There was not anything surprising with Geodesic distance implementation. The Fibonacci heap was quite noticeably more performant than a naive Set implementation as expected.
Also, using an early exit strategy when the target node is
known resulted in an even shorter execution time.
Using inversed distances in a Fibonacci Heap helped with the performance of finding the next point to sample (i.e. the point with maximum distance to its cluster root)
Also, dropping the initial randomly chosen point as soon as the second point is sampled resulted in a more accurate sample set.
The Iso-Curve Signature paper was not very clear on how the distribution of Iso-Curve radii. They were mentioning an x to the power of 4 function to use for selecting radii, yet that resulted in a very poor distribution. Therefore, I opted to use 20 uniformly sampled Iso-Curve radii.
Also, I needed to de-dupe the Iso-Curves created with the intersection formula given by the paper. For each radius, I was ending up creating 2 very closely resembling curves.
In order to not create a graph using faces, and instead be
able to re-use the existing vertices graph, I ended up
relying on a heuristic to estimate a face's distance to the
geodesic path. The estimation used the average geodesic distances
of a face's vertices and assigned it as the face's own distance.
Later, while calculating the Bilateral Maps' bin values, I relied on Heron's formula in order to find the area of a triangle using the 3 edge lengths.
I first implemented a free-formed parameterization where boundary vertices' Z values are simply set to 0. Then I implemented the parameterization where boundary vertices are mapped to a circle.
Both face and faceLow meshes had an extra boundary within the mouth. It
was not a problem for the free-formed parameterization where I simply fixated
the mouth boundary as I did with the outer face boundary. But with circle
parameterization I needed to identify which boundary to fixate to the circle.
I provided two different implementation where either mouth boundary is unpinned
or pinned with 0 Z-values.
A proper implementation of that would probably be to identify the longest continuous boundary edge and to map it to the circle, while keeping other boundaries unpinned. But I simply hacked my way around by providing a range of positions where I know mouth would end up in.
As a final note, I was surprised about how long it is taking for matrix inverse to be calculated. I initially relied on a popular library called math.js. But I quickly realized it is just too slow to rely on. Later I found an alternative called ml-matrix of which inverse function is 10x times faster than the mathjs's implementation. It still takes roughly around 2 to 5 minutes for high resolution meshes' matrices to be inversed. As a follow up, I am hoping to migrate the implementation to Web Workers so that the UI won't get frozen when the computationally-heavy code is running.