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POMatlab: create close packed layer of circles
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  1. POMatlab: create close packed layer of circles
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    copied!<p>I'm trying to create a close packed layer by generating my center points like a box and then shear the point in order to create a close packed layer of circles.. <a href="http://chemistry.osu.edu/~woodward/ch754/str_cp.htm" rel="nofollow noreferrer">more info can be found here</a></p> <p>but I'm having some difficulties.. My code so far is</p> <pre><code>%% Trying out the shear function rad=2; n=3; [X,Y] = meshgrid(0 : rad*2 : rad*(n-1)*2 , ... 0 : sqrt(2*(2*rad)^2)/2 : sqrt(2*(2*rad)^2)/2*(n-1)); xyBox = [reshape(X,1,numel(X)) ; reshape(Y,1,numel(Y))]; Sh = @(m) [1 m; 0 1]; % horizontal shear - slope is qual to 1/m slope = sqrt(3); shearedCoordinates = Sh(1/slope) * xyBox; figure; plot(xyBox(1,:),xyBox(2,:),'k.'); for i= 1:(numel(shearedCoordinates)/2) hold on; circle(shearedCoordinates(1,i),shearedCoordinates(2,i),rad) plot(shearedCoordinates(1,i),shearedCoordinates(2,i),'bx') hold off; end axis equal </code></pre> <p><img src="https://i.stack.imgur.com/TyHCl.png" alt="sorta packed circles"></p> <p>Don't really understand the math behind the Sh, but can just see that it does a damn good job twisting (shearing) points. I calculated a slope of square root 3 should give the right place, but it looks lige there is something wrong with my y distances...</p> <p>the circle function is</p> <pre><code>function circle(x,y,r) angle=0:0.01:2*pi; xp=r*cos(angle); yp=r*sin(angle); plot(x+xp,y+yp,'r'); end </code></pre> <p><strong>* SOLUTION *</strong></p> <pre><code>%% Trying out the shear function rad=2; n=3; [X,Y] = meshgrid(0 : rad*2 : rad*(n-1)*2 , ... 0 : sqrt(3)*rad : sqrt(3)*rad*(n-1)); xyBox = [reshape(X,1,numel(X)) ; reshape(Y,1,numel(Y))]; Sh = @(m) [1 m; 0 1]; % horizontal shear - slope is qual to 1/m slope = sqrt(3); shearedCoordinates = Sh(1/slope) * xyBox; figure; plot(xyBox(1,:),xyBox(2,:),'k.'); for i= 1:(numel(shearedCoordinates)/2) hold on; circle(shearedCoordinates(1,i),shearedCoordinates(2,i),rad) plot(shearedCoordinates(1,i),shearedCoordinates(2,i),'bx') hold off; end axis equal </code></pre> <p>(don't forget to vote up if you found it useful)</p>
 

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