C[omp]ute

From: andrew cooke <andrew@...>

Date: Sat, 23 Jul 2011 11:27:19 -0400

Someone just asked me how to implement the work at
http://acooke.org/random.pdf in Matlab.  Here's the code for Octave, which is
very similar:


n = 1000;  # the number of points
t = 0.1; # the 't' parameter from the paper

sq2 = sqrt(2);

# first, generate points in the u,v coordinates as in figure 4.
# u goes from 0 to sq2, v from -t*sq2 to t*sq2
uv = rand(n,2) * [sq2,0;0,2*t*sq2] - repmat([0,t*sq2],n,1);
# now rotate that by 45 degrees to xy
xy = uv * [1/sq2,1/sq2;-1/sq2,1/sq2];
# finally, "fold in" points outside the unit square
for i = 1:n
  #printf("%d x %f y %f\n", i, xy(i,1), xy(i,2));
  if (xy(i,1) < 0) xy(i,1) = -xy(i,1); endif
  if (xy(i,2) < 0) xy(i,2) = -xy(i,2); endif
  if (xy(i,1) > 1) xy(i,1) = 2-xy(i,1); endif
  if (xy(i,2) > 1) xy(i,2) = 2-xy(i,2); endif
endfor;

#xy
plot(xy(:,1),xy(:,2),'*')


If anyone with more experience than me know of a better way of folding the
points (ie without the explicit "for" loop), please let me know!

Andrew