Find the middle in the path
$begingroup$
I have to find a midpoint in a coordinates set. Let's suppose I have the following GeoJSON with coordinates
{
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"geometry": {
"type": "LineString",
"coordinates": [
[
18.060101866722107,
59.33226461448578
],
[
18.0600106716156,
59.33233028244786
],
[
18.05976927280426,
59.332565591603085
],
[
18.059420585632324,
59.33292676062448
],
[
18.05930256843567,
59.3329869550881
],
[
18.06055784225464,
59.333318022731746
],
[
18.060520291328427,
59.3333453835497
]
]
}
}
]
}
The coordinates are located on the streets as you can see at the image below (I used geojson.io to draw it):
I was able to calculate midpoint only between two coordinates, but in described case there are 7 coordinates and each coordinate has to be taken into account during calculation because the midpoint must be located at the route that is build by coordinates.
In order to calculate midpoint between two coordinates I used the following formula:
Bx = cos φ2 ⋅ cos Δλ
By = cos φ2 ⋅ sin Δλ
φm = atan2( sin φ1 + sin φ2, √(cos φ1 + Bx)² + By² )
λm = λ1 + atan2(By, cos(φ1)+Bx)
where φ is latitude, λ is longitude
How can I calculate midpoint for case with several coordinates?
Appreciate for your help!
coordinate-systems
asked Dec 10 '18 at 17:12
Bohdan KorinnyiBohdan Korinnyi
1033
$endgroup$
add a comment |
$begingroup$
I have to find a midpoint in a coordinates set. Let's suppose I have the following GeoJSON with coordinates
{
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"geometry": {
"type": "LineString",
"coordinates": [
[
18.060101866722107,
59.33226461448578
],
[
18.0600106716156,
59.33233028244786
],
[
18.05976927280426,
59.332565591603085
],
[
18.059420585632324,
59.33292676062448
],
[
18.05930256843567,
59.3329869550881
],
[
18.06055784225464,
59.333318022731746
],
[
18.060520291328427,
59.3333453835497
]
]
}
}
]
}
The coordinates are located on the streets as you can see at the image below (I used geojson.io to draw it):
I was able to calculate midpoint only between two coordinates, but in described case there are 7 coordinates and each coordinate has to be taken into account during calculation because the midpoint must be located at the route that is build by coordinates.
In order to calculate midpoint between two coordinates I used the following formula:
Bx = cos φ2 ⋅ cos Δλ
By = cos φ2 ⋅ sin Δλ
φm = atan2( sin φ1 + sin φ2, √(cos φ1 + Bx)² + By² )
λm = λ1 + atan2(By, cos(φ1)+Bx)
where φ is latitude, λ is longitude
How can I calculate midpoint for case with several coordinates?
Appreciate for your help!
coordinate-systems
asked Dec 10 '18 at 17:12
Bohdan KorinnyiBohdan Korinnyi
1033
$endgroup$
$begingroup$
I don't know what a "midpoint of a set of coordinates" would be. But what you showed on the map is not just a set of coordinates; it is a path that goes through some coordinates in sequence. Is the "midpoint" meant to be the point on that path so that it divides the path into two pieces of equal length?
$endgroup$
– David K
Dec 10 '18 at 18:35
$begingroup$
@DavidK yes, exactly!
$endgroup$
– Bohdan Korinnyi
Dec 10 '18 at 20:24
1
$begingroup$
It looks like you are assuming you will be creating a path travelling in straight lines from one point to the next one after another. Keep a tally of distance traveled at each point. Find the two points where have the total distance is between those points and the proportion thereof.
$endgroup$
– fleablood
Dec 10 '18 at 20:36
add a comment |
$begingroup$
I have to find a midpoint in a coordinates set. Let's suppose I have the following GeoJSON with coordinates
{
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"geometry": {
"type": "LineString",
"coordinates": [
[
18.060101866722107,
59.33226461448578
],
[
18.0600106716156,
59.33233028244786
],
[
18.05976927280426,
59.332565591603085
],
[
18.059420585632324,
59.33292676062448
],
[
18.05930256843567,
59.3329869550881
],
[
18.06055784225464,
59.333318022731746
],
[
18.060520291328427,
59.3333453835497
]
]
}
}
]
}
The coordinates are located on the streets as you can see at the image below (I used geojson.io to draw it):
I was able to calculate midpoint only between two coordinates, but in described case there are 7 coordinates and each coordinate has to be taken into account during calculation because the midpoint must be located at the route that is build by coordinates.
