Circle projection to be ellipse on the ground

Have an ellipse with r2 - major axis and r1 - minor axis, and tilted at some degree. Above of the ellipse at some arbitrary height need to draw a circle with radius r2. Theoritically, if we incline the circle under degree, it's projection to the ground plane must give us the ellipse.

For that, I have tried by using the rotate function. I have used it two time in the scretch. First, I inclined the circle around x-axis. Second, by saving the last properties of the first rotation, I have used them to rotate around z-axis. As a result, I have had kinda desirable but not well. I was working on the matter during this week, but still can't get a good result.

Here's my code:

% r1 and r2, minor and major axis of the ellipse
% xm and ym are mean values of the ellipse x and y parametres, so center of the circle and ellipse is the same
% 
% circle draw
r = r2;
teta = linspace(0, 2*pi, 100);
x = r*cos(teta) + xm;
y = r*sin(teta) + ym;
z = 10*ones(1,length(x));
inclined_angle = acosd(r1/r2);
g = plot3(x, y, z);
grid on
xlabel('x')
ylabel('y')
zlabel('z')
rotate(g, [1 0 0], inclined_angle);
newx = g.XData;
newy = g.YData;
newz = g.ZData;
gg = plot3(newx, newy, newz);
rotate(gg, [0 0 1], alpha)
grid on
xlabel('x')
ylabel('y')
zlabel('z')
% ellipse
hold on 
plot(xrange, yrange, 'color', [0.9290 0.6940 0.1250], 'LineWidth', 1.6);

Also,

xm = -0.769, ym = -0.148, r1 = 6.867, r2 = 10.073, alpha = 18.372, inclined_angle = 47.022

I have attached here some data of xrange and yrange for the ellipse in txt. files and my resultant plots.

3D:

if we look from above, 2D: From this picture we can see tha projection of the circle is not exactly on our ellipse, on a bit different positions. I need to find the besst solution for it.

I would be so appriciated if somebody help me to handle this issue.

[Matt J]

The code you've provided doesn't run to completion, in part because xrange, yrange are not defined.

[Mirzobek Malikov]

i have attached ellipse_xrange and ellipse_yrangle txt. files to the question already

[Mirzobek Malikov]

where you can find datas of xrange and yrange

[Matt J]

But your posted code does not include the code that you use to load it. Here's what I get,

>> xrange=readmatrix('ellipse_xrange.txt')

xrange =

   NaN

[Mirzobek Malikov]

To draw ellipse I used to calculate xrange and yrange points. xrange is 1x1000 and yrange contains 2x1000. The reason is I have calculated the ellipse upper and lower part separately, that's why yrange contains two raws, one is for the upper, another one is for the lower part, but for both has same xrange length. After uploading datas, if you run plot(xrange, yrange) you will get complete ellipse.

[Mirzobek Malikov]

To get xrange and yrange data, open the txt files, then copy it and past in Matlab command window by equalizing to variables xrange and yrange is recommended.

[Mirzobek Malikov]

Here also, I have uploaded plots of the ellipse with lower part and upper part only, and together

[Matt J]

To get xrange and yrange data, open the txt files, then copy it and past in Matlab command window by equalizing to variables xrange and yrange is recommended.

I have a better idea. Why don't you include xrange, yrange for us in a .mat file, which can be straightfowardly loaded in.

[Mirzobek Malikov]

sorry, i am rookie to Matlab. Here I have uploaded .mat files of xrange and yrange

Answer 1

[Matt J]

The final position of the projected ellipse will depend on the z-coordinates that you have before the rotation.

z = 10*ones(1,length(x));

You don't seem to have accounted for that anywhere in your comparison.

[Mirzobek Malikov]

yeah, i didn't add it, because i am not gonna rotate the ellipse, instead circle needs to be rotated.

[Matt J]

Is your question resolved, then? I can't tell from your response.

[Mirzobek Malikov]

no.

my aim is to get this picture

[Matt J]

Download this,

https://www.mathworks.com/matlabcentral/fileexchange/30864-3d-rotation-about-shifted-axis?tab=discussions

and then,

x = r*cos(teta) + xm;
y = r*sin(teta) + ym;
z = 10*ones(1,length(x));

XYZ=num2cell( AxelRot([x;y;z],inclined_angle,[1,0,0],[xm,ym,z(1)])  ,1);

[newx,newy,~]=deal(XYZ{:});

plot(xnew,ynew,xrange,yrange,'x')