Calculate a point on a map given one point and a distance

I'm working with google maps on an angular project. I've got a center point of a circle and the length of the radius in meters. I'm trying to find a coordinate of any point on the circumference of a circle - I just need one. How do I calculate this given what I have?

Example data :

Center = {

   Latitude : 53.388922117675236

   Longitude : -6.280994415283203

}

Radius = 527

edited Nov 15 '18 at 11:04

asked Nov 15 '18 at 10:58

abyrne85

658520

1

mathsisfun.com/algebra/circle-equations.html

– HoangHieu
Nov 15 '18 at 11:02

@NickParsons Sorry, I should have clarified, I just need one point

– abyrne85
Nov 15 '18 at 11:03

Ok, a point on the circumference should be let x = Center.Latitude+Radius and let y = Center.Longitude If I understand your question correctly :P

– Nick Parsons
Nov 15 '18 at 11:06

That would mean that the x coordinate is 53.388 + 527 = 605.392. Radius is in meters so I can't add that to a coordinate

– abyrne85
Nov 15 '18 at 11:16

@abyrne85 a distance and a point will give you the infinite points of a circle. If you want only a point, you should provide another constraint.

– David Lemon
Nov 16 '18 at 13:02

add a comment |

Example data :

Center = {

   Latitude : 53.388922117675236

   Longitude : -6.280994415283203

}

Radius = 527

edited Nov 15 '18 at 11:04

asked Nov 15 '18 at 10:58

abyrne85

658520

1

mathsisfun.com/algebra/circle-equations.html

– HoangHieu
Nov 15 '18 at 11:02

@NickParsons Sorry, I should have clarified, I just need one point

– abyrne85
Nov 15 '18 at 11:03

Ok, a point on the circumference should be let x = Center.Latitude+Radius and let y = Center.Longitude If I understand your question correctly :P

– Nick Parsons
Nov 15 '18 at 11:06

That would mean that the x coordinate is 53.388 + 527 = 605.392. Radius is in meters so I can't add that to a coordinate

– abyrne85
Nov 15 '18 at 11:16

@abyrne85 a distance and a point will give you the infinite points of a circle. If you want only a point, you should provide another constraint.

– David Lemon
Nov 16 '18 at 13:02

add a comment |

Example data :

Center = {

   Latitude : 53.388922117675236

   Longitude : -6.280994415283203

}

Radius = 527

edited Nov 15 '18 at 11:04

asked Nov 15 '18 at 10:58

abyrne85

658520

Example data :

Center = {

   Latitude : 53.388922117675236

   Longitude : -6.280994415283203

}

Radius = 527

javascript google-maps math

edited Nov 15 '18 at 11:04

asked Nov 15 '18 at 10:58

abyrne85

658520

edited Nov 15 '18 at 11:04

asked Nov 15 '18 at 10:58

abyrne85

658520

edited Nov 15 '18 at 11:04

asked Nov 15 '18 at 10:58

abyrne85

658520

asked Nov 15 '18 at 10:58

abyrne85

658520

asked Nov 15 '18 at 10:58

abyrne85

658520

1

mathsisfun.com/algebra/circle-equations.html

– HoangHieu
Nov 15 '18 at 11:02

@NickParsons Sorry, I should have clarified, I just need one point

– abyrne85
Nov 15 '18 at 11:03

Ok, a point on the circumference should be let x = Center.Latitude+Radius and let y = Center.Longitude If I understand your question correctly :P

– Nick Parsons
Nov 15 '18 at 11:06

That would mean that the x coordinate is 53.388 + 527 = 605.392. Radius is in meters so I can't add that to a coordinate

– abyrne85
Nov 15 '18 at 11:16

@abyrne85 a distance and a point will give you the infinite points of a circle. If you want only a point, you should provide another constraint.

