planes in three-dimensional space, stored by unit normals and signed offsets

Syntax

plane = plane3d(N, d)

Planes satisfying dot(N, v) = d.

plane = plane3d(N, v0)

Planes with normal N through v0.

plane = plane3d.byPoints(v)

Least-squares plane through a point cloud.

Description

Normals are normalised internally. A numeric offset is divided by the original normal length, so rescaling both N and d describes the same plane. With unit N, d is the signed distance from the origin, in the units of the positions. Arrays of normals and offsets represent arrays of planes. The normals carry the coordinate frame.

Input

`N`	vector3d plane normals, coordinate arrays, or a plane3d to copy
`d`	numeric offsets, or vector3d positions through which the planes pass; default 0

Output

plane plane3d

Properties

`N`	unit normals as vector3d
`d`	signed distances from the origin
`frame`	coordinate frame of the normals
`shape`	shape of the plane array

Signature

plane3d(N, d=0)

Used on

EBSD3Analysis, EBSD3Plotting, Grains3D, RotationImproper

MATLAB’s plane3d.plane3d

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/plane3d.plane3d_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.

plane3d.plane3d