Description

The volume is divided into cells n times the voxel size, and the vertices of a cell become one. Vertices that belong to different sets of grains, or to different faces of the outer hull, never merge: a triple line stays a triple line between the same grains, a quadruple point stays where four grains meet, and the hull stays flat. Faces whose vertices fell together vanish, so a grain smaller than a cell keeps its voxels but loses its surface and its volume drops to zero.

This is the blunt instrument: it thins a flat face and a curved one alike. The centroid of a cluster already averages the voxel steps, the 'quadric' placement keeps flat faces flat and triple lines sharp.

Syntax

grains = reduceBoundary(grains)
grains = reduceBoundary(grains,3)
grains = reduceBoundary(grains,2,'quadric')

Input

`grains`	`grain3d with triangular faces`
`n`	`coarsening factor (default 2)`

Options

cell size of the clustering cell (default n times the shortest edge)

Flags

quadric place each vertex where the faces it stands for are best approximated, instead of at the centroid of its cluster

Output

grains grain3d

References

J. Rossignac, P. Borrel, Multi-resolution 3D approximations for rendering complex scenes, Modeling in Computer Graphics, Springer 1993.
P. Lindstrom, Out-of-core simplification of large polygonal models, SIGGRAPH 2000, the quadric placement.

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/grain3d.reduceBoundary.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.

grain3d.reduceBoundary