In order to calculate midpoint between two coordinates I used the following formula:
Bx = cos φ2 ⋅ cos Δλ
By = cos φ2 ⋅ sin Δλ
φm = atan2( sin φ1 + sin φ2, √(cos φ1 + Bx)² + By² )
λm = λ1 + atan2(By, cos(φ1)+Bx)
where φ is latitude, λ is longitude
How can I calculate midpoint for case with several coordinates?
Appreciate for your help!
coordinate-systems
asked Dec 10 '18 at 17:12
Bohdan KorinnyiBohdan Korinnyi
1033
$endgroup$
I have to find a midpoint in a coordinates set. Let's suppose I have the following GeoJSON with coordinates
{
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"geometry": {
"type": "LineString",
"coordinates": [
[
18.060101866722107,
59.33226461448578
],
[
18.0600106716156,
59.33233028244786
],
[
18.05976927280426,
59.332565591603085
],
[
18.059420585632324,
59.33292676062448
],
[
18.05930256843567,
59.3329869550881
],
[
18.06055784225464,
59.333318022731746
],
[
18.060520291328427,
59.3333453835497
]
]
}
}
]
}
The coordinates are located on the streets as you can see at the image below (I used geojson.io to draw it):
I was able to calculate midpoint only between two coordinates, but in described case there are 7 coordinates and each coordinate has to be taken into account during calculation because the midpoint must be located at the route that is build by coordinates.
In order to calculate midpoint between two coordinates I used the following formula:
Bx = cos φ2 ⋅ cos Δλ
By = cos φ2 ⋅ sin Δλ
φm = atan2( sin φ1 + sin φ2, √(cos φ1 + Bx)² + By² )
λm = λ1 + atan2(By, cos(φ1)+Bx)
where φ is latitude, λ is longitude
How can I calculate midpoint for case with several coordinates?
Appreciate for your help!
coordinate-systems
coordinate-systems
asked Dec 10 '18 at 17:12
Bohdan KorinnyiBohdan Korinnyi
1033
asked Dec 10 '18 at 17:12
Bohdan KorinnyiBohdan Korinnyi
1033
edited Dec 10 '18 at 20:25
Bohdan Korinnyi
asked Dec 10 '18 at 17:12
Bohdan KorinnyiBohdan Korinnyi
1033
asked Dec 10 '18 at 17:12
Bohdan KorinnyiBohdan Korinnyi
1033
asked Dec 10 '18 at 17:12
Bohdan KorinnyiBohdan Korinnyi
1033
1033
$begingroup$
I don't know what a "midpoint of a set of coordinates" would be. But what you showed on the map is not just a set of coordinates; it is a path that goes through some coordinates in sequence. Is the "midpoint" meant to be the point on that path so that it divides the path into two pieces of equal length?
$endgroup$
– David K
Dec 10 '18 at 18:35
$begingroup$
@DavidK yes, exactly!
$endgroup$
– Bohdan Korinnyi
Dec 10 '18 at 20:24
1
$begingroup$
It looks like you are assuming you will be creating a path travelling in straight lines from one point to the next one after another. Keep a tally of distance traveled at each point. Find the two points where have the total distance is between those points and the proportion thereof.
$endgroup$
– fleablood
Dec 10 '18 at 20:36
add a comment |
$begingroup$
I don't know what a "midpoint of a set of coordinates" would be. But what you showed on the map is not just a set of coordinates; it is a path that goes through some coordinates in sequence. Is the "midpoint" meant to be the point on that path so that it divides the path into two pieces of equal length?
$endgroup$
– David K
Dec 10 '18 at 18:35
$begingroup$
@DavidK yes, exactly!
