Calculate distance between a point and a contour line

I want to calculate distance between points of the trajectory(grey line) and the 1000m contour (dash black line) as shown on the attached image. I want the distance to be in km/m

Thanks for the help in advance

[jonas]

Could you upload the contour matrix and the trajectory?

[Tumelo Maja]

I have attached the trajectory vectors of the glider paths (greyline) and the contour matrix, and lon/lat vectors for the contour values

[jonas]

Perfect, I will take a look!

Answer 1

[jonas]

Here is my code so far. The units of the output is not entirely correct, but should be quite easy to fix.

% Trajectory
lat = lat_track;
lon = lon_track;

% Contour matrix for Z = 1000
C = contour(lon_cont,lat_cont,cont_vals,'levellist',-1000);hold on
close all;

% Remove some unnecessary data and save contour coordinates
[~,idx] = find(C(1,:)==-1000);
poly = [C(1,idx(1)+1:idx(2)-1);C(2,idx(1)+1:idx(2)-1)]'
C(:,C(1,:)==-1000) = [];
Clat = C(2,:)';
Clon = C(1,:)';

% Calculate closest distance between trajectory and contour
[K,d] = dsearchn([Clon,Clat],[lon,lat]);

% Check if the pts are inside or outside of the contour
in = inpolygon(lon,lat,poly(:,1),poly(:,2));

% Change sign of those inside
d(in) = -d(in);

% Plot contour
plot(Clon,Clat,'k.');hold on

% plot trajectory
scatter3(lon,lat,d,[],d)

% plot closest points
plot(Clon(K),Clat(K),'r.')

% Calculate arclength
[arclen,az] = distance(lon,lat,Clon(K),Clat(K),'rad')

The minimum distance in each point is stored in d and the index on the corresponding index in the contour matrix is stored in K. This means that the distance d(1) is the distance between [lon(1);lat(1)] and [Clon(K);Clat(K)]. The distance is currently in a weird unit of latitudes and longitudes, but you could calculate the actual distance by the distance function.

[Tumelo Maja]

I think the levels are negative. try using -1000. I plot the contours with -1000.

e.g. m_contour(lon_cont,lat_cont,cont_vals,-1000,'color','k');

[jonas]

Aha! That is better, check the new code.

[arclen,az] = distance(lon,lat,Clon(K),Clat(K))

should give you the arclength and from there you can calculate the distance in units of [m].

[Tumelo Maja]

So K is the index for the contour matrix?

what are d, arclen and az? and their units

I want to have positive and negative displacements. i.e. right(left) side of the contour have positive(negative) values

[jonas]

K( n ) is the index of the closest point on the contour matrix to the trajectory point n. The d( n ) is the corresponding distance but in useless units, so you cannot use it. What you need to do is take the pairs of coordinates and calculate the arclength between the pts, as described in my previous comment. The arclength is the distance between two points on a sphere, and its unit is radians or degrees. You need to multiply by the radius of the earth to get the distance in units of [m]. Perhaps it would be easier to just use this FEX function

https://se.mathworks.com/matlabcentral/fileexchange/38812-latlon-distance

Negative distances? You could make a polygon of the contour and find points the points inside of it using inpolygon.

I've updated the code so that you have a subset of indices ( in ) that lies inside of the contour.

[Tumelo Maja]

Thank you very much. The solution works perfectly :-)

[jonas]

My pleasure. Interesting question!