Calculating square meter area with polygonal geographical coordinates (metric - not DMS system)
$begingroup$
I'm working on a program but my problem is not on software side but mathematical.
I have the following input :
{
"type":"Feature",
"id":"64100000BA0033",
"geometry":{
"type":"Polygon",
"coordinates":[
[
[
-1.4796836,
43.4414704
],
[
-1.4796624,
43.441522
],
[
-1.4797672,
43.4415449
],
[
-1.4797607,
43.4415605
],
[
-1.47976,
43.4415624
],
[
-1.4798095,
43.4415732
],
[
-1.479838,
43.4415041
],
[
-1.4796836,
43.4414704
]
]
]
},
"properties":{
"id":"64100000BA0033",
"commune":"64100",
"prefixe":"000",
"section":"BA",
"numero":"33",
"contenance":87,
"created":"2004-10-14",
"updated":"2018-01-19"
}
}
This input is, as you can imagine, variable (nbr of points) for every land available in my region. I'd need to know what is the formula to get the area in m² (square meters) from these coordinates.
I hope you can help me.
Thanks !
coordinate-systems area polygons
asked Nov 25 '18 at 12:06
JeanneD4RKJeanneD4RK
61
$endgroup$
add a comment |
$begingroup$
I'm working on a program but my problem is not on software side but mathematical.
I have the following input :
{
"type":"Feature",
"id":"64100000BA0033",
"geometry":{
"type":"Polygon",
"coordinates":[
[
[
-1.4796836,
43.4414704
],
[
-1.4796624,
43.441522
],
[
-1.4797672,
43.4415449
],
[
-1.4797607,
43.4415605
],
[
-1.47976,
43.4415624
],
[
-1.4798095,
43.4415732
],
[
-1.479838,
43.4415041
],
[
-1.4796836,
43.4414704
]
]
]
},
"properties":{
"id":"64100000BA0033",
"commune":"64100",
"prefixe":"000",
"section":"BA",
"numero":"33",
"contenance":87,
"created":"2004-10-14",
"updated":"2018-01-19"
}
}
This input is, as you can imagine, variable (nbr of points) for every land available in my region. I'd need to know what is the formula to get the area in m² (square meters) from these coordinates.
I hope you can help me.
Thanks !
coordinate-systems area polygons
asked Nov 25 '18 at 12:06
JeanneD4RKJeanneD4RK
61
$endgroup$
$begingroup$
What are the units for these coordinates? Without this, no conversion is possible.
$endgroup$
– MPW
Nov 25 '18 at 12:22
$begingroup$
It's decimal degrees
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:51
$begingroup$
Note that if those are latitude and longitude degrees, then they are equal only at the equator. That is, a degree of longitude relative to degree of latitude needs a factor of cosine of latitude.
$endgroup$
– Somos
Nov 25 '18 at 13:32
$begingroup$
I know. But I don't know the formula unfortunately
$endgroup$
– JeanneD4RK
Nov 25 '18 at 13:42
add a comment |
$begingroup$
I'm working on a program but my problem is not on software side but mathematical.
I have the following input :
{
"type":"Feature",
"id":"64100000BA0033",
"geometry":{
"type":"Polygon",
"coordinates":[
[
[
-1.4796836,
43.4414704
],
[
-1.4796624,
43.441522
],
[
-1.4797672,
43.4415449
],
[
-1.4797607,
43.4415605
],
[
-1.47976,
43.4415624
],
[
-1.4798095,
43.4415732
],
[
-1.479838,
43.4415041
],
[
-1.4796836,
43.4414704
]
]
]
},
"properties":{
"id":"64100000BA0033",
"commune":"64100",
"prefixe":"000",
"section":"BA",
"numero":"33",
"contenance":87,
"created":"2004-10-14",
"updated":"2018-01-19"
}
}
This input is, as you can imagine, variable (nbr of points) for every land available in my region. I'd need to know what is the formula to get the area in m² (square meters) from these coordinates.
I hope you can help me.
Thanks !
coordinate-systems area polygons
asked Nov 25 '18 at 12:06
JeanneD4RKJeanneD4RK
61
$endgroup$
I'm working on a program but my problem is not on software side but mathematical.