$endgroup$
– Bohdan Korinnyi
Dec 10 '18 at 20:24
1
$begingroup$
It looks like you are assuming you will be creating a path travelling in straight lines from one point to the next one after another. Keep a tally of distance traveled at each point. Find the two points where have the total distance is between those points and the proportion thereof.
$endgroup$
– fleablood
Dec 10 '18 at 20:36
$begingroup$
I don't know what a "midpoint of a set of coordinates" would be. But what you showed on the map is not just a set of coordinates; it is a path that goes through some coordinates in sequence. Is the "midpoint" meant to be the point on that path so that it divides the path into two pieces of equal length?
$endgroup$
– David K
Dec 10 '18 at 18:35
$begingroup$
I don't know what a "midpoint of a set of coordinates" would be. But what you showed on the map is not just a set of coordinates; it is a path that goes through some coordinates in sequence. Is the "midpoint" meant to be the point on that path so that it divides the path into two pieces of equal length?
$endgroup$
– David K
Dec 10 '18 at 18:35
$begingroup$
@DavidK yes, exactly!
$endgroup$
– Bohdan Korinnyi
Dec 10 '18 at 20:24
$begingroup$
@DavidK yes, exactly!
$endgroup$
– Bohdan Korinnyi
Dec 10 '18 at 20:24
1
1
$begingroup$
It looks like you are assuming you will be creating a path travelling in straight lines from one point to the next one after another. Keep a tally of distance traveled at each point. Find the two points where have the total distance is between those points and the proportion thereof.
$endgroup$
– fleablood
Dec 10 '18 at 20:36
$begingroup$
It looks like you are assuming you will be creating a path travelling in straight lines from one point to the next one after another. Keep a tally of distance traveled at each point. Find the two points where have the total distance is between those points and the proportion thereof.
$endgroup$
– fleablood
Dec 10 '18 at 20:36
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
There's no such thing as a midpoint between points. There is a midpoint of a segment between to endpoints. And a midpoint of a curved path.
It sounds to me you are travel from point to point and want to find the point where you've traveled half the difference.
Keep tally of distance travelled
Point A: 18.060101866722107,
59.33226461448578. Distance traveled = $0$.
Point B: 18.0600106716156,
59.33233028244786. Distance traveled Between A and B = $1.1237806144690070986243816541936e-4$
Point C: 18.05976927280426,
59.332565591603085. Distance traveled Between B and C = $3.3711093819256007255265270932638e-4$ Total so far $4.4948899963946078241509087474574e-4$.
Point D: 18.059420585632324,
59.33292676062448
Distance traveled between C and D = $5.0202171854228338129392415486338e-4$ Totals so far = $9.5151071818174416370901502960912e-4$
And I'm going to quit because this is a pain.
Half the total distance is: $4.7575535909087208185450751480456e-4$
That occurs somewher between point $C$ and $D$.
At point $C$ we have traveled: $4.4948899963946078241509087474574e-4$ and we need to travel $2.6266359451411299439416640058822e-5$ more.
The total distance between $C$ and $D$ is $5.0202171854228338129392415486338e-4$ so we need to travel $frac {2.6266359451411299439416640058822e-5}{5.0202171854228338129392415486338e-4} =0.05232116157779134771573009976586$ of that distance.
So $x = C_x + (D_x - C_x)cdot 0.05232116157779134771573009976586$ =
$18.05976927280426 + (18.059420585632324-18.05976927280426)cdot 0.05232116157779134771573009976586= 18.05975102908640$
And $x = C_y + (D_y - Cy)cdot 0.05232116157779134771573009976586=$
$59.332565591603085+(59.33292676062448-59.332565591603085)cdot 0.05232116157779134771573009976586=59.332584488385810301$
Of course this is only one interpretation. A more common interpretation would be the point, $p$ where the sum of the distances from $p$ to points A,B,C, D are least.
answered Dec 10 '18 at 21:05
fleabloodfleablood
69.6k22685
$endgroup$
$begingroup$
Okay, I assumed flat space linear distance. You'd use the trig distance for your tally and a trig calculation to find the proportion between the two but it's the same idea.
