| Name | gridding-py JSON |
| Version |
0.4.2
JSON |
| download |
| home_page | None |
| Summary | Build geographical grids |
| upload_time | 2024-11-22 19:19:23 |
| maintainer | None |
| docs_url | None |
| author | None |
| requires_python | >=3.10.2 |
| license | MIT License Copyright (c) 2024 Cyril Dever Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. |
| keywords |
geographical
grid
carreau
carroyage
geodesic
tile
wgs84
utm
|
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No requirements were recorded.
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|
# gridding
_Build geographical grids in Python_
This is a Python library implementing the "carroyage" for geographical data.
### Motivation
In order to be able to make analysis in the more granular level of the "carreau", this provides an easy reference to building custom grids by allowing to assign a unique tile / "carreau" ID to a geographical coordinate (latitude, longitude) or a French postal address.
Indeed, the result of the computation gives the ID according to the [EU directive INSPIRE](https://www.insee.fr/fr/information/5008701?sommaire=5008710#titre-bloc-14) in the following format:
`WGS84|RES200m|N2471400|E0486123`
that could be decomposed as a pipe-separated string with:
- the projection system, eg. `WGS84`;
- the resolution of the grid, ie. the size of the square, eg. `RES200m` for $200\text{ m}$;
- the bottom-left point of the grid's bounding box defined by:
* its latitude in decimal degrees, eg. `N2471400` for $\text{N }24.714000°$;
* its longitude, eg. `E0486123` for $\text{E }4.861230°$;
as well as the coordinate in the grid in the form of `<row>.<column>` from the initial bottom-left point.
It would need as input parameters:
- the coordinates of the initial point of the grid (by default the bottom-left point of the bounding box covering the French metropolitan territory: $\text{N }41.316666°$ / $\text{W }5.151110$);
- the size and scale of the grid, eg. `200m`, `1km`, ...;
- the projection system (default: `WGS84`).
Below are the calculation bases.
### Geographic Information System (GIS) computations
#### <u>Latitude</u>
In `WGS84`, one degree of latitude is almost equivalent to $111\text{ km}$ everywhere on Earth.
The distance in meter, $D_{lat}$, for one degree in latitude is given by the following formula:
```math
D_{lat} = \pi \cdot \frac{a (1 - e^2)}{(1 - e^2 \sin^2(\text{latitude}))^{3/2}} \times \frac{1}{180}
```
where
- $a$ is the semi-major axis of the Earth's ellipsoid (in `WGS84`, $a = 6378137$);
- $e$ is the excentricity of the ellipsoid, given by:
```math
e = \sqrt{1 - \frac{b^2}{a^2}}
```
(in `WGS84`, $b = 6356752.3142$)
- $latitude$ is the latitude of the point in radians.
From here, one can compute the degree in latitude for any size of tile / "carreau", eg. in `WGS84`, a "carreau" of height $200\text{ m} \approx 0.001796°$:
```math
\Delta latitude = \frac{distance}{D_{lat}}
```
where
- $distance$ is the vertical distance to convert in degrees of latitude, eg. $200$;
- $D_{lat}$ is the result of the computation above around the given $latitude$.
#### <u>Longitude</u>
The variation of longitude as a function of latitude is calculated by taking into account the decrease in the distance between the meridians as one moves away from the equator. This decrease is due to the fact that the Earth is spherical.
In `WGS84`, the formula that allows one to calculate the distance corresponding to a degree of longitude as a function of a latitude is the following:
```math
\Delta{longitude} = \frac{distance}{D_{lon} \times \cos(latitude)}
```
where
- $distance$ is the horizontal distance to convert in degrees of longitude, eg. $200$;
- $latitude$ is the starting point expressed in radians, eg. $45° = \frac{\pi}{4}$;
- $D_{lon}$ is the result of the computation below at the given $latitude$:
```math
D_\text{lon} = \pi \cdot a \cdot \cos(\text{latitude}) \cdot \frac{1}{180} \cdot \frac{1}{\sqrt{1 - e^2 \sin^2(\text{latitude})}}
```
#### <u>XY coordinates</u>
The UTM projection would be used to handle XY coordinates with the central longitude $\lambda_0$ being automatically calculated for the UTM zone with the longitude of the searched point, _eg._ $-3°$ _for the UTM zone `30T` covering France from_ $W 6°$ _to_ $0°$.
