I tried to plot the following function in spherical-coordinate system :
$$ r(\phi,\theta)=\left(\frac{\sin\phi}{\phi}\frac{\sin\theta}{\theta}\right)^2$$
(definition/references for spherical-coordinates are described) here
I got the following graphs (viewed from different angles):
As we progress through the zenith i-e (0 rad,0 rad) towards point($\pi$,0+$\delta$), the graph is Discontinuous,(as it jumps from 1 to 0 instantly)
I am confused with such type of pattern. Is it CORRECT plot or something I am missing ??
Help with be highly appreciated !
Let's slice this thing open and look at a cross-section to illustrate what's going on. Slicing with the plane $\phi = \pi/2$, we get the polar equation $$r(\theta) = \frac{4 \sin^2 \theta}{\pi \theta^2}$$
What does that look like? Let's plot it:
As you can see, it's a bunch of nested things. You're just seeing one of the inside ones peeking out.