– David Lemon
Nov 16 '18 at 13:02

add a comment |

1

mathsisfun.com/algebra/circle-equations.html

– HoangHieu
Nov 15 '18 at 11:02

@NickParsons Sorry, I should have clarified, I just need one point

– abyrne85
Nov 15 '18 at 11:03

Ok, a point on the circumference should be let x = Center.Latitude+Radius and let y = Center.Longitude If I understand your question correctly :P

– Nick Parsons
Nov 15 '18 at 11:06

That would mean that the x coordinate is 53.388 + 527 = 605.392. Radius is in meters so I can't add that to a coordinate

– abyrne85
Nov 15 '18 at 11:16

@abyrne85 a distance and a point will give you the infinite points of a circle. If you want only a point, you should provide another constraint.

– David Lemon
Nov 16 '18 at 13:02

mathsisfun.com/algebra/circle-equations.html

– HoangHieu
Nov 15 '18 at 11:02

@NickParsons Sorry, I should have clarified, I just need one point

– abyrne85
Nov 15 '18 at 11:03

Ok, a point on the circumference should be let x = Center.Latitude+Radius and let y = Center.Longitude If I understand your question correctly :P

– Nick Parsons
Nov 15 '18 at 11:06

That would mean that the x coordinate is 53.388 + 527 = 605.392. Radius is in meters so I can't add that to a coordinate

– abyrne85
Nov 15 '18 at 11:16

@abyrne85 a distance and a point will give you the infinite points of a circle. If you want only a point, you should provide another constraint.

– David Lemon
Nov 16 '18 at 13:02

add a comment |

2 Answers
2

active

oldest

votes

The Maps API has a geometry library that you can use to calculate distances, heading, etc.

So if you need to find 1 point at a given distance from another point, whatever heading, you can use the computeOffset method.

What the following code does, it adds a marker at position 0,0 (var myLatLng) then adds another marker, 5000 meters from that point, at a heading of 0 (North). You can change the heading of course if you need to.

function initialize() {



    var myLatLng = new google.maps.LatLng(0,0);

    var mapOptions = {

        zoom: 10,

        center: myLatLng,

        mapTypeId: google.maps.MapTypeId.ROADMAP

    };

    

    var point = google.maps.geometry.spherical.computeOffset(myLatLng, 5000, 0);

    

    var map = new google.maps.Map(document.getElementById("map-canvas"), mapOptions);

    

    new google.maps.Marker({

        position: myLatLng,

        map: map,

        title: 'Origin marker'

    });

    

    new google.maps.Marker({

        position: point,

        map: map,

        title: 'Offset marker'

    });

}



initialize();

#map-canvas {

  height: 200px;

}

<div id="map-canvas"></div>



<script src="https://maps.googleapis.com/maps/api/js?libraries=geometry"></script>

Note how the API is loaded, with including the geometry library.

answered Nov 15 '18 at 11:30

MrUpsidown

15.2k84995

1

I'm already using the geometry library so this is perfect. Thanks

– abyrne85
Nov 15 '18 at 11:54

add a comment |

If you need arbitrary point at given distance, the simplest way is to choose meridional direction

NewLong = Long

NewLat = Lat +- Radius / 111111.111  (meters per degree)

Or parallel direction:

NewLat = Lat

NewLong = Long +- Radius / 111111.111 / Cos(Lat)

For random direction generate random bearing and use formula from this page

Formula:

φ2 = asin( sin φ1 ⋅ cos δ + cos φ1 ⋅ sin δ ⋅ cos θ )

λ2 = λ1 + atan2( sin θ ⋅ sin δ ⋅ cos φ1, cos δ − sin φ1 ⋅ sin φ2 )

where   φ is latitude, λ is longitude, 

        θ is the bearing (clockwise from north), 

        δ is the angular distance d/R; 

        d being the distance travelled, R the earth’s radius



JavaScript:(all angles in radians)

var φ2 = Math.asin( Math.sin(φ1)*Math.cos(d/R) +

                    Math.cos(φ1)*Math.sin(d/R)*Math.cos(brng) );

var λ2 = λ1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(φ1),

                         Math.cos(d/R)-Math.sin(φ1)*Math.sin(φ2));

edited Nov 15 '18 at 11:46

answered Nov 15 '18 at 11:17

MBo

49.2k23051

This is certainly the right maths. But 1) you didn't provide a Javascript version and 2) you don't need to compute that manually as the API has a method for that (see my answer).

