Rectangular Conformal Map

version 1.0.0.1 (2.49 MB) by Gary Choi
Conformally map a simply-connected open triangle mesh to a rectangle

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Updated 29 Feb 2020

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This code computes the rectangular conformal parameterizations (i.e. angle-preserving mappings onto a rectangle) of triangle meshes with disk topology using the fast method in [1], which has been applied for texture mapping, surface registration, shape analysis and so on. Any comments and suggestions are welcome.

If you use this code in your own work, please cite the following paper:
[1] T. W. Meng, G. P.-T. Choi and L. M. Lui,
"TEMPO: Feature-Endowed Teichmüller Extremal Mappings of Point Clouds."
SIAM Journal on Imaging Sciences, 9(4), pp. 1922-1962, 2016.

Remarks:
1. Please make sure that the input mesh does not contain any unreferenced vertices/non-manifold vertices/non-manifold edges.
2. Please remove all valence 1 boundary vertices (i.e. vertices with only 1 face attached to them) before running the program.
3. Please make sure that the input triangulations are with anti-clockwise orientation.
4. The output rectangular domain will always have width = 1, while the height depends on the choice of the corners and may not be 1.

For more information, please visit: https://scholar.harvard.edu/choi

Cite As

T. W. Meng, G. P.-T. Choi and L. M. Lui, "TEMPO: Feature-Endowed Teichmüller Extremal Mappings of Point Clouds." SIAM Journal on Imaging Sciences, 9(4), pp. 1922-1962, 2016.

MATLAB Release Compatibility
Created with R2016a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements

Inspired by: Spherical Conformal Map, Disk Conformal Map

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