How to draw a rotated ellipse without any toolbox?

I need to draw rotated ellipse on a Gaussian distribution plot by surf. I am using a student version MATLAB. Can i still draw a ellipse center at estimated value without any toolbox that required money to buy. I search on internet somebody write ellipse function and allow to download. Are they work well on surf plot.

Answer 1

[Babak]

 t = linspace(0,2*pi,1000);
 theta0 = pi/6;
 a=2;
 b=1;
 x = a*sin(t+theta0);
 y = b*cos(t);
 plot(x,y)
 axis equal

[ManKit Tse]

A bug found on the code. When a or b is close to 0, the shape of ellipse is not tilted. When a or b is close to 0, only a horizontal line can be seen instead of tilted line. Can somebody tell me how to fix it?

[Image Analyst]

Well yeah, because if a or b is really close to zero, the width is really close to zero and the ellipse is essentially almost a line. And a line has to lie along the raster lines on your monitor. The line can be on line 1 or on line 2. You can't have pixels going across the screen at line 1, line 1.01, line 1.02, etc. up to line 1.88 or whatever. It's got to be just on line 1 or on line 2, not on fractional lines. For further reading: http://en.wikipedia.org/wiki/Jaggies

[Gabriel Hernandez]

This code did not work for me. The answer posted below is much more accurate.

Answer 2

[Oleksii Sidorov]

My version with general parametric equation of rotated ellipse, where 'theta' is angle of CCW rotation from X axis (center at (x0, y0))

 t = linspace(0,2*pi,100);
 theta = deg2rad(105);
 a=2;
 b=1;
 x0 = 0.15;
 y0 = 0.30;
 x = x0 + a*cos(t)*cos(theta) - b*sin(t)*sin(theta);
 y = y0 + b*sin(t)*cos(theta) + a*cos(t)*sin(theta);
 figure;
 plot(x,y);
 axis equal;

[Gabriel Hernandez]

Your code worked perfectly for me, much better than the one from the accepted answer. Thank you!

[Vivek Bhartiya]

Fantastic work. It was quite hard to find a functional code.