– MrUpsidown
Nov 15 '18 at 11:45

1

@MrUpsidown I did not believe that JS guys cannot write given formulas in JS ;)

– MBo
Nov 15 '18 at 11:48

Easy ;) But when the question mentions JS, I try to provide JS. Obviously not a big deal! Thanks for updating!

– MrUpsidown
Nov 15 '18 at 11:52

add a comment |

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

The Maps API has a geometry library that you can use to calculate distances, heading, etc.

So if you need to find 1 point at a given distance from another point, whatever heading, you can use the computeOffset method.

function initialize() {



    var myLatLng = new google.maps.LatLng(0,0);

    var mapOptions = {

        zoom: 10,

        center: myLatLng,

        mapTypeId: google.maps.MapTypeId.ROADMAP

    };

    

    var point = google.maps.geometry.spherical.computeOffset(myLatLng, 5000, 0);

    

    var map = new google.maps.Map(document.getElementById("map-canvas"), mapOptions);

    

    new google.maps.Marker({

        position: myLatLng,

        map: map,

        title: 'Origin marker'

    });

    

    new google.maps.Marker({

        position: point,

        map: map,

        title: 'Offset marker'

    });

}



initialize();

#map-canvas {

  height: 200px;

}

<div id="map-canvas"></div>



<script src="https://maps.googleapis.com/maps/api/js?libraries=geometry"></script>

Note how the API is loaded, with including the geometry library.

answered Nov 15 '18 at 11:30

MrUpsidown

15.2k84995

1

I'm already using the geometry library so this is perfect. Thanks

– abyrne85
Nov 15 '18 at 11:54

add a comment |

The Maps API has a geometry library that you can use to calculate distances, heading, etc.

So if you need to find 1 point at a given distance from another point, whatever heading, you can use the computeOffset method.

function initialize() {



    var myLatLng = new google.maps.LatLng(0,0);

    var mapOptions = {

        zoom: 10,

        center: myLatLng,

        mapTypeId: google.maps.MapTypeId.ROADMAP

    };

    

    var point = google.maps.geometry.spherical.computeOffset(myLatLng, 5000, 0);

    

    var map = new google.maps.Map(document.getElementById("map-canvas"), mapOptions);

    

    new google.maps.Marker({

        position: myLatLng,

        map: map,

        title: 'Origin marker'

    });

    

    new google.maps.Marker({

        position: point,

        map: map,

        title: 'Offset marker'

    });

}



initialize();

#map-canvas {

  height: 200px;

}

<div id="map-canvas"></div>



<script src="https://maps.googleapis.com/maps/api/js?libraries=geometry"></script>

Note how the API is loaded, with including the geometry library.

answered Nov 15 '18 at 11:30

MrUpsidown

15.2k84995

1

I'm already using the geometry library so this is perfect. Thanks

– abyrne85
Nov 15 '18 at 11:54

add a comment |

The Maps API has a geometry library that you can use to calculate distances, heading, etc.

