
Screen (2D) projection of 3D plot
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Oleg Komarov
am 13 Okt. 2015
Kommentiert: EMMANUEL VIRATEL
am 4 Apr. 2021
How can I get the screen projection (2D) of the following 3D plot:
h = ezplot3('t', 'sin(t)', '20*cos(t)', [0 10*pi]);

The following solution as in the example in viewmtx() does NOT achieve the expected result (although it does for e.g. h = ezplot3('cos(t)', 'sin(t)', 'sin(5*t)', [-pi pi])):

% Original data
data = get(h,{'XData','YData','Zdata'});
data = [cat(1,data{:})', ones(numel(data{1}),1)];
% Projection matrix
[az,el] = view();
A = viewmtx(az,el);
% Projected data
data_transformed = A*data';
plot(data_transformed(1,:), data_transformed(2,:))
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Mike Garrity
am 13 Okt. 2015
The basic idea is that you want to take the data from your object like this:
h = ezplot3('t', 'sin(t)', '20*cos(t)', [0 10*pi]);
pts = [h.XData; h.YData; h.ZData; ones(size(h.XData))];
and then multiply it by the view transform. Unfortunately accurately reproducing the view transform for an arbitrary 3D MATLAB plot can be a bit tricky. It is pretty close to this:
mat = viewmtx(-37.5,30) * makehgtform('scale',1./[20 1 20])
The first half of that is the azimuth and elevation. The second half is the DataAspectRatio.
Once you have that matrix, you can transform your points like this:
pt2 = mat * pts;
x = pt2(1,:) ./ pt2(4,:);
y = pt2(2,:) ./ pt2(4,:);
If we plot those, we'll see that I'm close, but slightly off:
plot(x,y)
axis equal

I think I've neglected to account for the PlotBoxAspectRatio, but I'm not 100% sure of that.
Hope that helps.
2 Kommentare
EMMANUEL VIRATEL
am 4 Apr. 2021
Hello Mike,
I'm emmanuel, an electronic student from TOULOUSE (France) I've seen your post above with the screw and, with homogenous coordinates, i want to draw with the instruction plot a sinus cardinal in 3D like in the end of my code but with plot and not with mesh. it takes months that i search the solution but i hope you will answer me quickly on my personnal email: viratelemmanuel@yahoo.fr
h = ezplot3('t', 'sin(t)', '20*cos(t)', [0 10*pi]);
pts = [h.XData; h.YData; h.ZData; ones(size(h.XData))];
mat = viewmtx(-37.5,30) * makehgtform('scale',1./[20 1 20])
pt2 = mat * pts;
x = pt2(1,:) ./ pt2(4,:);
y = pt2(2,:) ./ pt2(4,:);
plot(x,y)
axis equal
% Now, what i want to draw with plot
x=-pi/2:pi/100:pi/2;
y=x;
[X,Y]=meshgrid(x,y);
Z=sinc(X.^2+Y.^2);
h=mesh(X,Y,Z);
Thanks a lot
Best regard
Emmanuel
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