I'have seen this graph of a 2D function of $\theta$ and $\phi$ (let's call it $F(\theta,\phi)$):
You may see that it's not represented as a conventional surface plot. In fact, there aren't $\theta$ and $\phi$ on x and y axes, but there is $\theta$ at both x and y axis. Along x axis we have $F(\theta,\phi=0°)$, along y axis we have $F(\theta,\phi=90°)$.
Which kind of graph is this? If I plot $F(\theta,\phi=90°)$ with respect to $\theta,\phi$, I get a completely different result.
I need some formal clarifications about it so that I can make a similar graph on MATLAB or other tools.
It's a Cartesian plot of a scalar function $F(\theta, \phi)$ with $$\left\lbrace ~ \begin{aligned} x &= \frac{\theta}{2 \pi} \cos \phi \\ y &= \frac{\theta}{2 \pi} \sin \phi \\ z &= F(\theta, \phi) \\ \end{aligned} \right .$$ If $$\begin{array}{rccl} 0 & \le & F(\theta, \phi) & \le & 1 \\ 0 & \le & \theta & \lt & 2 \pi \\ 0 & \le & \phi & \lt & 2 \pi \\ \end{array}$$ then $$\begin{array}{rccl} -1 & \le & x & \le & 1 \\ -1 & \le & y & \le & 1 \\ 0 & \le & x^2 + y^2 & \le & 1 \\ 0 & \le & z & \le & 1 \\ \end{array}$$