Crate efd

Expand description

§EFD Rust Library

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.

§Example Images

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:

§Citations

§Original

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

§My Applications

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). http://doi.org/10.1007/s12206-024-0436-y

§Features

This crate supports no-std solution. Disable the “std” feature will enable it.

default-features = false

Re-exports§

pub extern crate nalgebra as na;

Modules§

posed: Posed EFD (Elliptic Fourier Descriptor) is a special shape to describe the pose of a curve. It is a combination of two curves, the first is the original curve, and the second is the pose unit vectors.
util: Utility functions for the library.

Structs§

Efd: Elliptical Fourier Descriptor coefficients. Provide transformation between discrete points and coefficients.
GeoVar: Geometric variables.
MotionSig: Motion signature with the target position.
PathSig: Path signature with the target position.
PosedEfd: An open-curve shape with a pose described by EFD.

Enums§

U: EFD dimension marker.

Traits§

Curve: Copy-on-write curve type.
Distance: Be able to calculate the distance between two instances.
EfdDim: Trait for the dimension U<D> of EFD.
RotHint: Rotation hint for GeoVar.

Functions§

get_norm_t: Get the normalized time parameters of the curve.
harmonic: Calculate the number of harmonics.
harmonic_nyquist: Calculate the number of harmonics with the Nyquist frequency.

Type Aliases§

Coeffs: Coefficients type.
Efd1: A 1D shape described by EFD.
Efd2: A 2D shape described by EFD.
Efd3: A 3D shape described by EFD.
GeoVar1: 1D geometric type.
GeoVar2: 2D geometric type.
GeoVar3: 3D geometric type.
Kernel: An owned matrix of specific coefficients. (Dx2)
PosedEfd1: A 1D shape with a pose described by EFD.
PosedEfd2: A 2D shape with a pose described by EFD.
PosedEfd3: A 3D shape with a pose described by EFD.
Rot: Rotation type of the EFD.

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