The following data and formula would be used in that case: _eg. for `WGS84`_
- $a = 6378137$
- $e = 0.0818191908426$
- $k_0 = 0.9996$
- $\varphi = latitude \times \frac{\pi}{180}$
- $\lambda = longitude \times \frac{\pi}{180}$
- $N = \frac{a}{\sqrt{1 - e^2\sin^2(\phi)}}$
- $T = \tan^2(\varphi)$
- $C = \frac{e^2\cos^2(\varphi)}{1 - e^2}$
- $A = (\lambda - \lambda_0)\cos(\varphi)$
- $M = a \left( (1 - \frac{e^2}{4} - \frac{3 e^4}{64} - \frac{5 e^6}{256}) \varphi - (\frac{3 e^2}{8} + \frac{3 e^4}{32} + \frac{45 e^6}{1024}) \sin(2 \varphi) + (\frac{15 e^4}{256} + \frac{45 e^6}{1024}) \sin(4 \varphi) - (\frac{35 e^6}{3072}) \sin(6 \varphi) \right)$
One can now compute the XY coordinates as follows:
- $X = k_0 \left( N ( A + \frac{(1 - T + C) A^3}{6} + \frac{(5 - 18 T + T^2 + 72 C - 58 e^2) A^5}{120} ) \right) + 500000$
- $Y = k_0 \left( M + N \tan(\varphi) ( \frac{A^2}{2} + \frac{(5 - T + 9 C + 4 C^2) A^4}{24} + \frac{(61 - 58 T + T^2 + 600 C - 330 e^2) A^6}{720} ) \right)$
_NB: If the searched point is in the south, add_ $10,000,000$ _to_ $Y$ _to avoid negative coordinates._
With all these formulas, one is now able to build a full system placing any GPS or XY coordinates into a unique "carreau". This library implements one way to do it.
### Install
```console
$ git clone https://github.com/cyrildever/gridding.git
$ cd gridding/packages/py/
$ python3 -m venv venv
$ source venv/bin/activate
$ pip install build twine
```
### Usage
```console
pip install gridding-py
```
If you want to use the `from_address()` feature, you need to build or upload the [address repository](https://huggingface.co/datasets/cyrildever/gridding/blob/main/fr_address_repository.csv.gz).
Your one-line address must be compliant with the following guidelines:
- elements must be in the following order: `<numero> <repetitor> <voie> <lieu_dit> <cp> <ville>`;
- `<numero>` is the street number;
- `<repetitor>` is the eventual addition to the number, eg. `bis`, `ter`, ...;
- `<voie>` is the street name including its type;
- `<lieu_dit>` is a distinct locality (neither the city nor a postal box information);
- `<cp>` is the postal code in a full integer format (`2A000` must be transformed in `20000` for Corsica for example);
- `<ville>` is the city name (ideally without further information, ie. no `Arrondissement` or `Cedex` mentions).
For now, only French addresses are fully covered, but the library can work with any other country providing you build the corresponding repository.\
Feel free to add any normalizing tools through pull requests in the library to help enriching it.
#### 1) <u>Module</u>
To get the tile / "carreau" from GPS coordinates:
```python
from gridding import METER, WGS84, GPS, Grid, Resolution
grid = Grid(
Resolution(200, METER),
GPS(-5.151110, 41.316666),
WGS84(),
)
carreau, tile = grid.from_gps(my_point)
print(f"This GPS point belongs to the carreau with code: {carreau}, and coordinate: {tile.to_string()}")
```
To get it from a French postal address:
```python
from gridding import FR
carreau, tile = grid.from_address("9 boulevard Gouvion Saint-Cyr 75017 Paris", FR())
print(f"This address belongs to the carreau with code: {carreau}, and coordinate: {tile.to_string()}")
```
To get it from X/Y coordinates:
```python
from gridding import XY
my_point = XY(647872.07, 5110548.44, "UTM", "WGS84")
carreau, tile = grid.from_xy(my_point)
print(f"This X/Y point belongs to the carreau with code: {carreau}, and coordinate: {tile.to_string()}")
```
You may want to use the "distance" between two tiles (which returns a sort of average radius in tiles from one tile to the other):
```python
distance = Tile.Distance(tile1, tile2)
print(f"The radius between these two tiles is equal to {distance} tiles")
```
The idea here is to be able to easily know if a tile is within a certain tile distance of another, eg. two tiles away in each direction.
