Other differences against Kazhdan et al. [2006] ?

[yilinliu77]

I want to figure out what is the difference between this implementation and the original one [Kazhdan et al. 2006].

As the README mentioned, the original implementation uses an adaptive grid to represent the scene, and it tracks the confidence of the input points.

I also find some other differences:

• The original implementation doesn't treat the g value of each node as a "black box". Instead, it uses a 3D Gaussian function (or 2nd B-spline) to represent the g value in each node.
• It uses a mechanism to estimate the sample density. Thus, it uses nodes in different depths to solve the problem in different places. In the original paper, they call it as "nonlinear sample".

The first difference above will significantly modify the implementation. By using the 3D Gaussian function or its approximation, we are able to export the analytical gradient and divergence of each node. Also, we need to project the gradient/divergence to the function space of the other nodes. The node function also influences the definition of the vector field.

I just want to make sure that I understood it correctly. Do I misunderstand or omit anything? How could the analytical gradient and the projection of the gradient/divergence affect the final result?