Finding unique closest point corresponding to latitude and longitude vectors for a given point with shortest distance.

I have two large vectors for the pair of latitudes and longitudes (Lat, Lon). I want to find a unique single pair of latitude and longitude corresponding to the point ([lat_deg, lon_deg]) which has shortest distance.

I am using this:

P = ([lat_deg, lon_deg]);

PQ = [Lat, Lon];

[k,dist] = dsearchn(P,PQ);

But at the end of this I get the distances of all the points and vector k contains all ones. Please guide if this is the right function if yes how can I correct it? if not what is the right function.

Sample vectors are:

Lat Lon

39.2591200000000 -85.9394200000000

39.2591300000000 -85.9392000000000

39.2590800000000 -85.9406300000000

39.2593500000000 -85.9406200000000

39.1949800000000 -85.9633400000000

39.1954200000000 -85.9633500000000

39.1954200000000 -85.9633500000000

39.1963300000000 -85.9633600000000

39.1957400000000 -85.9678800000000

39.1959300000000 -85.9682400000000

P=39.2005981000000 -85.9045842000000

Answer 1

[KALYAN ACHARJYA]

#It can verify from plot too, pls modify as per requirments-

PQ=[39.2591200000000    -85.9394200000000
    39.2591300000000    -85.9392000000000
    39.2590800000000    -85.9406300000000
    39.2593500000000    -85.9406200000000
    39.1949800000000    -85.9633400000000
    39.1954200000000    -85.9633500000000
    39.1954200000000    -85.9633500000000]
lat=PQ(:,1);
long=PQ(:,2);
P=[39,-85];
[k,dist]=dsearchn(P,PQ);
plot(lat,long,'rx',39,-85,'bo','linewidth',2);
idx=find(min(dist)==dist);
disp('Minimum distance Point is ');
PQ(idx,:)

Hope it Helps!

[Muhammad Qaisar Fahim]

Thanks, Yes I realized my input was wrong. Thanks for answering this. So it will calculate the sortest distance right?

[Bruno Luong]

No I argue that the geodesic distance on lon/lat is different than euclidian distance from lon/lat, therefore using dsearchn, which is based on euclidaian distance is inappropriate, of not wrong.

[KALYAN ACHARJYA]

Yes agreed @Bruno Luong thanks for pointing out the technical aspect

[Muhammad Qaisar Fahim]

@Bruno Luong Thanks for pointing out. Then what would be the right choice to use ?

[KALYAN ACHARJYA]

Yes, you can replace the D search function with actual Lat Long Distance measure procedure, rest are same, as mentioned

Answer 2

[Bruno Luong]

Use dsearchn on lon/lat is wrong.

The right procesure is

convert lat/lon to 3D coordinates (for both list P and PQ

use dnsearch on 3D coordinates

[k] = dsearchn(P3D,PQ3D)

Then compute the geodesic distance for all points PQ to P(k) by this formula

https://en.wikipedia.org/wiki/Great-circle_distance

Take the min of the list of the distances.

[Muhammad Qaisar Fahim]

Unfortunately I cannot access this page "https://en.wikipedia.org/wiki/Great-circle_distance.". what is it about? Can you please provide an alternate explanation?

[Muhammad Qaisar Fahim]

Also my coordinates are already in WGS84 coordinates

[Bruno Luong]

The wikipedia gives the formula of geodesic distance between

P1 with longitude/latitude in radian Lambda1, Phi1

P2 with longitude/latitude Lambda2, Phi2

as

d = r*dsigma
dsigma = acos(sin(Phi1)*sin(Phi2) + cos(Phi1)*cos(Phi2)*cos(Lambda1-Lambda2)

where r the radius of the earth, assumin a sphere approximation.