Elliptical Fourier Descriptor (EFD) implementation in Rust. This crate implements 1D/2D/3D EFD and its related functions.

This implementation is totally safe and supports no-std + alloc environment.

Keyword Alias:

• Elliptical Fourier Analysis (EFA)
• Elliptical Fourier Function (EFF)

Example of re-describing a new closed curve:

let curve = vec![
    [0., 0.],
    [1., 1.],
    [2., 2.],
    [3., 3.],
    [2., 2.],
    [1., 1.],
];
assert!(efd::util::valid_curve(&curve).is_some());
let described_curve = efd::Efd2::from_curve(curve, false).recon(20);

The harmonic number can be set with efd::Efd::from_curve_harmonic() method. The following figures show the reconstruction of a 2D closed curve with 1-8 harmonics.

2D and 3D closed curve:

2D and 3D open curve:

Posed EFD combined a curve with a pose (unit vectors) to describe the orientation of each point.

2D open curve and its full reconstruction:

• Kuhl, FP and Giardina, CR (1982). Elliptic Fourier features of a closed contour. Computer graphics and image processing, 18(3), 236-258. https://doi.org/10.1016/0146-664X(82)90034-X

• Chang, Y., Chang, JL., Lee, JJ. (2024). Atlas-Based Path Synthesis of Planar Four-Bar Linkages Using Elliptical Fourier Descriptors. In: Okada, M. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2023. Mechanisms and Machine Science, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-031-45709-8_20
• Chang, Y., Chang, JL. & Lee, JJ. Path Synthesis of Planar Four-bar Linkages for Closed and Open Curves Using Elliptical Fourier Descriptors. J Mech Sci Technol (2024). https://doi.org/10.1007/s12206-024-0436-y