Question

I’ve been using a function file [ret]=drawellipse(x,y,a,b,angle,steps,color,img). Calling the function through a script file to draw random ellipses in image. But once i set the random center point(x,y), and random a, b, there is high possibility that the ellipses intersection would occur. How can i prevent the intersection? (I’m supposed to draw the ellipses that are all separate from each other)
Well, over here i have a function file which is to check whether the ellipses got overlap or not,overlap = overlap_ellipses(x0,y0,a0,b0,angle0,x1,y1,a1,b1,angle1). If the two ellipses are overlap, then the ‘overlap=1’, otherwise ‘overlap=0’.
Based on all these, i tested in the command window:

x=rand(4,1)*400;  % x and y are the random coodinates for the center of ellipses
y=rand(4,1)*400;
a=[50 69 30 60];  % major axis   for a and b, i intend to use random also in the future
b=[20 40 10 40];  % minor axis
angle=[30 90 45 0]; % angle of ellipse
steps=10000;
color=[255 0 0];   % inputs for another function file to draw the ellipse
img=zeros(500,500,3);

The following i want to dispaly the ellipses if overlap==0, and ‘if overlap==1’, decrease the a and b, till there is no intersection. Lastly, to imshow the img.

for i=1:length(x)
img=drawellipse(x(i),y(i),a(i),b(i),angle(i),steps,color,img);
end

For me now, i have difficulty in coding the middle part. How can i use the if statement to get the value of overlap and how to make the index corresponding to the ellipse i need to draw.

i tested a bit like

for k=1:(length(x)-1)
overlap = overlap_ellipses(x(1),y(1),a(1),b(1),angle(1),x(1+k),y(1+k),a(1+k),b(1+k),angle(1+k))
end

it returns

overlap=0
overlap=0
overlap=1

it is not [0 0 1]. I can’t figure it out, thus stuck in the process.
The final image shoule look like the picture in this voronoi diagram of ellipses.
(There is no intersection between any two ellipses)

Answer 1

The solution proposed by @arne.b (the first one) is a good way to rasterize non-overlapping ellipses.

Let me illustrate that idea with an example. I will be extending my previous answer:

%# color image
I = imread('pears.png');
sz = size(I);

%# parameters of ellipses
num = 7;
h = zeros(1,num);
clr = lines(num);             %# color of each ellipse
x = rand(num,1) .* sz(2);     %# center x-coords
y = rand(num,1) .* sz(1);     %# center y-coords
a = rand(num,1) .* 200;       %# major axis length
b = rand(num,1) .* 200;       %# minor axis length
angle = rand(num,1) .* 360;   %# angle of rotation

%# label image, used to hold rasterized ellipses
BW = zeros(sz(1),sz(2));

%# randomly place ellipses one-at-a-time, skip if overlaps previous ones
figure, imshow(I)
axis on, hold on
for i=1:num
    %# ellipse we would like to draw directly on image matrix
    [ex,ey] = calculateEllipse(x(i),y(i), a(i),b(i), angle(i), 100);

    %# lets plot the ellipse (overlayed)
    h(i) = plot(ex,ey, 'LineWidth',2, 'Color',clr(i,:));

    %# create mask for image pixels inside the ellipse polygon
    mask = poly2mask(ex,ey,sz(1),sz(2));

    %# get the perimter of this mask
    mask = bwperim(mask,8);

    %# skip if there is an existing overlapping ellipse
    if any( BW(mask)~=0 ), continue, end

    %# use the mask to place the ellipse in the label image
    BW(mask) = i;
end
hold off
legend(h, cellstr(num2str((1:num)','Line%d')), 'Location','BestOutside')    %'

%# set pixels corresponding to ellipses using specified colors
clr = im2uint8(clr);
II = I;
for i=1:num
    BW_ind = bsxfun(@plus, find(BW==i), prod(sz(1:2)).*(0:2));
    II(BW_ind) = repmat(clr(i,:), [size(BW_ind,1) 1]);
end
figure, imshow(II, 'InitialMagnification',100, 'Border','tight')

Note how the overlap test is performed in the order the ellipses are added, thus after Line1 (blue) and Line2 (green) are drawn, Line3 (red) will be skipped because it overlaps one of the previous ones, and so on for the rest…