For now, only the `WGS-84` system is available and can be used in conjunction with the `UTM` projection if need be to get X/Y coordinates.
**IMPORTANT**: when using negative coordinates for a pivot point, be sure to give it a `0` as 6th decimal.
#### 2) <u>Script</u>
You may also use the main script to get the "carreau" from some GPS coordinates directly in a terminal, eg.
```
usage: python -m gridding [-h] -x LONGITUDE -y LATITUDE -r RESOLUTION [-o | --obfuscate | --no-obfuscate] [-t | --tile | --no-tile]
options:
-h, --help show this help message and exit
-x LONGITUDE, --longitude LONGITUDE
the longitude in decimal degrees
-y LATITUDE, --latitude LATITUDE
the latitude in decimal degrees
-r RESOLUTION, --resolution RESOLUTION
the grid resolution, eg. '200m'
-o, --obfuscate, --no-obfuscate
add to return a hashed result (default: no)
-t, --tile, --no-tile
add to return the tile coordinates instead of the carreau id (default: no)
```
_NB: The optional obfuscated result is a unique SHA-256 hexadecimal string._
### Tests
```console
$ pip install -e . && python3 -m unittest discover
```
### License
This module is distributed under a MIT license. \
See the [LICENSE](LICENSE) file.
<hr />
© 2024 Cyril Dever. All rights reserved.
Raw data
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"description": "# gridding\n_Build geographical grids in Python_\n\n\n\n\n\n\n\nThis is a Python library implementing the \"carroyage\" for geographical data.\n\n### Motivation\n\nIn order to be able to make analysis in the more granular level of the \"carreau\", this provides an easy reference to building custom grids by allowing to assign a unique tile / \"carreau\" ID to a geographical coordinate (latitude, longitude) or a French postal address.\n\nIndeed, the result of the computation gives the ID according to the [EU directive INSPIRE](https://www.insee.fr/fr/information/5008701?sommaire=5008710#titre-bloc-14) in the following format:\n`WGS84|RES200m|N2471400|E0486123`\nthat could be decomposed as a pipe-separated string with:\n- the projection system, eg. `WGS84`;\n- the resolution of the grid, ie. the size of the square, eg. `RES200m` for $200\\text{ m}$;\n- the bottom-left point of the grid's bounding box defined by:\n * its latitude in decimal degrees, eg. `N2471400` for $\\text{N }24.714000\u00b0$;\n * its longitude, eg. `E0486123` for $\\text{E }4.861230\u00b0$;\n\nas well as the coordinate in the grid in the form of `<row>.<column>` from the initial bottom-left point.\n\nIt would need as input parameters:\n- the coordinates of the initial point of the grid (by default the bottom-left point of the bounding box covering the French metropolitan territory: $\\text{N }41.316666\u00b0$ / $\\text{W }5.151110$);\n- the size and scale of the grid, eg. `200m`, `1km`, ...;\n- the projection system (default: `WGS84`).\n\nBelow are the calculation bases.\n\n### Geographic Information System (GIS) computations\n\n#### <u>Latitude</u>\n\nIn `WGS84`, one degree of latitude is almost equivalent to $111\\text{ km}$ everywhere on Earth.\n\nThe distance in meter, $D_{lat}$, for one degree in latitude is given by the following formula:\n```math\nD_{lat} = \\pi \\cdot \\frac{a (1 - e^2)}{(1 - e^2 \\sin^2(\\text{latitude}))^{3/2}} \\times \\frac{1}{180}\n```\nwhere\n- $a$ is the semi-major axis of the Earth's ellipsoid (in `WGS84`, $a = 6378137$);\n- $e$ is the excentricity of the ellipsoid, given by:\n```math\ne = \\sqrt{1 - \\frac{b^2}{a^2}}\n```\n (in `WGS84`, $b = 6356752.3142$)\n- $latitude$ is the latitude of the point in radians.