{"id":4953,"date":"2013-12-06T09:00:55","date_gmt":"2013-12-06T14:00:55","guid":{"rendered":"https:\/\/blogs.mathworks.com\/pick\/?p=4953"},"modified":"2013-12-06T11:12:50","modified_gmt":"2013-12-06T16:12:50","slug":"surface-to-solid","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/pick\/2013\/12\/06\/surface-to-solid\/","title":{"rendered":"Surface To Solid"},"content":{"rendered":"\r\n\r\n

Jiro<\/a>'s pick this week is surf2solid<\/tt><\/a> by Sven<\/a>.<\/p>

Sven is no stranger to Pick of the Week. His inpolyhedron<\/tt><\/a> was Picked<\/a> by Sean<\/a> recently, and he's also active in other areas of MATLAB Central. In fact, this entry was inspired by a post written by my colleague Paul on \"Printing the 3D L-Shaped Membrane\"<\/a>.<\/p>

3D Printing<\/a> allows you to easily create 3D objects from a digital model, such as models created in MATLAB. People are already using MATLAB for 3D printing, and we've written about it a few times, including the post above by Paul, as well as \"Printing Math\"<\/a> and \"Anamorphic 3D Printing\"<\/a>.<\/p>

In order to create a 3D object, we can't print a surface which has no thickness. Paul's post above talks about the process of adding that thickness. Sven took some of those techniques and created surf2solid<\/tt>. It's very easy to use with very good instructions (help). You simply provide the data that you would normally pass into surf<\/tt><\/a> or patch<\/tt><\/a>, and optionally specify the thickness (for a uniform thickness), the elevation (for a block with a flat bottom), and the triangulation method.<\/p>

Since I don't have one of those fancy 3D printing machines, I'll show an animation of a vibrating (thick) membrane. This is a modification of a shipping demo called vibes<\/tt>.<\/p>

% Eigenvalues<\/span>\r\nlambda = [9.6397238445, 15.19725192, 2*pi^2, ...<\/span>\r\n    29.5214811, 31.9126360, 41.4745099, 44.948488, ...<\/span>\r\n    5*pi^2, 5*pi^2, 56.709610, 65.376535, 71.057755];\r\n\r\n% Eigenfunctions<\/span>\r\nfor<\/span> k = 1:12\r\n    L{k} = membrane(k);\r\nend<\/span>\r\n\r\n% Get coefficients from eigenfunctions<\/span>\r\nfor<\/span> k = 1:12\r\n    c(k) = L{k}(25,23)\/3;\r\nend<\/span>\r\n\r\n% Construct solids for animation<\/span>\r\nS = struct('faces'<\/span>,cell(1,500),'vertices'<\/span>,cell(1,500));\r\nx = (-15:15)\/15;\r\nt = 0;\r\nfor<\/span> id = 1:length(S)\r\n    % Coefficients<\/span>\r\n    t = t + 0.02; % increment time<\/span>\r\n    s = c.*sin(sqrt(lambda)*t);\r\n\r\n    % Amplitude<\/span>\r\n    A = zeros(size(L{1}));\r\n    for<\/span> k = 1:12\r\n        A = A + s(k)*L{k};\r\n    end<\/span>\r\n\r\n    % Convert SURF data to SOLID data<\/span>\r\n    S(id) = surf2solid(x,x,A,'thickness'<\/span>,-0.1);\r\nend<\/span>\r\n\r\n% Create patch and modify view<\/span>\r\npHandle = patch(S(1),'EdgeColor'<\/span>,'r'<\/span>);\r\nview(3)\r\naxis([-1 1 -1 1 -.5 1])\r\naxis off<\/span>\r\n\r\n% Animate<\/span>\r\nfor<\/span> id = 1:length(S)\r\n    set(pHandle,'Faces'<\/span>,S(id).faces,'Vertices'<\/span>,S(id).vertices);\r\n    drawnow\r\nend<\/span>\r\n<\/pre>
\"\" <\/p>
Comments<\/b><\/p>
Let us know what you think here<\/a> or leave a comment<\/a> for Sven.<\/p>