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On a flat surface we can define any point on line which passes from point1 (x1,y1) to point2 (x2,y2) via simple trigonometry.

How can we do that with latitude and longitude of 2 points?

Imagine we have geographic points (54.977614, -103.710937) and (55.973798, -107.929687) on a globe. Using what mathematics can I define any point on the line which passes through these points? Or where can I read about this?

whuber
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shervin4030
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    Welcome to GIS.SE. I suggest some relevant tags to help you search for what must have already been asked here: spherical-geometry, cogo, geodesy – Martin F Feb 17 '14 at 02:10
  • @martinf: Entirely the fault of swyping on a tiny mobile keyboard. :-P – Devdatta Tengshe Feb 17 '14 at 03:22
  • @shervin: You need to clarify what kind of line you are looking for. Is it a great circle (shortest distance) line that you are looking for? or for a straight line in a specific projection? The answer will depend on that – Devdatta Tengshe Feb 17 '14 at 03:24
  • @Devdatta Because the question refers to the geometry of the globe, projections are irrelevant and no clarification appears necessary. – whuber Feb 17 '14 at 15:29
  • The Wikipedia article Geodesics on an ellipsoid is a good resource. It describes the problem and outlines the solution. – cffk Feb 17 '14 at 10:37
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    Shervin, for some intuition (and pointers to formulas) please see our thread at http://gis.stackexchange.com/questions/6822. I hope that helps make it clear that this simple question has a relatively straightforward answer. The name of the mathematical discipline concerned with finding lines between points in curved spaces is differential geometry (which Carl Gauss invented in the 1820's specifically to be able to perform wide-scale surveying). There exist many good introductions, but a choice of which to read depends on your background: they all require a working knowledge of Calculus. – whuber Feb 17 '14 at 15:34
  • @whuber very helpful – shervin4030 Feb 20 '14 at 11:11
  • The article recommended by @cffk is amazingly good--one of the best I have seen on Wikipedia. It's worth a look by anyone curious about geodesy, even if you don't follow the mathematics. – whuber Feb 28 '14 at 15:14

1 Answers1

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The question is pretty complicated. What you are asking about is calculations on the surface of the Earth, which is called spherical trigonometry. To get even more precise you need to use an ellipsoidal model of the Earth.

I'd suggest you use a program that can already do this for you, but if you want to do it yourself, here's a link to start on.

The shortest distance between two points of latitude and longitude is called a great circle distance. Here's some more reading.

Luís de Sousa
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Alex Leith
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