a list of line segments separating neighbouring grains in a two-dimensional map

Syntax

gB = grains.boundary
interphase = gB['Forsterite', 'Enstatite']
lengths = gB.segLength
mori = interphase.misorientation

Description

Grain reconstruction creates these segments together with the adjacent grain ids, EBSD pixel ids, phases and rotations. Segments are stored head to tail along chains, with the first adjacent grain on the left of the walk. A chain ends at a junction or closes on itself. Selecting segments keeps the shared vertex table; segment indices and vertex indices are different. All Python indices are zero-based.

Select by a mask, integer indices, one phase name, or a pair of phase names. Before asking for misorientation, select a single phase pair so its crystal frames are unambiguous. The exterior has grain id 0, pixel id -1 and phase id -1.

Input

`V`	array of shape (n, 2), vertex coordinates in the map plane
`F`	integer array of shape (m, 2), endpoint indices into V
`grainId`	array of shape (m, 2), adjacent grain ids
`ebsdId`	array of shape (m, 2), adjacent EBSD pixel ids
`phaseId`	array of shape (m, 2), adjacent phase-list indices
`misrotation`	rotation across each segment
`CSList`	list of phase frames
`plane`	map-plane coordinate system converting V to specimen positions
`frame`	specimenFrame of the geometry
`scanUnit`	unit of vertex coordinates; default ‘um’

Output

`gB`	grainBoundary, usually obtained as grains.boundary

Properties

`allV`	all stored vertices as vector3d specimen positions
`F`	segment endpoint indices into V
`grainId`	grain ids on the two sides; ids need not equal array positions
`segLength`	length of each segment in scanUnit
`direction`	segment vectors as antipodal vector3d, with segment length
`midPoint`	midpoint of each segment as vector3d
`misorientation`	symmetry-aware orientation relationship for one phase pair
`chainId`	chain membership of each segment
`arcLength`	distance along the chain to the end of each segment
`triplePoints`	junctions at which three grains meet

Members

allV	the vertices as framed points of the specimen, all of them and the ones in use
angle	the angle of every segment to a direction, or to the segments of another boundary, in [0, pi/2], the segments having no sense
arcLength	the length along the chain up to the end of each segment
calcGBND	the grain boundary normal distribution in the crystal frame, estimated from the traces of the boundaries in a planar section
calcMeanDirection	the direction of a segment averaged over 2n + 1 of them along the chain: the chord across a window, clamped at the end of an open chain and shorter than a closed one
cat	the segments of several parts of one boundary, MATLAB’s [gB1, gB2]: the parts share the vertices of the boundary they were taken from
chainId	the chain of every segment, counted from 0, from the walk order and the junctions: a chain breaks where the head of one segment is not the tail of the next, and at a junction (MATLAB counts the chains from 1)
chainLength	the length of the chain of every segment
chainNeighbors	the segment before and after each one along its chain: a closed chain wraps its two ends onto each other, an open one clamps them, so a filter along the chain does not spread the undefined end
chainSize	the number of segments of the chain of every segment
chainV	the vertices of every chain in walk order, the chains separated by -1
characteristicShape	the characteristic shape of a set of boundary segments
componentId	the connected component each segment lies in, junctions included, and its size
componentSize	the number of segments of the connected component of every segment
curvature	the signed curvature of every segment: the Menger curvature through the midpoints of a segment and its two neighbours along the chain, smoothed by a binomial filter along it
direction	the direction of the walk, as a framed axis of the specimen
flip	swap the two sides of the segments marked, or of all of them, and walk the chains again
grainBoundary	a list of line segments separating neighbouring grains in a two-dimensional map
hasPhase	the segments between the two phases named, in either order, or with one named on either side
inpolygon	the segments whose midpoint lies inside a polygon (N, 2), or the rectangle [x, y, w, h]
intersect	where the line from p to q crosses each segment, MATLAB’s [x, y] = intersect(gB, xy1, xy2): the coordinates per segment, NaN where it is not crossed
isChainEnd	whether a segment is the last of its chain
isChainStart	whether a segment is the first of its chain
isClosed	a chain that closes onto itself, so its walk returns to where it started
isempty	whether the boundary has no segments
isJunction	a vertex where any number of segments other than two meet
isTwinning	the segments whose misorientation is the given one up to a threshold
junctionId	the indices of the junctions, the vertices where a number of segments other than two meet
midPoint	the midpoint of every segment, a direction of the map as MATLAB’s is
misorientation	the misorientations of the boundary, which needs one pair of phases in one order throughout, with the grain exchange symmetry where both sides are one phase
perimeter	the total length of the boundary, the sum of the segment lengths
plot	the grain boundary segments, in one colour or coloured segment by segment
quiver	arrows: tangent vectors at directions, a vector or axis field on the sphere, arrows at orientations in the sections of the current figure, or directions on a map or a volume
reduce	the boundary coarsened by keeping every n-th vertex along each chain, whatever the shape
refine	split every segment into pieces of about length delta: the old vertices stay where they are and the new ones lie on the old segments, so the boundary keeps its shape and its length and only the sampling gets finer, which gives a smoothing that follows evenly spaced degrees of freedom
rotate	rotate(x, rot) is x.rotate(rot), or rot * x for an object without that method
segLength	the length of every segment
selectByGrainId	the segments with a grain of the list on either side, walked again: a junction of the whole boundary may have lost its third segment, so the chains of the subset are longer
simplify	the boundary with the vertices dropped that carry no shape, Douglas-Peucker chain by chain
size	the number of segments
subsref
surfor	the cumulative projection length of the boundary segments (Panozzo 1984)
triplePoints	the triple points of the network, of a selection those at a vertex of its segments, with boundaryId into the whole network, as MATLAB’s
V_used	the indices of the vertices the segments use, sorted
vertexDegree	the number of segments meeting at every vertex

MATLAB’s grainBoundary_index

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/grainBoundary_index_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.

The class grainBoundary