So if you need to find 1 point at a given distance from another point, whatever heading, you can use the computeOffset method.

function initialize() {



    var myLatLng = new google.maps.LatLng(0,0);

    var mapOptions = {

        zoom: 10,

        center: myLatLng,

        mapTypeId: google.maps.MapTypeId.ROADMAP

    };

    

    var point = google.maps.geometry.spherical.computeOffset(myLatLng, 5000, 0);

    

    var map = new google.maps.Map(document.getElementById("map-canvas"), mapOptions);

    

    new google.maps.Marker({

        position: myLatLng,

        map: map,

        title: 'Origin marker'

    });

    

    new google.maps.Marker({

        position: point,

        map: map,

        title: 'Offset marker'

    });

}



initialize();

#map-canvas {

  height: 200px;

}

<div id="map-canvas"></div>



<script src="https://maps.googleapis.com/maps/api/js?libraries=geometry"></script>

Note how the API is loaded, with including the geometry library.

answered Nov 15 '18 at 11:30

MrUpsidown

15.2k84995

The Maps API has a geometry library that you can use to calculate distances, heading, etc.

So if you need to find 1 point at a given distance from another point, whatever heading, you can use the computeOffset method.

function initialize() {



    var myLatLng = new google.maps.LatLng(0,0);

    var mapOptions = {

        zoom: 10,

        center: myLatLng,

        mapTypeId: google.maps.MapTypeId.ROADMAP

    };

    

    var point = google.maps.geometry.spherical.computeOffset(myLatLng, 5000, 0);

    

    var map = new google.maps.Map(document.getElementById("map-canvas"), mapOptions);

    

    new google.maps.Marker({

        position: myLatLng,

        map: map,

        title: 'Origin marker'

    });

    

    new google.maps.Marker({

        position: point,

        map: map,

        title: 'Offset marker'

    });

}



initialize();

#map-canvas {

  height: 200px;

}

<div id="map-canvas"></div>



<script src="https://maps.googleapis.com/maps/api/js?libraries=geometry"></script>

Note how the API is loaded, with including the geometry library.

function initialize() {



    var myLatLng = new google.maps.LatLng(0,0);

    var mapOptions = {

        zoom: 10,

        center: myLatLng,

        mapTypeId: google.maps.MapTypeId.ROADMAP

    };

    

    var point = google.maps.geometry.spherical.computeOffset(myLatLng, 5000, 0);

    

    var map = new google.maps.Map(document.getElementById("map-canvas"), mapOptions);

    

    new google.maps.Marker({

        position: myLatLng,

        map: map,

        title: 'Origin marker'

    });

    

    new google.maps.Marker({

        position: point,

        map: map,

        title: 'Offset marker'

    });

}



initialize();

#map-canvas {

  height: 200px;

}

<div id="map-canvas"></div>



<script src="https://maps.googleapis.com/maps/api/js?libraries=geometry"></script>

function initialize() {



    var myLatLng = new google.maps.LatLng(0,0);

    var mapOptions = {

        zoom: 10,

        center: myLatLng,

        mapTypeId: google.maps.MapTypeId.ROADMAP

    };

    

    var point = google.maps.geometry.spherical.computeOffset(myLatLng, 5000, 0);

    

    var map = new google.maps.Map(document.getElementById("map-canvas"), mapOptions);

    

    new google.maps.Marker({

        position: myLatLng,

        map: map,

        title: 'Origin marker'

    });

    

    new google.maps.Marker({

        position: point,

        map: map,

        title: 'Offset marker'

    });

}



initialize();

#map-canvas {

  height: 200px;

}

<div id="map-canvas"></div>



<script src="https://maps.googleapis.com/maps/api/js?libraries=geometry"></script>

answered Nov 15 '18 at 11:30

MrUpsidown

15.2k84995

answered Nov 15 '18 at 11:30

MrUpsidown

15.2k84995

answered Nov 15 '18 at 11:30

MrUpsidown

15.2k84995

answered Nov 15 '18 at 11:30

MrUpsidown

15.2k84995

1

I'm already using the geometry library so this is perfect. Thanks

– abyrne85
Nov 15 '18 at 11:54

add a comment |

1

I'm already using the geometry library so this is perfect. Thanks

– abyrne85
Nov 15 '18 at 11:54

I'm already using the geometry library so this is perfect. Thanks

– abyrne85
Nov 15 '18 at 11:54

add a comment |

If you need arbitrary point at given distance, the simplest way is to choose meridional direction