\n\nFrom here, one can compute the degree in latitude for any size of tile / \"carreau\", eg. in `WGS84`, a \"carreau\" of height $200\\text{ m} \\approx 0.001796\u00b0$:\n\n```math\n\\Delta latitude = \\frac{distance}{D_{lat}}\n```\nwhere\n- $distance$ is the vertical distance to convert in degrees of latitude, eg. $200$;\n- $D_{lat}$ is the result of the computation above around the given $latitude$.\n\n#### <u>Longitude</u>\n\nThe variation of longitude as a function of latitude is calculated by taking into account the decrease in the distance between the meridians as one moves away from the equator. This decrease is due to the fact that the Earth is spherical.\n\nIn `WGS84`, the formula that allows one to calculate the distance corresponding to a degree of longitude as a function of a latitude is the following:\n```math\n\\Delta{longitude} = \\frac{distance}{D_{lon} \\times \\cos(latitude)}\n```\nwhere\n- $distance$ is the horizontal distance to convert in degrees of longitude, eg. $200$;\n- $latitude$ is the starting point expressed in radians, eg. $45\u00b0 = \\frac{\\pi}{4}$;\n- $D_{lon}$ is the result of the computation below at the given $latitude$:\n\n```math\nD_\\text{lon} = \\pi \\cdot a \\cdot \\cos(\\text{latitude}) \\cdot \\frac{1}{180} \\cdot \\frac{1}{\\sqrt{1 - e^2 \\sin^2(\\text{latitude})}}\n```\n\n#### <u>XY coordinates</u>\n\nThe UTM projection would be used to handle XY coordinates with the central longitude $\\lambda_0$ being automatically calculated for the UTM zone with the longitude of the searched point, _eg._ $-3\u00b0$ _for the UTM zone `30T` covering France from_ $W 6\u00b0$ _to_ $0\u00b0$.\n\nThe following data and formula would be used in that case: _eg. for `WGS84`_\n- $a = 6378137$\n- $e = 0.0818191908426$\n- $k_0 = 0.9996$\n- $\\varphi = latitude \\times \\frac{\\pi}{180}$\n- $\\lambda = longitude \\times \\frac{\\pi}{180}$\n- $N = \\frac{a}{\\sqrt{1 - e^2\\sin^2(\\phi)}}$\n- $T = \\tan^2(\\varphi)$\n- $C = \\frac{e^2\\cos^2(\\varphi)}{1 - e^2}$\n- $A = (\\lambda - \\lambda_0)\\cos(\\varphi)$\n- $M = a \\left( (1 - \\frac{e^2}{4} - \\frac{3 e^4}{64} - \\frac{5 e^6}{256}) \\varphi - (\\frac{3 e^2}{8} + \\frac{3 e^4}{32} + \\frac{45 e^6}{1024}) \\sin(2 \\varphi) + (\\frac{15 e^4}{256} + \\frac{45 e^6}{1024}) \\sin(4 \\varphi) - (\\frac{35 e^6}{3072}) \\sin(6 \\varphi) \\right)$\n\nOne can now compute the XY coordinates as follows:\n- $X = k_0 \\left( N ( A + \\frac{(1 - T + C) A^3}{6} + \\frac{(5 - 18 T + T^2 + 72 C - 58 e^2) A^5}{120} ) \\right) + 500000$\n- $Y = k_0 \\left( M + N \\tan(\\varphi) ( \\frac{A^2}{2} + \\frac{(5 - T + 9 C + 4 C^2) A^4}{24} + \\frac{(61 - 58 T + T^2 + 600 C - 330 e^2) A^6}{720} ) \\right)$\n\n_NB: If the searched point is in the south, add_ $10,000,000$ _to_ $Y$ _to avoid negative coordinates._\n\nWith all these formulas, one is now able to build a full system placing any GPS or XY coordinates into a unique \"carreau\". This library implements one way to do it.\n\n\n### Install\n\n```console\n$ git clone https://github.com/cyrildever/gridding.git\n$ cd gridding/packages/py/\n$ python3 -m venv venv\n$ source venv/bin/activate\n$ pip install build twine\n```\n\n\n### Usage\n\n```console\npip install gridding-py\n```\n\nIf you want to use the `from_address()` feature, you need to build or upload the [address repository](https://huggingface.co/datasets/cyrildever/gridding/blob/main/fr_address_repository.csv.gz).