Draw a Semi-Ellipse using a loop

I would like to draw a semi-ellipse using dot products and a loop. I want to use the dot product of the x-value and the m-value to draw it (specifically where the dot product of x and m is greater than the given eccentricity e), but I can't get the while loop to draw the ellipse in polar coordinates. Let me know if you need me to explain any of the variables.

function polar_refracted_ellipse_dotted(t,e,m)
x=0:.01:2*pi;
x_dot_m=cos(x)*cos(m)+sin(x)*sin(m);
r=(t)./(1-e.*x_dot_m);
clf;
while x_dot_m>e
    for m_value=(m:pi/12:2*pi+m)
        new_m_dot_old_m=cos(m_value).*cos(m)+sin(m_value).*sin(m);
        r_1=(t)./(1-e*new_m_dot_old_m);
        r_2=(0:0.01:r_1);
        new_theta=m_value.*(r_2./r_2);
        polarplot(r)
        hold on
        polarplot(new_theta,r_2)
        rlim([0 t*6])
    end
end

[darova]

What values should be t, e, m to see how it works?

And what result you expect to see?

[Thales]

I don't quite understand what you are trying to draw. By 'semi-ellipse' do you mean half of an ellipse? If so, the parametric equations of an ellipsis is:

where a, b are the radius on the x and y axes respectively. With that in mind, you can simply code:

a = 7; b = 2;
t = 0:0.1:pi;
x = a*cos(t); y = b*sin(t);
plot(x,y); axis([-a a -b b])

[Destin Davis]

t is any given value, e should be a value between 0 and 1, and m is an angle given in radians.

[Destin Davis]

I expect to see a semi-ellipse with a focus located at the origin and with the major axis in the direction of m.

[Destin Davis]

It specifically has to be in polar coordinates and use the dot product of the two values. Mostly, I have to figure out how to get the while loop to work for an inequality.