$endgroup$
– fleablood
Dec 10 '18 at 21:07
$begingroup$
thanks, I was able to solve the problem using PostGIS functionst_lineInterpolatePoint.
$endgroup$
– Bohdan Korinnyi
Dec 13 '18 at 7:15
add a comment |
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1 Answer
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$begingroup$
There's no such thing as a midpoint between points. There is a midpoint of a segment between to endpoints. And a midpoint of a curved path.
It sounds to me you are travel from point to point and want to find the point where you've traveled half the difference.
Keep tally of distance travelled
Point A: 18.060101866722107,
59.33226461448578. Distance traveled = $0$.
Point B: 18.0600106716156,
59.33233028244786. Distance traveled Between A and B = $1.1237806144690070986243816541936e-4$
Point C: 18.05976927280426,
59.332565591603085. Distance traveled Between B and C = $3.3711093819256007255265270932638e-4$ Total so far $4.4948899963946078241509087474574e-4$.
Point D: 18.059420585632324,
59.33292676062448
Distance traveled between C and D = $5.0202171854228338129392415486338e-4$ Totals so far = $9.5151071818174416370901502960912e-4$
And I'm going to quit because this is a pain.
Half the total distance is: $4.7575535909087208185450751480456e-4$
That occurs somewher between point $C$ and $D$.
At point $C$ we have traveled: $4.4948899963946078241509087474574e-4$ and we need to travel $2.6266359451411299439416640058822e-5$ more.
The total distance between $C$ and $D$ is $5.0202171854228338129392415486338e-4$ so we need to travel $frac {2.6266359451411299439416640058822e-5}{5.0202171854228338129392415486338e-4} =0.05232116157779134771573009976586$ of that distance.
So $x = C_x + (D_x - C_x)cdot 0.05232116157779134771573009976586$ =
$18.05976927280426 + (18.059420585632324-18.05976927280426)cdot 0.05232116157779134771573009976586= 18.05975102908640$
And $x = C_y + (D_y - Cy)cdot 0.05232116157779134771573009976586=$
$59.332565591603085+(59.33292676062448-59.332565591603085)cdot 0.05232116157779134771573009976586=59.332584488385810301$
Of course this is only one interpretation. A more common interpretation would be the point, $p$ where the sum of the distances from $p$ to points A,B,C, D are least.
answered Dec 10 '18 at 21:05
fleabloodfleablood
69.6k22685
$endgroup$
$begingroup$
Okay, I assumed flat space linear distance. You'd use the trig distance for your tally and a trig calculation to find the proportion between the two but it's the same idea.
$endgroup$
– fleablood
Dec 10 '18 at 21:07
$begingroup$
thanks, I was able to solve the problem using PostGIS functionst_lineInterpolatePoint.
$endgroup$
– Bohdan Korinnyi
Dec 13 '18 at 7:15
add a comment |
$begingroup$
There's no such thing as a midpoint between points. There is a midpoint of a segment between to endpoints. And a midpoint of a curved path.
It sounds to me you are travel from point to point and want to find the point where you've traveled half the difference.
Keep tally of distance travelled
Point A: 18.060101866722107,
59.33226461448578. Distance traveled = $0$.
Point B: 18.0600106716156,
59.33233028244786. Distance traveled Between A and B = $1.1237806144690070986243816541936e-4$
Point C: 18.05976927280426,
59.332565591603085. Distance traveled Between B and C = $3.3711093819256007255265270932638e-4$ Total so far $4.4948899963946078241509087474574e-4$.
Point D: 18.059420585632324,
59.33292676062448
Distance traveled between C and D = $5.0202171854228338129392415486338e-4$ Totals so far = $9.5151071818174416370901502960912e-4$
And I'm going to quit because this is a pain.
Half the total distance is: $4.7575535909087208185450751480456e-4$
That occurs somewher between point $C$ and $D$.
At point $C$ we have traveled: $4.4948899963946078241509087474574e-4$ and we need to travel $2.6266359451411299439416640058822e-5$ more.
