arrows in space: tangent vectors in orientation space, a field on the sphere or SO(3), or arrows at positions; MATLAB’s quiver3

Syntax

quiver3d(t)

Tangent vectors at their orientations.

quiver3d(t, Rodrigues=True, normalize=True)

In Rodrigues space, all of one length.

quiver3d(sVF)

A field on the sphere as arrows on it.

quiver3d(F, axisAngle=True, resolution=7.5*degree)

A vector field on SO(3).

quiver3d(pos, d)

Arrows at the positions pos along d.

Description

A tangent vector is an arrow at its reference orientation, in the coordinates of the held axes, else in axis angle space, the orientations scattered first; the arrow ends where the exponential of the vector, scaled to the longest of the list, takes the orientation.

A vector or axis field on the sphere is drawn as arrows, or lines for an axis field, on an equispaced grid of the hemisphere facing the camera (keywords resolution, color, arrowSize). A vector field on SO(3) is drawn on an equispaced grid of its fundamental region (keyword resolution), the longest arrow nine tenths of the grid spacing. Two vector3d, positions and directions, are arrows in a 3D scene (keywords arrowSize, color, lineWidth), MATLAB’s vector3d/quiver3.

Input

`t`	SO3TangentVector, S2VectorField, S2AxisField or SO3VectorField
`pos, d`	vector3d, the tails of the arrows and their directions

Keywords

keyword	default	description
`lineWidth`	`1.5`	the width of the arrows’ lines
`color`	`None`	the colour of the arrows; blue for tangent vectors, black on the sphere
`normalize`	`False`	draw every arrow at one length, only its direction kept
`axisAngle`	`False`	draw in axis angle space
`Rodrigues`	`False`	draw in Rodrigues space
`Euler`	`False`	draw in Euler angle space
`maxHeadSize`	`None`	the length of the heads as a fraction of the arrows; by default 0.25 for tangent vectors and arrows at positions, 0.3 for fields

Output

`h`	the matplotlib Quiver3D, or the scene3d of the arrows at positions

Used on

Dream3dGrains, RotationTangentSpace, SO3FunVectorField, S2FunVectorField, BirefringenceDemo

MATLAB’s S2AxisField.quiver3

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/S2AxisField.quiver3_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

S2AxisField.quiver3