I wrote a program that creates an ellipse made of a series of points that can be rotated by an angle, psi, in the xy plane. I am using a rotation matrix to rotate the ellipse.

angle = linspace(0, Num_periods*2*pi, N_frames);

x1 = a1 * cos(angle);
y1 = b1 * sin(angle);

psi=pi/4;
R1 = [cos(psi), -sin(psi); sin(psi), cos(psi)];

ellipse1 = R1 * [x1; y1];

x1_rot = ellipse1(1, :) + x1_0;
y1_rot = ellipse1(2, :) + y1_0;

I am then attempting to add another point which should be located at a distance l_proj_1 from the center in the direction of the short axis, but it is located in different spots relative to the ellipse based on different angles. I also notice that the shape of the ellipse changes sometimes based on the rotation angle, which also should not happen. Is this an error in my code or Matlab and how do I fix either. Thank you.

phi_1 = pi/12; %angle of opening 
theta_1 = pi/4; %tilt angle
l_1 = a1/(sin(phi_1));
l_proj_1 = l_1*cos(phi_1)*cos(theta_1);

x0_base_1 = x1_0 + l_proj_1*cos(psi);
y0_base_1 = y1_0 + l_proj_1*sin(psi);

figure;
for i = 1:N_frames
    plot(x1_rot(i),y1_rot(i),'o')
    axis([0 nx 0 ny])
    hold on
    pause(.5)
    plot(x0_base_1,y0_base_1,'o')
end

I have tried altering the sin’s and cos’s of the bases and the negatives. It is never consistent.