NewLong = Long

NewLat = Lat +- Radius / 111111.111  (meters per degree)

Or parallel direction:

NewLat = Lat

NewLong = Long +- Radius / 111111.111 / Cos(Lat)

For random direction generate random bearing and use formula from this page

Formula:

φ2 = asin( sin φ1 ⋅ cos δ + cos φ1 ⋅ sin δ ⋅ cos θ )

λ2 = λ1 + atan2( sin θ ⋅ sin δ ⋅ cos φ1, cos δ − sin φ1 ⋅ sin φ2 )

where   φ is latitude, λ is longitude, 

        θ is the bearing (clockwise from north), 

        δ is the angular distance d/R; 

        d being the distance travelled, R the earth’s radius



JavaScript:(all angles in radians)

var φ2 = Math.asin( Math.sin(φ1)*Math.cos(d/R) +

                    Math.cos(φ1)*Math.sin(d/R)*Math.cos(brng) );

var λ2 = λ1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(φ1),

                         Math.cos(d/R)-Math.sin(φ1)*Math.sin(φ2));

edited Nov 15 '18 at 11:46

answered Nov 15 '18 at 11:17

MBo

49.2k23051

This is certainly the right maths. But 1) you didn't provide a Javascript version and 2) you don't need to compute that manually as the API has a method for that (see my answer).

– MrUpsidown
Nov 15 '18 at 11:45

1

@MrUpsidown I did not believe that JS guys cannot write given formulas in JS ;)

– MBo
Nov 15 '18 at 11:48

Easy ;) But when the question mentions JS, I try to provide JS. Obviously not a big deal! Thanks for updating!

– MrUpsidown
Nov 15 '18 at 11:52

add a comment |

If you need arbitrary point at given distance, the simplest way is to choose meridional direction

NewLong = Long

NewLat = Lat +- Radius / 111111.111  (meters per degree)

Or parallel direction:

NewLat = Lat

NewLong = Long +- Radius / 111111.111 / Cos(Lat)

For random direction generate random bearing and use formula from this page

Formula:

φ2 = asin( sin φ1 ⋅ cos δ + cos φ1 ⋅ sin δ ⋅ cos θ )

λ2 = λ1 + atan2( sin θ ⋅ sin δ ⋅ cos φ1, cos δ − sin φ1 ⋅ sin φ2 )

where   φ is latitude, λ is longitude, 

        θ is the bearing (clockwise from north), 

        δ is the angular distance d/R; 

        d being the distance travelled, R the earth’s radius



JavaScript:(all angles in radians)

var φ2 = Math.asin( Math.sin(φ1)*Math.cos(d/R) +

                    Math.cos(φ1)*Math.sin(d/R)*Math.cos(brng) );

var λ2 = λ1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(φ1),

                         Math.cos(d/R)-Math.sin(φ1)*Math.sin(φ2));

edited Nov 15 '18 at 11:46

answered Nov 15 '18 at 11:17

MBo

49.2k23051

This is certainly the right maths. But 1) you didn't provide a Javascript version and 2) you don't need to compute that manually as the API has a method for that (see my answer).

– MrUpsidown
Nov 15 '18 at 11:45

1

@MrUpsidown I did not believe that JS guys cannot write given formulas in JS ;)

– MBo
Nov 15 '18 at 11:48

Easy ;) But when the question mentions JS, I try to provide JS. Obviously not a big deal! Thanks for updating!

