polatory

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Fast radial basis function interpolation and kriging for large scale data

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**Polatory** is a fast and memory-efficient framework for radial basis function (RBF) interpolation.

## Features

- Interpolation of 1D, 2D, and 3D scattered data
- Surface reconstruction from 2.5D and 3D point clouds
- Fast kriging prediction ([dual kriging](https://github.com/polatory/polatory/wiki/Dual-kriging))
- Full control of absolute fitting tolerance and evaluation accuracy
- Fast and high-quality isosurface generation
  - Gradient search and surface tracking
  - Vertex position refinement
  - Vertex clustering
- Handling of 1M+ input points
- Inequality constraints
- Gradient constraints (Hermite–Birkhoff interpolation)

## Documentation

Please check out the [wiki](https://github.com/polatory/polatory/wiki).

## Contribution

Contributions are welcome! You can contribute to this project in several ways:

### Star the Repo

Just click <kbd>⭐️ Star</kbd> at the top of the page to show your interest!

### <a href="https://github.com/polatory/polatory/issues">File an Issue</a>

Do not hesitate to file an issue if you have any questions, feature requests, or have encountered unexpected results (please include a minimal reproducible example).

### <a href="https://github.com/polatory/polatory/pulls">Submit a Pull Request</a>

You can fork the repo to make improvements, then feel free to submit a pull request!

## References

1. J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans. Reconstruction and representation of 3D objects with radial basis functions. In _Computer Graphics SIGGRAPH 2001 proceedings_, ACM Press/ACM SIGGRAPH, pages 67–76, 12-17 August 2001. [https://doi.org/10.1145/383259.383266](https://doi.org/10.1145/383259.383266)

1. R. K. Beatson, W. A. Light, and S. Billings. Fast solution of the radial basis function interpolation equations: Domain decomposition methods. _SIAM J. Sci. Comput._, 22(5):1717–1740, 2000. [http://doi.org/10.1137/S1064827599361771](http://doi.org/10.1137/S1064827599361771)

1. G. M. Treece, R. W. Prager, and A. H. Gee. Regularised marching tetrahedra: improved iso-surface extraction. _Computers and Graphics_, 23(4):583–598, 1999. [https://doi.org/10.1016/S0097-8493(99)00076-X](<https://doi.org/10.1016/S0097-8493(99)00076-X>)

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