% Tschirnhausen cubic illustration

function main()

   % linewidth and font size
   lw= 6; 
   fs = 20;

% colors
   red=[0.867 0.06 0.14];
   blue = [0, 129, 205]/256;
   green = [0, 200,  70]/256;
   black = [0, 0, 0];
   white = 0.99*[1, 1, 1];


   N=500;  % number of points (don't make it big, code will be slow)

   Lx1 = -5; Lx2 = 5; Ly1 = -4; Ly2 = -Ly1;

   bd = 0.1;
   for i = 1:1

% Set up the plotting window
	  figure(1); clf; set(gca, 'fontsize', fs, 'linewidth', lw/4);
	  hold on; axis equal; grid on;
	  figure(2); clf; hold on; axis equal; axis off;
	  
	  [X, Y]=meshgrid(linspace(Lx1, Lx2, N), linspace(Ly1, Ly2, N));  
	  
	  x = X; y = Y;
	  a = 1; b = 1;
	  Z = y.^2-(x.^3+3*x.^2);
	  
%  graph the curves using 'contour' in figure (2)
	  figure(2); [c, stuff] = contour(X, Y, Z, [0, 0]);
	  
%  extract the curves from c and graph them in figure(1) using 'plot'
%  need to do this kind of convoluted work since plot2svg can't save
%  the result of 'contour' but can save the result of 'plot'   

	  
	  [m, n] = size(c);
	  while n > 0
		 
		 l=c(2, 1);
		 x=c(1,2:(l+1));  y=c(2,2:(l+1)); % get x and y of contours
		 figure(1); plot(x, y, 'color', red, 'linewidth', lw/2);
		 
		 c = c(:, (l+2):n);
		 [m, n] = size(c);

%		 Lx1 = min(Lx1, min(x) - bd); Lx2 = max(Lx2, max(x) + bd);
%		 Ly1 = min(Ly1, min(y) - bd); Ly2 = max(Ly2, max(y) + bd);
		 Lx1 = min(x) - bd; Lx2 = max(x) + bd;
		 Ly1 = min(y) - bd; Ly2 = max(y) + bd;
	  end
	  
	  figure(1); axis equal; axis([-3.2 2 -4 4]);
   end

   saveas(gcf, 'Tschirnhausen cubic.eps', 'psc2')