I have the following input :
{
"type":"Feature",
"id":"64100000BA0033",
"geometry":{
"type":"Polygon",
"coordinates":[
[
[
-1.4796836,
43.4414704
],
[
-1.4796624,
43.441522
],
[
-1.4797672,
43.4415449
],
[
-1.4797607,
43.4415605
],
[
-1.47976,
43.4415624
],
[
-1.4798095,
43.4415732
],
[
-1.479838,
43.4415041
],
[
-1.4796836,
43.4414704
]
]
]
},
"properties":{
"id":"64100000BA0033",
"commune":"64100",
"prefixe":"000",
"section":"BA",
"numero":"33",
"contenance":87,
"created":"2004-10-14",
"updated":"2018-01-19"
}
}
This input is, as you can imagine, variable (nbr of points) for every land available in my region. I'd need to know what is the formula to get the area in m² (square meters) from these coordinates.
I hope you can help me.
Thanks !
coordinate-systems area polygons
coordinate-systems area polygons
asked Nov 25 '18 at 12:06
JeanneD4RKJeanneD4RK
61
asked Nov 25 '18 at 12:06
JeanneD4RKJeanneD4RK
61
asked Nov 25 '18 at 12:06
JeanneD4RKJeanneD4RK
61
asked Nov 25 '18 at 12:06
JeanneD4RKJeanneD4RK
61
asked Nov 25 '18 at 12:06
JeanneD4RKJeanneD4RK
61
61
$begingroup$
What are the units for these coordinates? Without this, no conversion is possible.
$endgroup$
– MPW
Nov 25 '18 at 12:22
$begingroup$
It's decimal degrees
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:51
$begingroup$
Note that if those are latitude and longitude degrees, then they are equal only at the equator. That is, a degree of longitude relative to degree of latitude needs a factor of cosine of latitude.
$endgroup$
– Somos
Nov 25 '18 at 13:32
$begingroup$
I know. But I don't know the formula unfortunately
$endgroup$
– JeanneD4RK
Nov 25 '18 at 13:42
add a comment |
$begingroup$
What are the units for these coordinates? Without this, no conversion is possible.
$endgroup$
– MPW
Nov 25 '18 at 12:22
$begingroup$
It's decimal degrees
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:51
$begingroup$
Note that if those are latitude and longitude degrees, then they are equal only at the equator. That is, a degree of longitude relative to degree of latitude needs a factor of cosine of latitude.
$endgroup$
– Somos
Nov 25 '18 at 13:32
$begingroup$
I know. But I don't know the formula unfortunately
$endgroup$
– JeanneD4RK
Nov 25 '18 at 13:42
$begingroup$
What are the units for these coordinates? Without this, no conversion is possible.
$endgroup$
– MPW
Nov 25 '18 at 12:22
$begingroup$
What are the units for these coordinates? Without this, no conversion is possible.
$endgroup$
– MPW
Nov 25 '18 at 12:22
$begingroup$
It's decimal degrees
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:51
$begingroup$
It's decimal degrees
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:51
$begingroup$
Note that if those are latitude and longitude degrees, then they are equal only at the equator. That is, a degree of longitude relative to degree of latitude needs a factor of cosine of latitude.
$endgroup$
– Somos
Nov 25 '18 at 13:32
$begingroup$
Note that if those are latitude and longitude degrees, then they are equal only at the equator. That is, a degree of longitude relative to degree of latitude needs a factor of cosine of latitude.
$endgroup$
– Somos
Nov 25 '18 at 13:32
$begingroup$
I know. But I don't know the formula unfortunately
$endgroup$
– JeanneD4RK
Nov 25 '18 at 13:42
$begingroup$
I know. But I don't know the formula unfortunately
$endgroup$
– JeanneD4RK
Nov 25 '18 at 13:42
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The formula/algorithm you are looking for can be found here: https://en.wikipedia.org/wiki/Shoelace_formula
Some comments for your application:
1) To apply the formula you need to be sure that the order the points are given corresponds to the order they form the outer border of the area you want to measure.
2) Your input data does not to mention units, so you have to make sure to get the conversion right. From the data it looks like the unit is something much bigger than m, maybe km or miles or something else (maybe some angles from a spherical coordinate system; make sure you completely understand what those numbers mean).
3) Make sure to use enough precision in the numerics, as the values are all very much the same and once you start subtracting them your remaining precision will go down much.
answered Nov 25 '18 at 12:27
IngixIngix
3,389146
$endgroup$
1
$begingroup$
4) The shoelace formula is only valid in a plane, make sure the approximation is not too coarse when applied to a spherical surface (ok if the region is small).