– MrUpsidown
Nov 15 '18 at 11:52

add a comment |

If you need arbitrary point at given distance, the simplest way is to choose meridional direction

NewLong = Long

NewLat = Lat +- Radius / 111111.111  (meters per degree)

Or parallel direction:

NewLat = Lat

NewLong = Long +- Radius / 111111.111 / Cos(Lat)

For random direction generate random bearing and use formula from this page

Formula:

φ2 = asin( sin φ1 ⋅ cos δ + cos φ1 ⋅ sin δ ⋅ cos θ )

λ2 = λ1 + atan2( sin θ ⋅ sin δ ⋅ cos φ1, cos δ − sin φ1 ⋅ sin φ2 )

where   φ is latitude, λ is longitude, 

        θ is the bearing (clockwise from north), 

        δ is the angular distance d/R; 

        d being the distance travelled, R the earth’s radius



JavaScript:(all angles in radians)

var φ2 = Math.asin( Math.sin(φ1)*Math.cos(d/R) +

                    Math.cos(φ1)*Math.sin(d/R)*Math.cos(brng) );

var λ2 = λ1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(φ1),

                         Math.cos(d/R)-Math.sin(φ1)*Math.sin(φ2));

edited Nov 15 '18 at 11:46

answered Nov 15 '18 at 11:17

MBo

49.2k23051

If you need arbitrary point at given distance, the simplest way is to choose meridional direction

NewLong = Long

NewLat = Lat +- Radius / 111111.111  (meters per degree)

Or parallel direction:

NewLat = Lat

NewLong = Long +- Radius / 111111.111 / Cos(Lat)

For random direction generate random bearing and use formula from this page

Formula:

φ2 = asin( sin φ1 ⋅ cos δ + cos φ1 ⋅ sin δ ⋅ cos θ )

λ2 = λ1 + atan2( sin θ ⋅ sin δ ⋅ cos φ1, cos δ − sin φ1 ⋅ sin φ2 )

where   φ is latitude, λ is longitude, 

        θ is the bearing (clockwise from north), 

        δ is the angular distance d/R; 

        d being the distance travelled, R the earth’s radius



JavaScript:(all angles in radians)

var φ2 = Math.asin( Math.sin(φ1)*Math.cos(d/R) +

                    Math.cos(φ1)*Math.sin(d/R)*Math.cos(brng) );

var λ2 = λ1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(φ1),

                         Math.cos(d/R)-Math.sin(φ1)*Math.sin(φ2));

edited Nov 15 '18 at 11:46

answered Nov 15 '18 at 11:17

MBo

49.2k23051

edited Nov 15 '18 at 11:46

answered Nov 15 '18 at 11:17

MBo

49.2k23051

answered Nov 15 '18 at 11:17

MBo

49.2k23051

answered Nov 15 '18 at 11:17

MBo

49.2k23051

This is certainly the right maths. But 1) you didn't provide a Javascript version and 2) you don't need to compute that manually as the API has a method for that (see my answer).

– MrUpsidown
Nov 15 '18 at 11:45

1

@MrUpsidown I did not believe that JS guys cannot write given formulas in JS ;)

– MBo
Nov 15 '18 at 11:48

Easy ;) But when the question mentions JS, I try to provide JS. Obviously not a big deal! Thanks for updating!

– MrUpsidown
Nov 15 '18 at 11:52

add a comment |

This is certainly the right maths. But 1) you didn't provide a Javascript version and 2) you don't need to compute that manually as the API has a method for that (see my answer).

– MrUpsidown
Nov 15 '18 at 11:45

1

@MrUpsidown I did not believe that JS guys cannot write given formulas in JS ;)

– MBo
Nov 15 '18 at 11:48

Easy ;) But when the question mentions JS, I try to provide JS. Obviously not a big deal! Thanks for updating!

– MrUpsidown
Nov 15 '18 at 11:52

This is certainly the right maths. But 1) you didn't provide a Javascript version and 2) you don't need to compute that manually as the API has a method for that (see my answer).

– MrUpsidown
Nov 15 '18 at 11:45

@MrUpsidown I did not believe that JS guys cannot write given formulas in JS ;)

– MBo
Nov 15 '18 at 11:48

Easy ;) But when the question mentions JS, I try to provide JS. Obviously not a big deal! Thanks for updating!

– MrUpsidown
Nov 15 '18 at 11:52

add a comment |

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