[Plotting] Two x and y axes for the same data, with different units, and axis equal

Hello all,

I have asked a similar question before, but have yet to find/create a satisfactory solution. I am attempting to plot position data that comes in latitude-longitude. These are over a relatively small area, so there is a direct conversion from lat/lon into meters N/E relative to some reference point. I am attempting to plot the data with the meters-E and meters-N on the x and y axes respectively. I want a second pair of xx and yy axes on the top and right side respectively plotting the latitude and longitude. This I have managed to do. The sticking point is that I want to lock the figure to equal axes in x-y direction in meters so that the data has a realistic aspect ratio. This then kills the second pair of axes. Two sample image, and then some pseudo-code below:

Here we can see what I am going for with two major problems: the y-tick labels are cut-off on the right side, and the x-y axes are squished.

Now, I use axis equal on the first axes (the one in meters). This actually has the correct aspect ratio, but you can see that the second axies has not remained locked with the first. This is bad.

This whole process is really kludgey. The closest I got was to add a pbaspect command to the second axes and I get. It is still definitely not correct.

I am simply floored that there isn't really a way to have multiple axes for the same data. I will attach a gross code example below, and hope that someone has a suggestion. The core technique was suggested in this Mathworks page.

% Lat/lon, convert to meters
lat0 = 51.2697; % deg
lon0 =  -77.3379; % deg
dLat =    1.5696e-07; %meters/radian lat here 
dLon =   2.5087e-07;  %meters/radian lon here

% Set up some random walk
dx = rand(100,1);
dy = rand(100,1); 
x = cumsum(dx);
y = cumsum(dy);

% Convert that to lat/lon
lat = 360/(2*pi)*y*dLat + lat0; 
lon =  360/(2*pi)*x*dLon + lon0;

% Plot our walk in meters
close all
figure();
plot(x,y,'b.'); 
 xlabel('Easting (m)');
 ylabel('Northing (m)');
 set(gca,'box','off')
% Set axes as equal. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% comment out for other option
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
axis equal; axis tight;

% Suggested by Mathworks
ax1 = gca; % current axes

ax1_pos = ax1.Position; % position of first axes
ax2 = axes('Position',ax1_pos,...
    'XAxisLocation','top',...
    'YAxisLocation','right',...
    'Color','none');

% Super Kludge, try to set our x/y-ticks
 xt = xticks;
 yt = yticks;
 % Only grab 1/3 of them for spacing
xticks(xt(1:3:end));
yticks(yt(1:3:end));
xt = xticks;
yt = yticks;

% Set up some tick labels
 latL = linspace(min(lat),max(lat),length(xt));

  lonL = linspace(min(lon),max(lon),length(yt));

 xticklabels(lonL);
 yticklabels(latL);
 
 % TRY to fix our aspect ratio issue. 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% comment out for other option
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  pbaspect([dLat/dLon,1,1]);

Answer 1

[Cris LaPierre]

You are not setting the same properties on ax2 as ax1 (axis equal; axis tight). However, position of an axis does not change with 'axis tight', but plotting canvas does. This will cause the two axes to still be unaligned. If you don't do axis tight, you'd get this:

Here's the code I used

% Lat/lon, convert to meters
lat0 = 51.2697; % deg
lon0 =  -77.3379; % deg
dLat =    1.5696e-07; %meters/radian lat here 
dLon =   2.5087e-07;  %meters/radian lon here
% Set up some random walk
dx = rand(100,1);
dy = rand(100,1); 
x = cumsum(dx);
y = cumsum(dy);
% Convert that to lat/lon
lat = 360/(2*pi)*y*dLat + lat0; 
lon =  360/(2*pi)*x*dLon + lon0;
% Plot our walk in meters
close all
figure();
scatter(x,y,'b.'); 
 xlabel('Easting (m)');
 ylabel('Northing (m)');
set(gca,'box','off')
% Set axes as equal. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% comment out for other option
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
axis equal; 
% axis tight;

% Suggested by Mathworks
ax1 = gca; % current axes
ax1_pos = ax1.Position; % position of first axes
ax2 = axes('Position',ax1_pos,...
    'XAxisLocation','top',...
    'YAxisLocation','right',...
    'Color','none');

axis equal
% axis tight

% Add labels
ax1Xtck = ax1.XTick';
ax1Ytck = ax1.YTick';

ax2.XTickLabel = num2str(interp1(x,lon,ax1Xtck,'linear','extrap'));
ax2.YTickLabel = num2str(interp1(y,lat,ax1Ytck,'linear','extrap'));

[Cris LaPierre]

If you really want axis tight as well, you have to put some data on ax2 so that it knows what it is tightening to. It doesn't have to be visible, but does have to be there. Try this. It's not pretty, but it works.

% Lat/lon, convert to meters
lat0 = 51.2697; % deg
lon0 =  -77.3379; % deg
dLat =    1.5696e-07; %meters/radian lat here 
dLon =   2.5087e-07;  %meters/radian lon here
% Set up some random walk
dx = rand(100,1);
dy = rand(100,1); 
x = cumsum(dx);
y = cumsum(dy);
% Convert that to lat/lon
lat = 360/(2*pi)*y*dLat + lat0; 
lon =  360/(2*pi)*x*dLon + lon0;
% Plot our walk in meters
close all
figure();
scatter(x,y,'b.'); 
 xlabel('Easting (m)');
 ylabel('Northing (m)');
 set(gca,'box','off')
% Set axes as equal. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% comment out for other option
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
axis equal; 
axis tight;

% Suggested by Mathworks
ax1 = gca; % current axes
ax1_pos = ax1.Position; % position of first axes
ax2 = axes('Position',ax1_pos,...
    'XAxisLocation','top',...
    'YAxisLocation','right',...
    'Color','none');
line(x([1 end]),y([1 end]),'Parent',ax2,'Linestyle','none')
axis equal
axis tight

% Add labels
ax1Xtck = ax1.XTick';
ax1Ytck = ax1.YTick';

ax2.XTickLabel = num2str(interp1(x,lon,ax1Xtck,'linear','extrap'));
ax2.YTickLabel = num2str(interp1(y,lat,ax1Ytck,'linear','extrap'));

[Cris LaPierre]

BTW, Tick labels are strings and don't have to correspond to the actual x or y value where they are. Because the labels already align with ax1, I thought it might be easier to use the values of lon and lat you already computed, so I use interp1 to interpolate the values for ax2 using the vectors for x, y, lat, lon and the current ax1 tick values.

[D. Plotnick]

Thanks! A slightly modified version of the above work correctly, with the exception of "axis tight" still being squirelly.

I got around this by adding in 'linkaxes(ax1,ax2)', which prevents issues when I slide the view (canvas?) around, and then I can approximate 'axis tight' using 'axis([min(x) max(x) min(y) max(y)]);'

I now have some of the tick labels running into each other, but I know how to fix that.

Thanks again for your help. I do think that this would be a useful type of command to have in the core Matlab plotting library, and may submit a feature request for it. One where you can add a second set of tick-marks/units automatically locked to the view set using the initial set. Very useful for plotting things that have 2 standard units associated with them, pressure in bars vs psi for example. For some of these cases, there may be 3 or 4 standard units, but that may be asking for a bit much from the right side axis.

Cheers,

-Dan

[Cris LaPierre]

This isn't the first time this request has come up. If it would be useful to you, please do submit the request.