A harmonic framework for vector fields and differential operators on SO(3)
R. Hielscher, E. Wünsche
Preprint
Publications
The papers behind MTEX
If MTEX was part of your research, please cite the paper that describes the method you used. Most of them come with the MTEX scripts that draw their figures.
Citing MTEX in general
F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox. Solid State Phenomena 160, 63-68 (2010). doi:10.4028/www.scientific.net/SSP.160.63
@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}
}Which paper for what
- MTEX in generalBachmann et al. 2010
- Grain boundary distributionsHielscher et al. 2026
- Fast harmonic transforms on SO(3)Hielscher & Wünsche 2026
- Habit planesNyyssönen et al. 2023
- Parent grain reconstructionNiessen et al. 2022
- Embeddings of orientationsHielscher & Lippert 2021
- Kikuchi pattern analysisHielscher et al. 2019
- Denoising EBSD mapsHielscher et al. 2019
- Misorientation spacesKrakow et al. 2017
- Orientation colour keysNolze & Hielscher 2016
- Texture strength and componentsMainprice et al. 2014
- Tensors and physical propertiesMainprice et al. 2011
- Grain reconstructionBachmann et al. 2011
- Orientation statistics within grainsBachmann et al. 2010
- ODFs from pole figuresHielscher & Schaeben 2008
2026
A unified framework for grain boundary distributions in textured materials
R. Hielscher, R. Kilian, E. Wünsche, K. Marquardt
Preprint
Three-dimensional shape metrics for martensite and bainite from two-dimensional orientation maps
T. Nyyssönen, A. Ståhlkrantz, A. A. Gazder, R. Hielscher, F. Niessen
Acta Materialia 313, 122306
On the role of the double Fourier sphere method in fast algorithms on SO(3)
R. Hielscher, E. Wünsche
Applied and Computational Harmonic Analysis 85, 101907
2024
An optimal ansatz space for moving least squares approximation on spheres
R. Hielscher, T. Pöschl
Advances in Computational Mathematics 50, 107
2023
Habit plane determination from reconstructed parent phase orientation maps
T. Nyyssönen, A. A. Gazder, R. Hielscher, F. Niessen
Acta Materialia 255, 119035
Approximating the derivative of manifold-valued functions
R. Hielscher, L. Lippert
Journal of Approximation Theory 285, 105832
2022
The variant graph approach to improved parent grain reconstruction
R. Hielscher, T. Nyyssönen, F. Niessen, A. A. Gazder
Materialia 22, 101399
Parent grain reconstruction from partially or fully transformed microstructures in MTEX
F. Niessen, T. Nyyssönen, A. A. Gazder, R. Hielscher
Journal of Applied Crystallography 55, 180–194
Interplay between habit plane and orientation relationship in an electron backscatter diffraction analysis: using the example of η′-Al8Fe3 in η-Al5Fe2
H. Becker, R. Hielscher, A. Leineweber
Crystals 12, 813
2021
Locally isometric embeddings of quotients of the rotation group modulo finite symmetries
R. Hielscher, L. Lippert
Journal of Multivariate Analysis 185, 104764
2019
Gazing at crystal balls: electron backscatter diffraction pattern analysis and cross correlation on the sphere
R. Hielscher, F. Bartel, T. B. Britton
Ultramicroscopy 207, 112836
Denoising of crystal orientation maps
R. Hielscher, C. Silbermann, E. Schmidl, J. Ihlemann
Journal of Applied Crystallography 52, 984–996
2017
On three-dimensional misorientation spaces
R. Krakow, R. J. Bennett, D. N. Johnstone, Z. Vukmanovic, W. Solano-Alvarez, S. J. Lainé, J. F. Einsle, P. A. Midgley, C. M. F. Rae, R. Hielscher
Proceedings of the Royal Society A 473, 20170274
2016
Orientations – perfectly colored
G. Nolze, R. Hielscher
Journal of Applied Crystallography 49, 1786–1802
2014
Descriptive tools for the analysis of texture projects with large datasets using MTEX: strength, symmetry and components
D. Mainprice, F. Bachmann, R. Hielscher, H. Schaeben
Geological Society, London, Special Publications 409, 251–271
Calculating anisotropic piezoelectric properties from texture data using the MTEX open source package
D. Mainprice, F. Bachmann, R. Hielscher, H. Schaeben, G. E. Lloyd
Geological Society, London, Special Publications 409, 223–249
2011
Calculating anisotropic physical properties from texture data using the MTEX open source package
D. Mainprice, R. Hielscher, H. Schaeben
Geological Society, London, Special Publications 360, 175–192
Grain detection from 2d and 3d EBSD data – specification of the MTEX algorithm
F. Bachmann, R. Hielscher, H. Schaeben
Ultramicroscopy 111, 1720–1733
2010
Inferential statistics of electron backscatter diffraction data from within individual crystalline grains
F. Bachmann, R. Hielscher, P. E. Jupp, W. Pantleon, H. Schaeben, E. Wegert
Journal of Applied Crystallography 43, 1338–1355
Texture analysis with MTEX – free and open source software toolbox
F. Bachmann, R. Hielscher, H. Schaeben
Solid State Phenomena 160, 63–68
Orientation distribution within a single hematite crystal
R. Hielscher, H. Schaeben, H. Siemes
Mathematical Geosciences 42, 359–375
2008
A novel pole figure inversion method: specification of the MTEX algorithm
R. Hielscher, H. Schaeben
Journal of Applied Crystallography 41, 1024–1037