$endgroup$
– Jean-Claude Arbaut
Nov 25 '18 at 12:31
$begingroup$
Yes, the points are sorted. The unit is Decimal Degrees. Since I'll only apply this to small areas (500 - 5000 m²) I can use a plane surface formula. Maybe getting the average between 2 points, get the length of 1 degree at this average point, multiply thids length by the distance in deg (0.00???) of these two points and I'll have something accurate enough with the shoelace formula, right ?
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:54
$begingroup$
Yes, at those close ranges anything like this will produce something that is accurate enough.
$endgroup$
– Ingix
Nov 25 '18 at 13:04
add a comment |
Your Answer
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The formula/algorithm you are looking for can be found here: https://en.wikipedia.org/wiki/Shoelace_formula
Some comments for your application:
1) To apply the formula you need to be sure that the order the points are given corresponds to the order they form the outer border of the area you want to measure.
2) Your input data does not to mention units, so you have to make sure to get the conversion right. From the data it looks like the unit is something much bigger than m, maybe km or miles or something else (maybe some angles from a spherical coordinate system; make sure you completely understand what those numbers mean).
3) Make sure to use enough precision in the numerics, as the values are all very much the same and once you start subtracting them your remaining precision will go down much.
answered Nov 25 '18 at 12:27
IngixIngix
3,389146
$endgroup$
1
$begingroup$
4) The shoelace formula is only valid in a plane, make sure the approximation is not too coarse when applied to a spherical surface (ok if the region is small).
$endgroup$
– Jean-Claude Arbaut
Nov 25 '18 at 12:31
$begingroup$
Yes, the points are sorted. The unit is Decimal Degrees. Since I'll only apply this to small areas (500 - 5000 m²) I can use a plane surface formula. Maybe getting the average between 2 points, get the length of 1 degree at this average point, multiply thids length by the distance in deg (0.00???) of these two points and I'll have something accurate enough with the shoelace formula, right ?
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:54
$begingroup$
Yes, at those close ranges anything like this will produce something that is accurate enough.
$endgroup$
– Ingix
Nov 25 '18 at 13:04
add a comment |
$begingroup$
The formula/algorithm you are looking for can be found here: https://en.wikipedia.org/wiki/Shoelace_formula
Some comments for your application:
1) To apply the formula you need to be sure that the order the points are given corresponds to the order they form the outer border of the area you want to measure.
2) Your input data does not to mention units, so you have to make sure to get the conversion right. From the data it looks like the unit is something much bigger than m, maybe km or miles or something else (maybe some angles from a spherical coordinate system; make sure you completely understand what those numbers mean).
3) Make sure to use enough precision in the numerics, as the values are all very much the same and once you start subtracting them your remaining precision will go down much.
answered Nov 25 '18 at 12:27
IngixIngix
3,389146
$endgroup$
1
$begingroup$
4) The shoelace formula is only valid in a plane, make sure the approximation is not too coarse when applied to a spherical surface (ok if the region is small).
$endgroup$
– Jean-Claude Arbaut
Nov 25 '18 at 12:31
$begingroup$
Yes, the points are sorted. The unit is Decimal Degrees. Since I'll only apply this to small areas (500 - 5000 m²) I can use a plane surface formula. Maybe getting the average between 2 points, get the length of 1 degree at this average point, multiply thids length by the distance in deg (0.00???) of these two points and I'll have something accurate enough with the shoelace formula, right ?
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:54
$begingroup$
Yes, at those close ranges anything like this will produce something that is accurate enough.
$endgroup$
– Ingix
Nov 25 '18 at 13:04
add a comment |
$begingroup$
The formula/algorithm you are looking for can be found here: https://en.wikipedia.org/wiki/Shoelace_formula
Some comments for your application:
1) To apply the formula you need to be sure that the order the points are given corresponds to the order they form the outer border of the area you want to measure.
2) Your input data does not to mention units, so you have to make sure to get the conversion right. From the data it looks like the unit is something much bigger than m, maybe km or miles or something else (maybe some angles from a spherical coordinate system; make sure you completely understand what those numbers mean).
3) Make sure to use enough precision in the numerics, as the values are all very much the same and once you start subtracting them your remaining precision will go down much.
answered Nov 25 '18 at 12:27
IngixIngix
3,389146
$endgroup$
The formula/algorithm you are looking for can be found here: https://en.wikipedia.org/wiki/Shoelace_formula
Some comments for your application:
1) To apply the formula you need to be sure that the order the points are given corresponds to the order they form the outer border of the area you want to measure.
