ferreus_rbf

Fast, memory‑efficient global radial basis function (RBF) interpolation in Rust.

Overview

Direct RBF solvers based on dense linear algebra require O(N²) memory and O(N³) work, which quickly becomes impractical beyond tens of thousands of points. ferreus_rbf provides a scalable alternative suitable for millions of points in up to three dimensions.

The crate combines:

• Domain decomposition (following established RBF preconditioning schemes), used as a preconditioner within a Flexible GMRES (FGMRES) iterative solver, and
• A fast multipole method (FMM) evaluator via the ferreus_bbfmm crate, which accelerates matrix–vector products during each iteration.

Together these techniques reduce the asymptotic cost to roughly O(N log N), enabling fast global interpolation and 3D surface extraction on large scattered datasets.

Features

• Supports 1D, 2D and 3D input domains
• Scales to datasets with over 1,000,000 source points (subject to hardware)
• Optional global trend transforms to capture large‑scale structure in the data
• Fast 3D isosurface extraction using a surface‑following, non‑adaptive Surface Nets method
• Built on faer for linear algebra, avoiding complex external dependencies

Limitations

The current isosurface extraction method does not guarantee manifold or watertight meshes. Surfaces may contain trifurcations or self‑intersections and may therefore be unsuitable for downstream boolean or other topology‑ sensitive operations without additional post‑processing.

Getting started

Add the crate to your Cargo.toml:

[dependencies]
ferreus_rbf = "0.1"

Then construct an RBFInterpolator with your source points, values and configuration. See the crate documentation and the examples/ directory for complete examples.

Attribution and licensing

This crate was developed while the author was working at Maptek and has been approved for open‑source distribution under the terms of the MIT license.

Unless otherwise stated, the following copyright applies:

Copyright (c) 2025 Maptek Pty Ltd.
All rights reserved.

This copyright applies to all files in this repository, whether or not an individual file contains an explicit notice.

The code is released under the MIT License – see the top‑level LICENSE file for details.