Draw ellipse in image

I would like to draw an ellipse (black-filled) in a white canvas given the center coordinates of the ellipse.

For rectangle, I did it this way (need to fill the rectangle) but for ellipse it seems to be more difficult.

width = 300;
objectWidth = 60; 
    canvas = ones(width, width);
    figure, imshow (canvas);
    square = rectangle('Position', [60-objectWidth/2, 40-objectWidth/2,  objectWidth, objectWidth], ...
'EdgeColor', [0.5 0.5 0.2]);

I was thinking of the following formula for the ellipse:

   a = 1/2*sqrt((x2-x1)^2+(y2-y1)^2);
   b = a*sqrt(1-e^2);
   t = linspace(0,2*pi);
   X = a*cos(t);
   Y = b*sin(t);
   w = atan2(y2-y1,x2-x1);
   x = (x1+x2)/2 + X*cos(w) - Y*sin(w);
   y = (y1+y2)/2 + X*sin(w) + Y*cos(w):
   plot(x,y,'y-')
   axis equal

Any hints would be great. Btw. Happy New Year!

Answer 1

[Image Analyst]

See the FAQ: http://matlab.wikia.com/wiki/FAQ#How_do_I_create_an_ellipse.3F

Also see my attached demos.

[Kamu]

Thanks, your demos were useful to understand the implementation of ellipse better. However, before I try to apply ellipse I still stuck with rectangle. I would like to have a filled rectangle. With 'patch' function it did not work because of the rectangle function.

[Image Analyst]

What values were you using for the 'FaceColor' and 'Edgecolor' properties in rectangle(). I didn't see where you set those. What did you use?

Answer 2

[KSSV]

clc; clear all ;
% An ellipse can be defined as the locus of all points that satisfy the equations
% x = a cos t 
% y = b sin t
% where:
% x,y are the coordinates of any point on the ellipse, 
% a, b are the radius on the x and y axes respectively,
t = linspace(0,2*pi) ;
a = 30 ; b = 15 ;
x = a*cos(t) ;
y = b*sin(t) ;
plot(x,y,'r')
axis equal

[Hossein Sahhaf]

Very well. Brief and complete.

[Frank Uhlig]

So, this draws an ellipse that has major axes parallel to the coordinate axes and has center at the origin ... . How about a general lay for the axes? and a general lay for the center point?

[Jiawei Xu]

Just adding to the answer to KSSV: To tilt the ellipse, you can multiply the points with a rotation matrix generated with the function:

function R = Rot2D(angle)
    R = [cos(angle), -sin(angle); 
        sin(angle), cos(angle)];
end

such that

R = Rot2D(angle);
XY_rotated = R*[x;y];
plot(x,y,'r')

We do not know the `angle` here, but if you have the long radius and short radius available to you in vector form, such as

a = [1;5];
b = [-2,0.4];

you can find this angle by applying

angle = atan2(a(2), a(1));

Answer 3

[sashidhar]

clc

clear all

t=linspace(0,2*pi);

a=input('Enter the xcoordinate of the ellipse: ');

b=input('Enter the ycoordinate of the ellipse: ');

x=a*cos(t);

y=b*sin(t);

plot(x,y)

axis equal