The total distance between $C$ and $D$ is $5.0202171854228338129392415486338e-4$ so we need to travel $frac {2.6266359451411299439416640058822e-5}{5.0202171854228338129392415486338e-4} =0.05232116157779134771573009976586$ of that distance.
So $x = C_x + (D_x - C_x)cdot 0.05232116157779134771573009976586$ =
$18.05976927280426 + (18.059420585632324-18.05976927280426)cdot 0.05232116157779134771573009976586= 18.05975102908640$
And $x = C_y + (D_y - Cy)cdot 0.05232116157779134771573009976586=$
$59.332565591603085+(59.33292676062448-59.332565591603085)cdot 0.05232116157779134771573009976586=59.332584488385810301$
Of course this is only one interpretation. A more common interpretation would be the point, $p$ where the sum of the distances from $p$ to points A,B,C, D are least.
answered Dec 10 '18 at 21:05
fleabloodfleablood
69.6k22685
$endgroup$
$begingroup$
Okay, I assumed flat space linear distance. You'd use the trig distance for your tally and a trig calculation to find the proportion between the two but it's the same idea.
$endgroup$
– fleablood
Dec 10 '18 at 21:07
$begingroup$
thanks, I was able to solve the problem using PostGIS functionst_lineInterpolatePoint.
$endgroup$
– Bohdan Korinnyi
Dec 13 '18 at 7:15
add a comment |
$begingroup$
There's no such thing as a midpoint between points. There is a midpoint of a segment between to endpoints. And a midpoint of a curved path.
It sounds to me you are travel from point to point and want to find the point where you've traveled half the difference.
Keep tally of distance travelled
Point A: 18.060101866722107,
59.33226461448578. Distance traveled = $0$.
Point B: 18.0600106716156,
59.33233028244786. Distance traveled Between A and B = $1.1237806144690070986243816541936e-4$
Point C: 18.05976927280426,
59.332565591603085. Distance traveled Between B and C = $3.3711093819256007255265270932638e-4$ Total so far $4.4948899963946078241509087474574e-4$.
Point D: 18.059420585632324,
59.33292676062448
Distance traveled between C and D = $5.0202171854228338129392415486338e-4$ Totals so far = $9.5151071818174416370901502960912e-4$
And I'm going to quit because this is a pain.
Half the total distance is: $4.7575535909087208185450751480456e-4$
That occurs somewher between point $C$ and $D$.
At point $C$ we have traveled: $4.4948899963946078241509087474574e-4$ and we need to travel $2.6266359451411299439416640058822e-5$ more.
The total distance between $C$ and $D$ is $5.0202171854228338129392415486338e-4$ so we need to travel $frac {2.6266359451411299439416640058822e-5}{5.0202171854228338129392415486338e-4} =0.05232116157779134771573009976586$ of that distance.
So $x = C_x + (D_x - C_x)cdot 0.05232116157779134771573009976586$ =
$18.05976927280426 + (18.059420585632324-18.05976927280426)cdot 0.05232116157779134771573009976586= 18.05975102908640$
And $x = C_y + (D_y - Cy)cdot 0.05232116157779134771573009976586=$
$59.332565591603085+(59.33292676062448-59.332565591603085)cdot 0.05232116157779134771573009976586=59.332584488385810301$
Of course this is only one interpretation. A more common interpretation would be the point, $p$ where the sum of the distances from $p$ to points A,B,C, D are least.
answered Dec 10 '18 at 21:05
fleabloodfleablood
69.6k22685
$endgroup$
There's no such thing as a midpoint between points. There is a midpoint of a segment between to endpoints. And a midpoint of a curved path.
It sounds to me you are travel from point to point and want to find the point where you've traveled half the difference.
Keep tally of distance travelled
Point A: 18.060101866722107,
59.33226461448578. Distance traveled = $0$.
Point B: 18.0600106716156,
59.33233028244786. Distance traveled Between A and B = $1.1237806144690070986243816541936e-4$
Point C: 18.05976927280426,
59.332565591603085. Distance traveled Between B and C = $3.3711093819256007255265270932638e-4$ Total so far $4.4948899963946078241509087474574e-4$.