\n\nYour one-line address must be compliant with the following guidelines:\n- elements must be in the following order: `<numero> <repetitor> <voie> <lieu_dit> <cp> <ville>`;\n- `<numero>` is the street number;\n- `<repetitor>` is the eventual addition to the number, eg. `bis`, `ter`, ...;\n- `<voie>` is the street name including its type;\n- `<lieu_dit>` is a distinct locality (neither the city nor a postal box information);\n- `<cp>` is the postal code in a full integer format (`2A000` must be transformed in `20000` for Corsica for example);\n- `<ville>` is the city name (ideally without further information, ie. no `Arrondissement` or `Cedex` mentions).\n\nFor now, only French addresses are fully covered, but the library can work with any other country providing you build the corresponding repository.\\\nFeel free to add any normalizing tools through pull requests in the library to help enriching it.\n\n#### 1) <u>Module</u>\n\nTo get the tile / \"carreau\" from GPS coordinates:\n```python\nfrom gridding import METER, WGS84, GPS, Grid, Resolution\n\ngrid = Grid(\n Resolution(200, METER),\n GPS(-5.151110, 41.316666),\n WGS84(),\n)\ncarreau, tile = grid.from_gps(my_point)\nprint(f\"This GPS point belongs to the carreau with code: {carreau}, and coordinate: {tile.to_string()}\")\n```\n\nTo get it from a French postal address:\n```python\nfrom gridding import FR\n\ncarreau, tile = grid.from_address(\"9 boulevard Gouvion Saint-Cyr 75017 Paris\", FR())\nprint(f\"This address belongs to the carreau with code: {carreau}, and coordinate: {tile.to_string()}\")\n```\n\nTo get it from X/Y coordinates:\n```python\nfrom gridding import XY\n\nmy_point = XY(647872.07, 5110548.44, \"UTM\", \"WGS84\")\ncarreau, tile = grid.from_xy(my_point)\nprint(f\"This X/Y point belongs to the carreau with code: {carreau}, and coordinate: {tile.to_string()}\")\n```\n\nYou may want to use the \"distance\" between two tiles (which returns a sort of average radius in tiles from one tile to the other):\n```python\ndistance = Tile.Distance(tile1, tile2)\nprint(f\"The radius between these two tiles is equal to {distance} tiles\")\n```\nThe idea here is to be able to easily know if a tile is within a certain tile distance of another, eg. two tiles away in each direction.\n\nFor now, only the `WGS-84` system is available and can be used in conjunction with the `UTM` projection if need be to get X/Y coordinates.\n\n**IMPORTANT**: when using negative coordinates for a pivot point, be sure to give it a `0` as 6th decimal.\n\n#### 2) <u>Script</u>\n\nYou may also use the main script to get the \"carreau\" from some GPS coordinates directly in a terminal, eg.\n```\nusage: python -m gridding [-h] -x LONGITUDE -y LATITUDE -r RESOLUTION [-o | --obfuscate | --no-obfuscate] [-t | --tile | --no-tile]\n\noptions:\n -h, --help show this help message and exit\n -x LONGITUDE, --longitude LONGITUDE\n the longitude in decimal degrees\n -y LATITUDE, --latitude LATITUDE\n the latitude in decimal degrees\n -r RESOLUTION, --resolution RESOLUTION\n the grid resolution, eg. '200m'\n -o, --obfuscate, --no-obfuscate\n add to return a hashed result (default: no)\n -t, --tile, --no-tile\n add to return the tile coordinates instead of the carreau id (default: no)\n```\n_NB: The optional obfuscated result is a unique SHA-256 hexadecimal string._\n\n\n### Tests\n\n```console\n$ pip install -e . && python3 -m unittest discover\n```\n\n\n### License\n\nThis module is distributed under a MIT license. \\\nSee the [LICENSE](LICENSE) file.\n\n\n<hr />\n© 2024 Cyril Dever. All rights reserved.\n",
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