% matlab file for plotting optimal polygon of radius 1
load ngon_coords.dat;

% transfer to X and Y matrices
X = ngon_coords(:,1); Y = ngon_coords(:,2);
N = size(X,1);

% figure the range, making sure the area is square to prevent distortion
xmin = min(X); xmax = max(X); xmid = (xmax+xmin)/2; xdiff = xmax-xmin;
ymin = min(Y); ymax = max(Y); ymid = (ymax+ymin)/2; ydiff = ymax-ymin;

diff = 1.2 * max([xdiff  ydiff]);
xmin = xmid - diff/2; xmax = xmid + diff/2;
ymin = ymid - diff/2; ymax = ymid + diff/2;

% now plot it as slices of pie, centered at (xmid,ymid)

% first construct the matrices the define each wedge

Xplot = zeros(3,N); Yplot = zeros(3,N);
Xplot(1,:) = xmid;  Yplot(1,:) = ymid;
for i=1:N-1,
  Xplot(2,i) = X(i); Xplot(3,i) = X(i+1);
  Yplot(2,i) = Y(i); Yplot(3,i) = Y(i+1);
end
  Xplot(2,N) = X(N); Xplot(3,N) = X(1);
  Yplot(2,N) = Y(N); Yplot(3,N) = Y(1);

% now plot a wedge at a time, using "patch" to avoid deleting earlier
% plots

for i=1:N,
	patch(Xplot(:,i), Yplot(:,i), [.2 0 0] + (i/N)*.8*[1 0 0]);
end
axis([xmin xmax ymin ymax]); axis square;

% try: fiddling with "rand" and the "central" color
% to give darker/lighter/redder colors

% give it a title (specify number of vertices)
title(['Optimal Polygon with ',num2str(size(X,1)),' Vertices and Radius 1']);