How to create a secondary Cartesian coordinate system (three perpendicular coordinate axes) in Matlab?

Hi, is it possible to create a secondary Cartesian coordinate system (i.e. the three mutually perpendicular coordinate axes) with origin at one of the three objects in this figure? If Yes, how? Any command or example?

Answer 1

[Adam Danz]

To add the additional axis lines,

box on

% Or

box(ax, 'on') % ax is the axis handle

but I didn't understand this part: with origin at one of the three objects

Update

The undocumented Matlab blog shows how to move the location of axes origin

figure()
tiledlayout(1,2,'padding','none')
ax1 = nexttile; 
xyz = [.5, .5, .5]; 
plot3(ax1, xyz(1), xyz(2), xyz(3), 'o', 'MarkerSize', 14)
grid(ax1, 'on')

axis(ax1, 'equal')
xlim(ax1, [0,1])
ylim(ax1, [0,1])
zlim(ax1, [0,1])

ax1.XRuler.FirstCrossoverValue = xyz(2);   % y
ax1.XRuler.SecondCrossoverValue  = xyz(3); % z

ax1.YRuler.FirstCrossoverValue = xyz(1);   % x
ax1.YRuler.SecondCrossoverValue  = xyz(3); % z

ax1.ZRuler.FirstCrossoverValue = xyz(1);   % x
ax1.ZRuler.SecondCrossoverValue  = xyz(2); % y

% Axis labels will also move with the axes
%     xlabel(ax1, 'X axis')
%     ylabel(ax1, 'Y axis')
%     zlabel(ax1, 'Z axis')
title(ax1, 'Origin at xyz coordinate')

ax2 = nexttile; 
xyz = [.5, .5, .5]; 
plot3(ax2, xyz(1), xyz(2), xyz(3), 'o', 'MarkerSize', 14)
grid(ax2, 'on')

axis(ax2, 'equal')
xlim(ax2, [0,1])
ylim(ax2, [0,1])
zlim(ax2, [0,1])

ax2.XRuler.FirstCrossoverValue = xyz(2);   % y

ax2.YRuler.FirstCrossoverValue = xyz(1);   % x

ax2.ZRuler.FirstCrossoverValue = xyz(1);   % x
ax2.ZRuler.SecondCrossoverValue  = xyz(2); % y

title(ax2, 'Origin on XY plane')

% Axis labels will also move with the axes
%     xlabel(ax2, 'X axis')
%     ylabel(ax2, 'Y axis')
%     zlabel(ax2, 'Z axis')

If all you're looking for is reference lines without the ticks, you can use xline() and yline() to add the x and y ref lines. There is no zline() so you'll have to use plot3 something related. Note that xline and yline lines will update when the axis limits change but that won't happen with the plot3 line. Also note that the xline and yline lines are partially transparent by default. You can set the alpha levels to 1 to remove transparency or you can set the transparency of the z-line to match the x & y lines by adding a 4th value to the RGB color (ie, set(..., 'Color', [0 0 0 .4]))

figure()
ax = gca(); 
xyz = [.5, .5, .5]; 
plot3(ax, xyz(1), xyz(2), xyz(3), 'o', 'MarkerSize', 14)
grid(ax, 'on')

axis equal
xlim(ax, [0,1])
ylim(ax, [0,1])
zlim(ax, [0,1])

xline(ax, xyz(1), 'k--', 'XAxis') % see xline properties to control label placement
yline(ax, xyz(2), 'k--', 'YAxis')
hold(ax,'on')
plot3(ax, xyz([1,1]), xyz([2,2]), zlim(ax), 'k--')
title(ax, 'line objects')

[Sim]

Hi @Adam, many thanks for your reply :)

...with the term "origin" I mean the origin of the Cartesian coordinates system, i.e. the point (0,0,0).. in other words, I mean the point from where the three perpendicular x, y and z axes "start"...

About the "three objects", you can see that in that Figure there are three coloured objects/items/elements, one orange, one green, one blue...

In summary, I would like to create a secondary Cartesian system, i.e. another triplet of three perpendicular axes, where its origin is located/positioned at one of the three coloured objects/items (either over the orange, or the green or the blue one)....

Alternatively, instead of creating a secondary/additional cartesian system (i.e. the triplet of perpendicular x, y, a axes), would it be possible to move the current triplet of x, y and z axes over one of the three coloured objects/items/elements in my Figure?

[Adam Danz]

I've updated my answer with two additional solutions.

The first one that sets crossover values for each axis can only be applied to 1 datapoint.

[Sim]

Many many thanks!! Both solutions are cool and very useful!

P.S.:I did not know about the undocumented Matlab blog... very interesting!

[Adam Danz]

No problem.

I just added another example of the crossover approach with the x and y axis lines along the XY plane.

[Sim]

Chapeau! I am really confident that all these examples will be very useful to the Matlab community! Many many thanks! :)