visualizing orientation (zenith and azimuth) data (e.g. with a circular or spherical histogram)? I want to understand the distribution of orientation angles in a 3D image (represented as a triangular mesh). 
For each triangle in the image I have zenith ($\Theta$) and azimuth ($\phi$)

And I can compute histograms for each:

Is there a way that I can combine the information contained in these images into a single histogram representing the joint distribution of these variables?
 A: The way to determine a two-dimensional histogram is very similar to the one-dimensional case.
Basically in 1D, you sum up all knots within a certain interval or bin. That is for $\varphi$, you count all points in the "beam" $\varphi \in [\varphi_i-\Delta \varphi_i, \varphi + \Delta \varphi]$, $\theta \in [-1,1]$, and divide by the total number of points. This procedure can be seen to give a Monte-Carlo estimate of the integral
$$P_i =\int_{\varphi_i-\Delta \varphi}^{\varphi_i-\Delta \varphi} d\varphi \int_{0}^\pi  d\theta \, \sin(\theta) \ p(r,\varphi, \theta)\\
=\int_{\varphi_i-\Delta \varphi}^{\varphi_i-\Delta \varphi} d\varphi \int_{-1}^1  dz \ \tilde p(r,\varphi, z)=\frac{N_i}{N} $$
where $p(r,\varphi, \theta)$ is the density which generates the points (which admittedly will hardly become continuous for your picture), and $\tilde p(r,\varphi, z)$ is the transformed density for $z=\cos \theta$.
In result, you get for each azimuthal grid point $\varphi_i$ a real number $P_i$ (alternatively, you can also plot unnormalized values $N_i$). The same goes for $z_j$ (caution: due to the volume element of the sphere, if you look for equally space bins, you have to work in the transformed coordinate $z$, otherwise you won't get consistent bin-volumes).
Similarly, in the two-dimensional case, you span a two-dimensional grid of regions  $\varphi \in [\varphi_i-\Delta \varphi_i, \varphi + \Delta \varphi]$, $z \in [z_j - \Delta z,z_j + \Delta z]$, count the number of knots and obtain the coresponding approximate probabilities $P_{ij}$. Finally, you simply plot the data in a 3D picture with the data given in the form
$$\varphi_i, \ z_j, \ P_{ij}$$
Such three-dimensional plots are supported by almost any plot program.
A: Given that you're ignoring r for each triangle, your coordinates describe points on a sphere and your problem corresponds to visualization of data across longitude/latitude values. The good news is that that's a well-studied problem with lots of tools available. The bad news is no really good solutions have been found for representing a globe in 2D. Nonetheless, it's such a common problem that we've come to accept the limitations of a few common projections. A 2D heatmap with a map projection may be useful.
