Changing the axes in a figure from geographical coordinates to distance in km

Several lines originate from one given point to different places on Earth, shown here in geographical coordinates.

I want the origin on the axes to be displayed as "0 km" and then scale the axes according to the distance from the origin, which can be easily calculated using

distance(lat1,lon1,lat2,lon2,Earth)

How can I include this in my figure programming?

[jonas]

It seems fairly easy with the function you already have. Just plug your latitude data into the equation by setting everything else (lon1, lat2, lon2) to your reference location, then repeat for your longitude data. Upload data if you need help.

[Matthes Müller]

That is correct, but how can I apply the resulting distances to my axes?

[jonas]

Well, the output of this operation will be a new set of x and y-data (one set for every line), expressed in distance. Then you just plot it and the axes will adjust accordingly.

Or are you looking to include both geo coordinates and distances in the same plot?

[Matthes Müller]

Yes, I want to keep the image as it is (since there is information about the path of each line) and just adjust the axes so you can see the distance in km, how far each line has travelled.

[Simon Streit]

I am sure this is not possible for at least the x-Axis, because 1° in x-direction at the equator in W or E is a lot more distance travelled than 1° close the poles. This is the old problem of mapping a sphere to 2D, it's not possible!

[jonas]

Geomapping is a bit outside of my expertise but I am inclined to agree with Simon. One axis will become non-linear.

Answer 1

[jonas]

I found your figure in another question and attached it to this answer. You could try something like this:

% Units of lat/lon
openfig('Figure.fig')

% Extract data
h=get(gca,'children')
xdata=get(h,'xdata')
ydata=get(h,'ydata')

% Calculate arclength from the origin
yd=cellfun(@(x,y) distance(x(1),y,x(1),y(1)),xdata,ydata,'uniformoutput',false);
xd=cellfun(@(x,y) distance(x,y(1),x(1),y(1)),xdata,ydata,'uniformoutput',false);

% Paths going west and south set to negative
for i=1:length(xdata)
  xd{i}(xdata{i}<xdata{i}(1))=xd{i}(xdata{i}<xdata{i}(1)).*-1;
  yd{i}(ydata{i}<ydata{i}(1))=yd{i}(ydata{i}<ydata{i}(1)).*-1;
end

% Units of arclength 
figure;hold on
h=cellfun(@plot,xd,yd)

However, combining the two figures in the same axes will be difficult.