2) Your input data does not to mention units, so you have to make sure to get the conversion right. From the data it looks like the unit is something much bigger than m, maybe km or miles or something else (maybe some angles from a spherical coordinate system; make sure you completely understand what those numbers mean).
3) Make sure to use enough precision in the numerics, as the values are all very much the same and once you start subtracting them your remaining precision will go down much.
answered Nov 25 '18 at 12:27
IngixIngix
3,389146
answered Nov 25 '18 at 12:27
IngixIngix
3,389146
answered Nov 25 '18 at 12:27
IngixIngix
3,389146
answered Nov 25 '18 at 12:27
IngixIngix
3,389146
3,389146
1
$begingroup$
4) The shoelace formula is only valid in a plane, make sure the approximation is not too coarse when applied to a spherical surface (ok if the region is small).
$endgroup$
– Jean-Claude Arbaut
Nov 25 '18 at 12:31
$begingroup$
Yes, the points are sorted. The unit is Decimal Degrees. Since I'll only apply this to small areas (500 - 5000 m²) I can use a plane surface formula. Maybe getting the average between 2 points, get the length of 1 degree at this average point, multiply thids length by the distance in deg (0.00???) of these two points and I'll have something accurate enough with the shoelace formula, right ?
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:54
$begingroup$
Yes, at those close ranges anything like this will produce something that is accurate enough.
$endgroup$
– Ingix
Nov 25 '18 at 13:04
add a comment |
1
$begingroup$
4) The shoelace formula is only valid in a plane, make sure the approximation is not too coarse when applied to a spherical surface (ok if the region is small).
$endgroup$
– Jean-Claude Arbaut
Nov 25 '18 at 12:31
$begingroup$
Yes, the points are sorted. The unit is Decimal Degrees. Since I'll only apply this to small areas (500 - 5000 m²) I can use a plane surface formula. Maybe getting the average between 2 points, get the length of 1 degree at this average point, multiply thids length by the distance in deg (0.00???) of these two points and I'll have something accurate enough with the shoelace formula, right ?
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:54
$begingroup$
Yes, at those close ranges anything like this will produce something that is accurate enough.
$endgroup$
– Ingix
Nov 25 '18 at 13:04
1
1
$begingroup$
4) The shoelace formula is only valid in a plane, make sure the approximation is not too coarse when applied to a spherical surface (ok if the region is small).
$endgroup$
– Jean-Claude Arbaut
Nov 25 '18 at 12:31
$begingroup$
4) The shoelace formula is only valid in a plane, make sure the approximation is not too coarse when applied to a spherical surface (ok if the region is small).
$endgroup$
– Jean-Claude Arbaut
Nov 25 '18 at 12:31
$begingroup$
Yes, the points are sorted. The unit is Decimal Degrees. Since I'll only apply this to small areas (500 - 5000 m²) I can use a plane surface formula. Maybe getting the average between 2 points, get the length of 1 degree at this average point, multiply thids length by the distance in deg (0.00???) of these two points and I'll have something accurate enough with the shoelace formula, right ?
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:54
$begingroup$
Yes, the points are sorted. The unit is Decimal Degrees. Since I'll only apply this to small areas (500 - 5000 m²) I can use a plane surface formula. Maybe getting the average between 2 points, get the length of 1 degree at this average point, multiply thids length by the distance in deg (0.00???) of these two points and I'll have something accurate enough with the shoelace formula, right ?
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:54
$begingroup$
Yes, at those close ranges anything like this will produce something that is accurate enough.
$endgroup$
– Ingix
Nov 25 '18 at 13:04
$begingroup$
Yes, at those close ranges anything like this will produce something that is accurate enough.
$endgroup$
– Ingix
Nov 25 '18 at 13:04
add a comment |
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$begingroup$
What are the units for these coordinates? Without this, no conversion is possible.
$endgroup$
– MPW
Nov 25 '18 at 12:22
$begingroup$
It's decimal degrees
$endgroup$
– JeanneD4RK
Nov 25 '18 at 12:51
$begingroup$
Note that if those are latitude and longitude degrees, then they are equal only at the equator. That is, a degree of longitude relative to degree of latitude needs a factor of cosine of latitude.
$endgroup$
– Somos
Nov 25 '18 at 13:32
$begingroup$
I know. But I don't know the formula unfortunately
$endgroup$
– JeanneD4RK
Nov 25 '18 at 13:42