Image:F(r,theta)=r sin(2 theta).png

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Size of this preview: 433 × 599 pixels
Full resolution‎ (555 × 768 pixels, file size: 88 KB, MIME type: image/png)

[edit] Summary

A depiction of the function $f (r,θ) = r sin(2θ)$ around the origin.

In x, y coordinates, this function is equal to

$f(r,\theta)= \left\| (x,y) \right\| \sin\left( 2 \tan^{-1}\left( \frac{y}{x} \right)\right)$

The graph was created with matlab, using the following script:

D = [-1:0.1:1];
[X Y] = meshgrid(D,D);
L=sqrt(X.^2+Y.^2);
A=atan(Y./X);
A(isnan(A))=0;
Z=L.*sin(2*A);
surfc(X,Y,Z);
view(15,40)
xlabel('x')
ylabel('y')
zlabel('f(x,y)')
axis equal
camlight headlight
lighting gouraud
print -dpng f.png
%print -depsc2 f.eps
%!pstoedit -f plot-svg f.eps f.svg
%!firefox f.svg
%!gv f.eps

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.

[edit] Licensing

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible,

I grant any entity the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	09:50, 11 December 2007	555×768 (88 KB)	Rubybrian (Talk \| contribs)	(I used the wrong shading model.)
	09:35, 11 December 2007	594×826 (45 KB)	Rubybrian (Talk \| contribs)	(A corrected version of the graph, by the original contributor)
	16:06, 10 December 2007	563×721 (34 KB)	Rubybrian (Talk \| contribs)	(A depiction of the function f(r,theta)=r sin(2 theta) around the origin.)