Now that we've seen a few examples of how GNNs work, let's go a step further and see how we can apply neural networks to meshes.
First, we use a patch that is defined at each point in a local system of d-dimensional pseudo-coordinates, 
, around x. This is referred to as a geodesic polar. On each of these coordinates, we apply a set of parametric kernels, 
, that produces local weights.
The kernels here differ in that they are Gaussian and not fixed, and are produced using the following equation:
These parameters (
and 
) are trainable and learned.
A spatial convolution with a filter, g, can be defined as follows:
Here, 
is a feature at vertex i.
Previously, we mentioned geodesic polar coordinates, but what are they? Let's define them and find out. We can write them as follows:
Here, 
is the geodesic distance between i and j and 
is the...