How can I rotate the axes' labels parallel to the orientation of the axes?

Hi. I would like to know how to rotate labels and keep them centered with their orientation. Please see Fig 1. This figure is the default view output using the following syntax.

xlabel('x','Rotation',35)

ylabel('y','Rotation',-35)

However, in Fig 2, the plot view is set to:

view([73 24])

Is there a solution to rotate the labels parallel to the orientation of the axes by changing the view values? In this case, the 'Rotation' value (in this example, 35 and -35) changes as a function of the 'View' value (i.e., 73 and 24). Thank you so much for your time and consideration.

[X,Y,Z] = peaks(25);
figure
subplot(1,2,1)
surf(X,Y,Z);
xlabel('x','Rotation',35)
ylabel('y','Rotation',-35)
zlabel('z')
title('Fig.1')

subplot(1,2,2)
surf(X,Y,Z);
xlabel('x')
ylabel('y')
zlabel('z')
view([73 24])
title('Fig.2')

Answer 1

[Bruno Luong]

Try this (the letters of label are rotated but the aspect ratio remain constant so they can be read easily but are not look like "projected" on the xy plane)

The angles depend on figure/axes aspect ratio, so if you resize them you have to compute the angle again.

[X,Y,Z] = peaks(25);

fig = figure(1);
clf(fig);
t = tiledlayout(2,2);
for k = 1:prod(t.GridSize)
    ax = nexttile(t);
    surf(ax, X, Y, Z);
    %axis(ax, 'equal')
    view(ax, rand*360, 40); % random azimuth

    set(ax,'unit','pixel');
    axPosition = ax.Position;
    dx = axPosition(3);
    dy = axPosition(4);

    [xx, xy] = ScreenProjection(ax, xlim(ax), [0 0], [0 0]);
    thetax = atan(diff(xy)/diff(xx)*dy/dx);
    xlabel('here is the x-label', 'Rotation', rad2deg(thetax))

    [xx, xy] = ScreenProjection(ax, [0 0], ylim(ax), [0 0]);
    thetay = atan(diff(xy)/diff(xx)*dy/dx);
    ylabel('here is the y-label', 'Rotation', rad2deg(thetay))
    
    zlabel('z')
end

% https://www.mathworks.com/matlabcentral/answers/430790-how-can-i-get-the-screen-coordinates-from-perspective-projection?s_tid=srchtitle
function [xcam, ycam] = ScreenProjection(ax, X, Y, Z)
dataRatio = get(ax, 'DataAspectRatio');
matrixRescale = diag(1./dataRatio);
CT = get(ax,'CameraTarget');
CP = get(ax,'CameraPosition');
CU = get(ax,'CameraUpVector');
cadeg = get(ax,'CameraViewAngle');

CT = CT(:);
CP = CP(:);
CU = CU(:);
ca = cadeg*pi/180;
%
c = CT-CP;
d = norm(c);
c = c / d;
u = CU - dot(c, CU)*c;
u = u/norm(u);
p = cross(c,u);
R=[c,p,u];
XYZ = [X(:),Y(:),Z(:)]';
CPU = R'*(matrixRescale*(XYZ-CP));
XYcam = CPU(2:3,:)./CPU(1,:);
xcam = XYcam(1,:);
ycam = XYcam(2,:);
end

[Navid]

Thank you for your assistance. Regrettably, the 'tiledlayout' syntax is not supported in my version.

[Bruno Luong]

tiltelayout It is not important to compute the angle of labels, replace nextile with subplot command

[X,Y,Z] = peaks(25);

fig = figure(1);
clf(fig);
for k = 1:4
    ax = subplot(2,2,k);
    surf(ax, X, Y, Z);
    %axis(ax, 'equal')
    view(ax, rand*360, 40); % random azimuth

    set(ax,'unit','pixel');
    axPosition = ax.Position;
    dx = axPosition(3);
    dy = axPosition(4);

    [xx, xy] = ScreenProjection(ax, xlim(ax), [0 0], [0 0]);
    thetax = atan(diff(xy)/diff(xx)*dy/dx);
    xlabel('here is the x-label', 'Rotation', rad2deg(thetax))

    [xx, xy] = ScreenProjection(ax, [0 0], ylim(ax), [0 0]);
    thetay = atan(diff(xy)/diff(xx)*dy/dx);
    ylabel('here is the y-label', 'Rotation', rad2deg(thetay))
    
    zlabel('z')
end

% https://www.mathworks.com/matlabcentral/answers/430790-how-can-i-get-the-screen-coordinates-from-perspective-projection?s_tid=srchtitle
function [xcam, ycam] = ScreenProjection(ax, X, Y, Z)
dataRatio = get(ax, 'DataAspectRatio');
matrixRescale = diag(1./dataRatio);
CT = get(ax,'CameraTarget');
CP = get(ax,'CameraPosition');
CU = get(ax,'CameraUpVector');
cadeg = get(ax,'CameraViewAngle');

CT = CT(:);
CP = CP(:);
CU = CU(:);
ca = cadeg*pi/180;
%
c = CT-CP;
d = norm(c);
c = c / d;
u = CU - dot(c, CU)*c;
u = u/norm(u);
p = cross(c,u);
R=[c,p,u];
XYZ = [X(:),Y(:),Z(:)]';
CPU = R'*(matrixRescale*(XYZ-CP));
XYcam = CPU(2:3,:)./CPU(1,:);
xcam = XYcam(1,:);
ycam = XYcam(2,:);
end

[Navid]

Thank you for sharing your time. The code was executed successfully. Fig (a) was obtained from your code. However, it would be great if the axes labels were centered. Thank you anyway.

Fig (a):

[Bruno Luong]

However, it would be great if the axes labels were centered

See option 'HorizontalAlignment'

xlabel(..., 'HorizontalAlignment','center')
ylabel(..., 'HorizontalAlignment','center')

EDIT: the option seems to perform incorrectly when figure has position different than the default.

[Navid]

Indeed, this option may not deliver accurate performance when utilized for a position other than the default. Thank you again for your consideration.

[Steven Lord]

FYI, there is a discussion of the interaction between the *Alignment properties and the Position property here.

[Navid]

Thank you for sharing this content.

[Bruno Luong]

Disapointly the authority's answer of this thread explains the reason of the flaw and unable to suggest a satisfactition way to center label to axe position, beside "do it manually".

When I have time I'll make a code to position and center the labels.

[Navid]

Thank you very much for your kindness and for taking the time to help me. Your assistance is greatly appreciated.