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

Summary
A depiction of the function $$f(r,\theta)=r \sin(2 \theta)$$ 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.