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# Hierarchical Interpolation with Projection, Evaluation and Derivation

[![GitHub license](https://img.shields.io/github/license/tcherrie/Hiped)](https://github.com/tcherrie/Hiped) [![GitHub release](https://img.shields.io/github/release/tcherrie/Hiped.svg)](https://github.com/tcherrie/Hiped/releases/) [![GitHub stars](https://img.shields.io/github/stars/tcherrie/Hiped)](https://github.com/tcherrie/Hiped/stargazers)
[![DOI](https://zenodo.org/badge/763998095.svg)](https://zenodo.org/doi/10.5281/zenodo.10718117)



The purpose of this code is to define arbitrary interpolation trees with some utilities (evaluation, projection and derivation) that can be used for instance in multimaterial topology optimization algorithms [^1][^2] as well as in other applications using projected gradient descent.

This code is a major upgrade of [^3], based itself on [^4].
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## Quickstart


Start by running the example files in the folder "examples". If your Matlab version supports it, you can run the LiveScripts (in "examples/notebooks"), or traditional .m files (in "examples/mfiles"), in the alphabetical order.
Start by running the example files in the folder "examples". If your Matlab version supports it, you can run the LiveScripts (in "examples/notebooks"), or traditional .m files (in "examples/mfiles"), in alphabetical order.

**NB** : The code has been tested with success on Matlab R2023a.

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Please use the following citation reference if you use the code:

T. Cherrière tcherrie/hiped: Hiped (v1.0.1), March 2024. Zenodo.

Bibtex entry :
T. Cherrière. tcherrie/Hiped: Hierarchical Interpolation with Projection, Evaluation and Derivation (v1.0.1), February 2024. Zenodo. https://doi.org/10.5281/zenodo.10718117

Bibtex entry:

@software{tcherrie_2024_10718117,
author = {Cherrière, Théodore},
title = {tcherrie/Hiped: Hierarchical Interpolation with Projection, Evaluation and Derivation},
month = feb,
year = 2024,
publisher = {Zenodo},
version = {v1.0.1},
doi = {10.5281/zenodo.10718117},
url = {https://doi.org/10.5281/zenodo.10718117}
}

**NB: version number and DOI must be adapted from [Zenodo's repository.](XXX)**
**NB: version number and DOI must be adapted from [Zenodo's repository](https://doi.org/10.5281/zenodo.10718117)**, according to the version used.

## License

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https://doi.org/10.1007/s00158-022-03460-1

[^2]: Cherrière, T. (2024) "Toward topology optimization of hybrid-excited
electrical machines using recursive material interpolation"
electrical machines using recursive material interpolation",
SCEE 2024, Darmstadt, Germany.

[^3]: Cherrière, T. and Laurent, L. (2023), Wachspress2D3D,
https://doi.org/10.5281/zenodo.7701776
[^3]: Cherrière, T. and Laurent, L. (2023), Wachspress2D3D, https://doi.org/10.5281/zenodo.7701776

[^4]: M. Floater, A. Gillette, and N. Sukumar, (2014).
“Gradient bounds for Wachspress coordinates on polytopes,”
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