numerique-de-terrain.
You also have continuous methods that can be based on spline surfaces.
answered Feb 1 at 16:18
mathcounterexamples.netmathcounterexamples.net
26.9k22158
$endgroup$
add a comment |
$begingroup$
RBF based interpolation worked great. I divide the world in degree blocks e.. 31-32 lat 40-41 lon would be one block, I sample about 40k elevation pts from each block and fit RBF Gaussian bumps, or multiquadric functions to smaller sections of a block. I save W matrix and lat, lons for the fit and I have my continuous function to recreate the terrain at any point.
https://hal.archives-ouvertes.fr/hal-00308008/document
answered Feb 9 at 19:52
BB_MLBB_ML
6,07652644
$endgroup$
add a comment |
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2 Answers
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2 Answers
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$begingroup$
This is a huge question...
It depends on the precision you'd like and on the kind of input data you have.
For discrete methods, you can use Delaunay triangulation. See for example Delaunay Triangulation Algorithm and Application to Terrain Generation. You have commercial packages like https://www.geo-media.com/solutions/logiciel-covadis/modele-numerique-de-terrain.
You also have continuous methods that can be based on spline surfaces.
answered Feb 1 at 16:18
mathcounterexamples.netmathcounterexamples.net
26.9k22158
$endgroup$
add a comment |
$begingroup$
This is a huge question...
It depends on the precision you'd like and on the kind of input data you have.
For discrete methods, you can use Delaunay triangulation. See for example Delaunay Triangulation Algorithm and Application to Terrain Generation. You have commercial packages like https://www.geo-media.com/solutions/logiciel-covadis/modele-numerique-de-terrain.
You also have continuous methods that can be based on spline surfaces.
answered Feb 1 at 16:18
mathcounterexamples.netmathcounterexamples.net
26.9k22158
$endgroup$
add a comment |
$begingroup$
This is a huge question...
It depends on the precision you'd like and on the kind of input data you have.
For discrete methods, you can use Delaunay triangulation. See for example Delaunay Triangulation Algorithm and Application to Terrain Generation. You have commercial packages like https://www.geo-media.com/solutions/logiciel-covadis/modele-numerique-de-terrain.
You also have continuous methods that can be based on spline surfaces.
answered Feb 1 at 16:18
mathcounterexamples.netmathcounterexamples.net
26.9k22158
$endgroup$
This is a huge question...
It depends on the precision you'd like and on the kind of input data you have.
For discrete methods, you can use Delaunay triangulation. See for example Delaunay Triangulation Algorithm and Application to Terrain Generation. You have commercial packages like https://www.geo-media.com/solutions/logiciel-covadis/modele-numerique-de-terrain.
You also have continuous methods that can be based on spline surfaces.
answered Feb 1 at 16:18
mathcounterexamples.netmathcounterexamples.net
26.9k22158
edited Feb 1 at 16:25
answered Feb 1 at 16:18
mathcounterexamples.netmathcounterexamples.net
26.9k22158
answered Feb 1 at 16:18
mathcounterexamples.netmathcounterexamples.net
26.9k22158
answered Feb 1 at 16:18
mathcounterexamples.netmathcounterexamples.net
26.9k22158
26.9k22158
add a comment |
add a comment |
$begingroup$
RBF based interpolation worked great. I divide the world in degree blocks e.. 31-32 lat 40-41 lon would be one block, I sample about 40k elevation pts from each block and fit RBF Gaussian bumps, or multiquadric functions to smaller sections of a block. I save W matrix and lat, lons for the fit and I have my continuous function to recreate the terrain at any point.
https://hal.archives-ouvertes.fr/hal-00308008/document
answered Feb 9 at 19:52
BB_MLBB_ML
6,07652644
$endgroup$
add a comment |
$begingroup$
RBF based interpolation worked great. I divide the world in degree blocks e.. 31-32 lat 40-41 lon would be one block, I sample about 40k elevation pts from each block and fit RBF Gaussian bumps, or multiquadric functions to smaller sections of a block. I save W matrix and lat, lons for the fit and I have my continuous function to recreate the terrain at any point.
https://hal.archives-ouvertes.fr/hal-00308008/document
answered Feb 9 at 19:52
BB_MLBB_ML
6,07652644
$endgroup$
add a comment |
$begingroup$
RBF based interpolation worked great. I divide the world in degree blocks e.. 31-32 lat 40-41 lon would be one block, I sample about 40k elevation pts from each block and fit RBF Gaussian bumps, or multiquadric functions to smaller sections of a block. I save W matrix and lat, lons for the fit and I have my continuous function to recreate the terrain at any point.
https://hal.archives-ouvertes.fr/hal-00308008/document
answered Feb 9 at 19:52
BB_MLBB_ML
6,07652644
$endgroup$
RBF based interpolation worked great. I divide the world in degree blocks e.. 31-32 lat 40-41 lon would be one block, I sample about 40k elevation pts from each block and fit RBF Gaussian bumps, or multiquadric functions to smaller sections of a block. I save W matrix and lat, lons for the fit and I have my continuous function to recreate the terrain at any point.
https://hal.archives-ouvertes.fr/hal-00308008/document
answered Feb 9 at 19:52
BB_MLBB_ML
6,07652644
edited Feb 25 at 11:47
answered Feb 9 at 19:52
BB_MLBB_ML
6,07652644
answered Feb 9 at 19:52
BB_MLBB_ML
6,07652644
answered Feb 9 at 19:52
BB_MLBB_ML
6,07652644
6,07652644
add a comment |
add a comment |
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$begingroup$
The answer probably depends on what you are going to use it for. My starting point would be 2-d interpolation of which there are many methods. en.wikipedia.org/wiki/Multivariate_interpolation
$endgroup$
– user121049
Feb 1 at 16:09
$begingroup$
Thanks for the share. I will be going over the links referenced in the article. My goal: is finding a "flattest path" from source to a destination. That would probably trigger another question here! But if you've heard of any approaches, please do share. I worked with discretized PDEs, ODEs, and level sets before.
$endgroup$
– BB_ML
Feb 1 at 16:17