Is this code correct for the ellipse equation given below..?? Will I get rotated ellipse from this code..??

My equation is

I have used Parametric equations of an ellipse here. I need rotated ellipse from this code. But I am getting bent ellipse. Kindly check and let me know the solution asap. *.Mat file is also attached.

th = 0:pi/50:2*pi;
m1=9;
m2=9;
sd1=3;
sd2=2;
r=0.7;   
x1 = m1+ (sqrt(1-r^2)*sd1).* cos(th); 
x2 = m2+ (sqrt(1-r^2)*sd2).* sin(th);
knum = (2*r*((sqrt(1-r^2)*sd1).* cos(th))* (sqrt(1-r^2)*sd2).* sin(th));
kdenom = (sd1*sd2*(1-r^2));
k=-(knum/kdenom);
h = plot3(x1,x2,k, 'black','linewidth',0.3);

Bent ellipse is like this...

Kindly correct my code to get rotated ellipse properly.

Answer 1

[Roger Stafford]

Your attempt to parameterize is invalid, Santhosh. If you do a plot of your original expression, you will see it does not have a constant value.

Here is a parametrization that will produce your ellipse:

t = linspace(0,2*pi);
x1 = m1 + s1*(sqrt(1+r)*cos(t)+sqrt(1-r)*sin(t))/sqrt(2);
x2 = m2 + s2*(sqrt(1+r)*cos(t)-sqrt(1-r)*sin(t))/sqrt(2);
plot(x1,x2)
axis equal

If you use this to evaluate the original expression above, you will see that it is a constant 1 as t varies, (which is the value I assume you wish to set the expression to.)

[Santhosh LG]

@ Roger Stafford: It's worked.. I thank you very very much for providing me the code.. Very helpful.. :) :)