Image:Level set method.jpg

[edit] License information

This image has been (or is hereby) released into the public domain by its author, Olegalexandrov at the wikipedia project. This applies worldwide. In case this is not legally possible: Olegalexandrov grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

[edit] Matlab source code (public domain)

function level_set_method()
   figure(1); clf; % pop up a figure, and clean it up
for i=1:3 % make a loop to draw the six pictures in pairs
   level_disp(i);
end

print('-djpeg100',  '-r100', 'level_set_method.jpg') % save to file. 

function level_disp(p)

   Lx=2.5; Ly=2.5; % box is [-Lx Lx] x [-Ly, Ly]
   N=60;  % number of points (don't make it big, code will be slow)
   heights=[0.7+eps, 0.00001, -0.7+eps]; % cut the surface at these heights 
   height=heights(p); % current cut

   [X, Y]=meshgrid(-Lx:(1/N):Lx, -Ly:(1/N):Ly);     % X and Y coordinates
   Z=height-0.5*(X-1.78).*X.^2.*(X+1.78)-Y.^2;  % Z=f(X, Y) -surface

   lowest=-4;
   [m, n]=size(Z); 
   for i=1:m
      for j=1:n
 if Z(i, j)< lowest; % truncate the surface somewhere
    Z(i, j)=NaN;
 end
      end
   end

% draw the sufrace and the plane cut
   figure(1); subplot('Position', [(p-1)/3, 0., 0.33, 0.5]); hold on; 
   surf(X, Y, Z, 'FaceColor','red', 'EdgeColor','none', 'FaceAlpha', 1); 
   surf(X, Y, zeros(m, n), 'FaceColor','blue', 'EdgeColor','none', 'FaceAlpha', 0.3); 
   camlight left;lighting phong; % make nice lightning 
   axis([-Lx Lx -Ly Ly lowest 1.8]); axis equal;  axis off; %the coordinate box
   view(-23, 34)        % angle of view (polar coordinates)

% draw the shape (cross-section)
   figure(1); subplot('Position', [(p-1)/3, 0.5, 0.33, 0.5]); % subwindow
   [c, stuff] = contour(X, Y, Z, [0, 0]); % draw the contours.
   l=c(2, 1);
   x=c(1,2:(l+1));  y=c(2,2:(l+1)); % get x and y of contours
   H=fill(x, y, 0.6*[1, 1, 1]); set(H, 'EdgeColor', 'none'); % draw the shape

   [u, v]=size(c);
   if v > l+2 % special case: two connected components
      x=c(1,(l+3):(2*l)); y=c(2,(l+3):(2*l)); % contours
      hold on; % hold the graph for the second component
      H=fill(x, y, 0.6*[1, 1, 1]); set(H, 'EdgeColor', 'none'); 
   end
   axis equal; axis off; axis([-Lx Lx -Ly Ly]); % frame size

[edit] Original upload log

(All user names refer to en.wikipedia)

• 2004-11-25 03:20 Olegalexandrov 800×600×8 (90808 bytes) Illustration of level set method. {{PD}}

• Level set method
• User:Oleg Alexandrov/Pictures