Screen (2D) projection of 3D plot

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Oleg Komarov on 13 Oct 2015
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,:))

Mike Garrity on 13 Oct 2015
I talked about the theory behind this in this recent post on the MATLAB Graphics blog.
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.
EMMANUEL VIRATEL on 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