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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,'.') 
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    Please, write in $\LaTeX$. You can learn some codes like, `${x}^{2n+1}$` makes ${x}^{2n+1}$, `$\sin \theta$` makes $\sin \theta$ and `$T_{2n}$` makes $T_{2n}$2012-03-05

2 Answers 2

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Problem solved: General parametric form parameter does not require origin inside ellipse, but I think general polar form parameter does because 'Q' in general polar form parameter could be complex number if r0 is large

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Maybe $r=\sqrt{t_X^2+t_Y^2}$. Else you got a part of a circle.

(I'm french. I hope you will excuse my english.)

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    I did it like this, but Peter T.off edit my question and he had a typo2012-03-05