Crate efd

EFD Rust Library

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

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

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.