Point D: 18.059420585632324,
59.33292676062448
Distance traveled between C and D = $5.0202171854228338129392415486338e-4$ Totals so far = $9.5151071818174416370901502960912e-4$
And I'm going to quit because this is a pain.
Half the total distance is: $4.7575535909087208185450751480456e-4$
That occurs somewher between point $C$ and $D$.
At point $C$ we have traveled: $4.4948899963946078241509087474574e-4$ and we need to travel $2.6266359451411299439416640058822e-5$ more.
The total distance between $C$ and $D$ is $5.0202171854228338129392415486338e-4$ so we need to travel $frac {2.6266359451411299439416640058822e-5}{5.0202171854228338129392415486338e-4} =0.05232116157779134771573009976586$ of that distance.
So $x = C_x + (D_x - C_x)cdot 0.05232116157779134771573009976586$ =
$18.05976927280426 + (18.059420585632324-18.05976927280426)cdot 0.05232116157779134771573009976586= 18.05975102908640$
And $x = C_y + (D_y - Cy)cdot 0.05232116157779134771573009976586=$
$59.332565591603085+(59.33292676062448-59.332565591603085)cdot 0.05232116157779134771573009976586=59.332584488385810301$
Of course this is only one interpretation. A more common interpretation would be the point, $p$ where the sum of the distances from $p$ to points A,B,C, D are least.
answered Dec 10 '18 at 21:05
fleabloodfleablood
69.6k22685
answered Dec 10 '18 at 21:05
fleabloodfleablood
69.6k22685
answered Dec 10 '18 at 21:05
fleabloodfleablood
69.6k22685
answered Dec 10 '18 at 21:05
fleabloodfleablood
69.6k22685
69.6k22685
$begingroup$
Okay, I assumed flat space linear distance. You'd use the trig distance for your tally and a trig calculation to find the proportion between the two but it's the same idea.
$endgroup$
– fleablood
Dec 10 '18 at 21:07
$begingroup$
thanks, I was able to solve the problem using PostGIS functionst_lineInterpolatePoint.
$endgroup$
– Bohdan Korinnyi
Dec 13 '18 at 7:15
add a comment |
$begingroup$
Okay, I assumed flat space linear distance. You'd use the trig distance for your tally and a trig calculation to find the proportion between the two but it's the same idea.
$endgroup$
– fleablood
Dec 10 '18 at 21:07
$begingroup$
thanks, I was able to solve the problem using PostGIS functionst_lineInterpolatePoint.
$endgroup$
– Bohdan Korinnyi
Dec 13 '18 at 7:15
$begingroup$
Okay, I assumed flat space linear distance. You'd use the trig distance for your tally and a trig calculation to find the proportion between the two but it's the same idea.
$endgroup$
– fleablood
Dec 10 '18 at 21:07
$begingroup$
Okay, I assumed flat space linear distance. You'd use the trig distance for your tally and a trig calculation to find the proportion between the two but it's the same idea.
$endgroup$
– fleablood
Dec 10 '18 at 21:07
$begingroup$
thanks, I was able to solve the problem using PostGIS function
st_lineInterpolatePoint.$endgroup$
– Bohdan Korinnyi
Dec 13 '18 at 7:15
$begingroup$
thanks, I was able to solve the problem using PostGIS function
st_lineInterpolatePoint.$endgroup$
– Bohdan Korinnyi
Dec 13 '18 at 7:15
add a comment |
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$begingroup$
I don't know what a "midpoint of a set of coordinates" would be. But what you showed on the map is not just a set of coordinates; it is a path that goes through some coordinates in sequence. Is the "midpoint" meant to be the point on that path so that it divides the path into two pieces of equal length?
$endgroup$
– David K
Dec 10 '18 at 18:35
$begingroup$
@DavidK yes, exactly!
$endgroup$
– Bohdan Korinnyi
Dec 10 '18 at 20:24
1
$begingroup$
It looks like you are assuming you will be creating a path travelling in straight lines from one point to the next one after another. Keep a tally of distance traveled at each point. Find the two points where have the total distance is between those points and the proportion thereof.
$endgroup$
– fleablood
Dec 10 '18 at 20:36