Annular ring pattern with alternate bright and dark rings: using matlab - matlab

Question

I am attempting to make a pattern consisting of annular rings with radii proportional to the square root of the natural numbers. Also I want the inner most circle to be white followed by a black circle followed by a white and so on.
c = [0 0; 0 0];
r = [5.2494 9.0922];
viscircles(c, r)
r1 = [7.4328 10.4988];
viscircles(c, r1)
I have generated the above code to form the annular ring structure but I want to fill in the color as well. What should I do?

Answer 1

You could go the mathematical route and plot the function ceil(sin(pi*(X.^2 + Y.^2))):
zoomlevel = 50;
for n = 1:zoomlevel
[X,Y] = ndgrid(linspace(-n,n,500));
I = ceil(sin(pi*(X.^2 + Y.^2)));
imshow(mat2gray(I));
drawnow;
pause(0.03);
end
Of course this will only be a raster graphic instead of a vector one, so don't zoom in too much. ;-) (Although the aliasing artefacts will look quite cool if you zoom out. Plot at your own risk.)

Answer 2

My Matlab version doesn't have viscircles, so here's an approach which plots each individual circle with alternating colors. It uses the rectangle function, which lets you define the curvature of the corners so that the rectangle/square becomes an ellipse/circle. Bigger circles should be drawn first, so that they don't completely cover smaller circles.
colors = [.9 .9 .9; 0 0 0]; %// light gray and black
N = 16; %// maximum number
hold on
for n = N:-1:1; %// bigger circles first
s = sqrt(n);
rectangle('curvature', [1 1], 'position', [-s/2 -s/2 s s], ...
'edgecolor', 'none', 'facecolor', colors(mod(n-1,2)+1,:));
end
axis square

Answer 3

You can also create a "surface" with value 1 for all your r radiuses and 0 for the r1. Then either plot as a surface seen form top, or directly use pcolor.
r = [0 5.2494 7.4328 9.0922 10.4988] ; %// define all your radiuses
bw = mod( 1:numel(r) , 2 ) ; %// create an alternance of 0 and 1 (same size as "r")
ntt = 50 ; %// define how many angular division for the plot
theta = linspace(0,2*pi,ntt) ; %// create all the angular divisions
[rr,tt]=meshgrid(r,theta) ; %// generate a grid
z = repmat( bw , ntt , 1 ) ; %// replicate our [0 1 0 ...] vector to match the grid
[xx,yy,zz] = pol2cart(tt,rr,z) ; %// convert everything to cartesian coordinates
pcolor(xx,yy,zz) %// plot everything
colormap(gray(2)) %// make sure we use only 2 colors (black and white)
shading flat ; axis equal %// refine the view (axis ratio and "spokes" not visible)
You can send as many radiuses as you like in the original r.
This will render:
This method look a bit longer at first than other solution, but you could remove many intermediate steps by consolidating some lines, and if you are to reuse the graphics later on, it may present 2 benefits:
if you get the handle of the graphic object (hp=pcolor(xx,yy,zz)), you only have one graphic object to handle.
if you need to change the color, you do not need to cycle through each circle, just change the colormap to the 2 colors you want (for example if you want "red" and "green", just call the colormap colormap([1 0 0;0 1 0]) and you're done.

Answer 4

viscircles returns an hggroup object. One of the properties of such an object is its Children, which is an array of handles to the graphics objects it creates. For instance you could write
h1 = viscircles(c, r)
c1 = h1.Children
The children here should just be the handles to the circular patches defined by viscircles. Now, to set the color of the ith circular patch, you can set the FaceColor property of the handle c1(i).