Register to reply 
Distance between a point on a sphere and a great circle arc 
Share this thread: 
#1
Mar2311, 07:28 AM

P: 2

Hi all,
Let me state up front that I'm a math idiot. I minored in it in college 20+ years ago and haven't needed it as a software engineer...until now. I'm trying to solve a problem for work that's got me pulling my hair out, mostly because I'm having to relearn so much math I'd forgotten. What I'm currently struggling with is this: Given two points (A and B) on the Earth, which I can assume is spherical because my calculations don't have to be superaccurate, imagine the minor great circle arc connecting them. If I have a third point C, I'd like to know the distance between AB and C. I know how to find the distance between C and the great circle itself, but that's not exactly what I need unless C happens to be perpendicular to the great circle somewhere along AB. Chances are very good that C will most often actually be closest to A or B. I've been doing all my other work with these points as unit vectors instead of lat/lon, and if there's a solution to my problem that's easily done with vectors, I'd like to do it that way. I've implemented the algorithm here: http://mathforum.org/library/drmath/view/51785.html and what I'm really hoping is that I can just put a couple of checks at the beginning to see if C happens to be closest to A or B before doing those calculations. In a linear system, I can use the dot product to determine where C lies relative to AB, and I suspect (or at least hope!) that something similar can be done in a spherical system. I just don't know what to do. Thanks in advance for anyone who can help out, and please use small words because l'm easily confused. :) 


#2
Mar2311, 09:01 AM

P: 2

To make a stab at answering my own question, if I calculate the angle O between BC and BA and it's greater than 90 degrees, B is the closest point to C; the same would apply to the angle between AC and AB.
Am I at least in the vicinity of a workable solution? 


#3
Aug711, 08:21 AM

P: 1

Hi Fredster,
I'm not a math expert either. But in my Master's thesis I made some calculations that seem similar to your request. You can find it here: http://www.ai.rug.nl/~axel/publ.html It is the link at the bottom of the page ("Speeding up the computation..."). Please let me know if this is of any help to you. Regards, Axel Brink. 


Register to reply 
Related Discussions  
Parametric path of great circle on sphere  Calculus  1  
Distance between a point and a surface (sphere)  Calculus & Beyond Homework  5  
What the formula for the distance from a point to a sphere  Calculus & Beyond Homework  2  
Distance of a great circle  Differential Geometry  5  
Distance from a point on a sphere to a point on a plane...  Calculus  6 