This project has two goals. One goal is mathematical, the project wants to estimate the abstract curve’s Non-Local Mean Curvature (NLC). The estimations will help analytical mathematicians observe various properties of curves in euclidian space. The second goal is much more computer science-oriented. The second goal is to write the algorithm to compute the NLC. This is not simple and there has never been a proper algorithm to perform this computation in an abstract sense.
We plan to write the first algorithm to compute the NLC for any function. Although, one thing that the math tells us is that most implementations will be slow due to the intensity of the integrals. We plan to then write the integration algorithm using the CUDA API.