I am facing problem to convert ellipse standard parameters. Everything I say here is refer to http://en.wikipedia.org/wiki/Ellipse
I know what are the General parametric form parameter . Lets call them $a$,$b$,$\varphi$, $t_X$, $t_Y$
Now I need to find the general polar form parameter. I follow the equation in wikipedia But I may misunderstand what it says.
Here is what I think
$r_0 = \sqrt{tx^2+ty^2}$ $\theta_0 = \tan^{-1} \frac{t_Y}{t_X}$ and $ \phi = \varphi$
I think I am worng, because the output plot was not right. Please help
The following is my MATLAB code, the upper section is the general parametric form, I also draw the ellispe. The lower section is my incorrect general polar form
%==================
close all
data = [0.6397 0.9520 15.9195 1.1430 -0.3844]; a = data(1); b = data(2); ang = data(3); tranX = -data(4); tranY = -data(5); x = zeros(1,3601); y = zeros(1,3601); counter = 1; for t = 0:.1:360 x(counter) = tranX + a*cosd(t)*cosd(ang) - b*sind(t)*sind(ang); y(counter) = tranY + a*cosd(t)*sind(ang) + b*sind(t)*cosd(ang); counter=counter+1; end figure;plot(x,y) %============================================= r0 = norm([tranX tranY]); theta0 = atand(tranY/tranX); rho = ang; rr = zeros(1,3601); counter = 1; for t = 0:.1:360 P(counter) = r0*[(b*b-a*a)*cosd(t+theta0-2*rho)+(a*a+b*b)*cosd(t-theta0)]; R(counter) = (b*b-a*a)*cosd(2*t-2*rho)+a*a+b*b; Q(counter) = sqrt(2)*a*b*sqrt(R(counter)-2*r0*r0*(sind(t-theta0))^2); rr(counter) = (P(counter)+Q(counter))/R(counter); counter = counter + 1; end [XX,YY] = pol2cart((0:.1:360)*2*pi/180,rr); figure; plot(XX,YY,'.')