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2026-07-18T23:27:00Z
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https://en.formulasearchengine.com/w/index.php?title=Paracrystalline&diff=20877
Paracrystalline
2014-01-29T11:36:30Z
<p>108.101.253.72: /* Paracrystalline model */</p>
<hr />
<div>==Summary==<br />
A depiction of the function <math>f(r,\theta)=r \sin(2 \theta)</math> around the origin.<br />
<br />
In x, y coordinates, this function is equal to<br />
<br />
<math><br />
f(r,\theta)= \left\| (x,y) \right\| \sin\left( 2 \tan^{-1}\left( \frac{y}{x} \right)\right)<br />
</math><br />
<br />
The graph was created with matlab, using the following script:<br />
<blockquote><br />
D = [-1:0.1:1];<br /><br />
[X Y] = meshgrid(D,D);<br /><br />
L=sqrt(X.^2+Y.^2);<br /><br />
A=atan(Y./X);<br /><br />
A(isnan(A))=0;<br /><br />
Z=L.*sin(2*A);<br /><br />
surfc(X,Y,Z);<br /><br />
view(15,40)<br /><br />
xlabel('x')<br /><br />
ylabel('y')<br /><br />
zlabel('f(x,y)')<br /><br />
axis equal<br /><br />
camlight headlight<br /><br />
lighting gouraud<br /><br />
print -dpng f.png<br /><br />
%print -depsc2 f.eps<br /><br />
%!pstoedit -f plot-svg f.eps f.svg<br /><br />
%!firefox f.svg<br /><br />
%!gv f.eps<br /><br />
</blockquote><br />
<br />
If anyone now how to get an SVG file with lighting enabled out of matlab, please feel free to supersede this image with a vectorized version.<br />
<br />
== Licensing ==<br />
{{PD-self|date=December 2007}}<br />
<br />
{{Orphan image}}<br />
<br />
{{Copy to Wikimedia Commons|bot=Fbot|date=March 2012}}</div>
108.101.253.72