Questions tagged [great-circle]

A great circle of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere. Used in navigation to determine the shortest distance between two points on the globe.

A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere. This partial case of a circle of a sphere is opposed to a small circle, the intersection of the sphere and a plane which does not pass through the center. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, and have the same center as the sphere. A great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean 3-space is a great circle of exactly one sphere.

For most pairs of points on the surface of a sphere there is a unique great circle through the two points. The exception is a pair of antipodal points, for which there are infinitely many great circles. The minor arc of a great circle between two points is the shortest surface-path between them. In this sense the minor arc is analogous to “straight lines” in Euclidean geometry. The length of the minor arc of a great circle is taken as the distance between two points on a surface of a sphere in Riemannian geometry. The great circles are the geodesics of the sphere.

Great-circle navigation is the practice of navigating a vessel (a ship or aircraft) along a great circle. A great circle track is the shortest distance between two points on the surface of a sphere; the Earth isn't exactly spherical, but the formulas for a sphere are simpler and are often accurate enough for navigation.

Useful Links

92 questions
2
votes
2 answers

Minimum bounding rectangle of a circle on a sphere

What R packages are available to calculate the minimum bounding box for a great circle? For example: box <- polycirc( c( longitude, latitude ), distance=35 ) This would return the bounding box for the circle with a radius of 35 kilometres from the…
Dave Jarvis
  • 30,436
  • 41
  • 178
  • 315
2
votes
4 answers

If I am here and heading towards there and I've covered this much ground, where am I?

I need help writing the following method: def get_new_location(current_location, target_location, distance_travelled): ... ... return new_location where all locations are (lat,long) I realize that there are different models for the…
carrier
  • 32,209
  • 23
  • 76
  • 99
2
votes
0 answers

Using R data.table to calculate great circle distance for large dataset

I have a fairly large dataset of georeferenced data. It's about 49 million records. Using data.table package I've been able to subset it (originally was 100 millions records) and make some simple calculations, like the mean center for the geographic…
2
votes
1 answer

Calculating great-circle distance matrix

dist(coords) provides the distance matrix using Euclidean distances; it also provides several other options. But it doesn't provide any option such as the haversine formula. distHaversine() calculates the distance I want (great-circle) for given two…
cmelan
  • 247
  • 5
  • 13
2
votes
0 answers

Antipodal error in Great Circles code

I'm trying to build something like this http://flowingdata.com/2011/05/11/how-to-map-connections-with-great-circles/ but with my own data in csv files. The code runs well if I use the same csv files as the author, but with mine , this is what I get…
2
votes
1 answer

Draw a path around a globe?

So basically I would like to: Draw a path between two positions in Earth, with longitude and latitude coordinates Be able to render this path with multiple straight lines (e.g. with OpenGL) Specify an altitude, and bonus points for being able to…
gak
  • 32,061
  • 28
  • 119
  • 154
1
vote
2 answers

Rotate a sphere from coord1 to coord2, where will coord3 be?

I have three coordinates (lat,lon) on a sphere. If you would rotate the whole sphere from coord1 to coord2, where will coord3 now be located? I've been trying this out in Python using Great Circle…
joosthoek
  • 173
  • 1
  • 3
  • 9
1
vote
3 answers

How to calculate shortest route?

I have a list of 80 towns each with their geographical longitude and latitude. I need to find the shortest closed route (taking into account the curvature of the earth). I was thinking I could calculate the distance between each one (using…
Darkphenom
  • 647
  • 2
  • 8
  • 14
1
vote
1 answer

Why does my implementation of the Great Circle distance formula give wrong results?

I'm trying to implement algorithm which will calculate distance between 2 points using great circle distance formula according to guide My function: from math import sin, cos, radians def get_great_circle_distance(first_coords, second_coords,…
max_bstr
  • 15
  • 8
1
vote
2 answers

Circle shape with center text not working React Native iOS

I am trying to drawing circle shape view for textview inside that some text. It is working with Android, But, iOS not working properly. Text is coming top of the view. NA styles na: { width: 60, …
1
vote
0 answers

Interpolate additional points between two GPS points based on a predetermined interval

My Erlang module loads a GPX file and performs a certain function for every set of lat/long coordinates in the file. I want to increase the resolution, so to speak, of the GPX file by filling in more GPS points between the existing points. For…
grgoelyk
  • 397
  • 1
  • 3
  • 12
1
vote
2 answers

calculate distance and time between points along animal movement path

I have a large dataset (> 9 million rows) of times and locations when individual animals were detected at stations. I would like to calculate the distance between each station along each animal's path as it travelled between stations, as well as…
tnt
  • 1,149
  • 14
  • 24
1
vote
1 answer

Plot equation to represent the wire frame of a sphere? (Great Circle)

I found someone else's example that showed how to plot a sphere in python, but I was curious if there was an equation that represents individual longitudinal lines along a sphere. Example: Python/matplotlib : plotting a 3d cube, a sphere and a…
NoviceCoder
  • 424
  • 1
  • 4
  • 20
1
vote
1 answer

Bounding box on flat map VS Spherical i.e. straight line vs great circle distance

I am designing an application in which I have to tell whether an item like fb video or instagram photo lies inside a region or originated from particular region for example Melbourne. So till now, when I want to find bounding box for some country…
Arjun Chaudhary
  • 2,373
  • 2
  • 19
  • 36
1
vote
1 answer

How to group by trip id and find the straight distance traveled?

I have the following data : Trip Start_Lat Start_Long End_lat End_Long Starting_point Ending_point Trip_1 56.5624 -85.56845 58.568 45.568 A B Trip_1 58.568 45.568 -200.568 …
user7779326