https://github.com/justachetan/DiffGeoOps
Python implementation of the paper "Discrete Differential-Geometry Operators for Triangulated 2-Manifolds" by Meyer et. al. VisMath 2002
https://github.com/justachetan/DiffGeoOps
2-manifolds 3d curvature differential-geometry differential-geometry-operators discrete-differential-geometry manifolds mayavi mother-son-mesh numerical-methods python python3 scientific-computing torus triangulation
Last synced: about 1 year ago
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Python implementation of the paper "Discrete Differential-Geometry Operators for Triangulated 2-Manifolds" by Meyer et. al. VisMath 2002
- Host: GitHub
- URL: https://github.com/justachetan/DiffGeoOps
- Owner: justachetan
- License: mit
- Created: 2019-05-07T15:12:49.000Z (about 7 years ago)
- Default Branch: master
- Last Pushed: 2023-08-14T23:42:04.000Z (almost 3 years ago)
- Last Synced: 2024-10-28T07:41:11.164Z (over 1 year ago)
- Topics: 2-manifolds, 3d, curvature, differential-geometry, differential-geometry-operators, discrete-differential-geometry, manifolds, mayavi, mother-son-mesh, numerical-methods, python, python3, scientific-computing, torus, triangulation
- Language: Python
- Homepage: http://multires.caltech.edu/pubs/diffGeoOps.pdf
- Size: 2.03 MB
- Stars: 53
- Watchers: 1
- Forks: 6
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# DiffGeoOps
This repository contains a Python implementation of the paper:
>[Discrete Differential-Geometry Operators for Triangulated 2-Manifolds. *Mark Meyer*, *Mathieu Desbrun*, *Peter Schröder* and *Alan H. Barr*. *VisMath 2002*](http://www.multires.caltech.edu/pubs/diffGeoOps.pdf)
This module implements the discrete versions of three differential geometry operators for Triangulated 2-manifolds that have been discussed in the paper. They are:
- Mean Curvature
- Gaussian Curvature
- Principal Curvature
## Usage
```
$ python3 DiffGeoOps.py -h
usage: DiffGeoOps.py [-h] --mode MODE [--ops OPS] [--mesh MESH] [--save]
[--title TITLE]
i [i ...]
First, use '--mode 0' to generate files for containing value of the
operator and then plot the operatore using '--mode 1' and '--mesh'. For
'--ops', the operations are encoded as:
- 1: Mean Curvature
- 2: Gaussian Curvature
- 3: Principal Curvatures
Note that each operation is performed for all the input files.
positional arguments:
i path to input file(s)
optional arguments:
-h, --help show this help message and exit
--mode MODE specifies mode for program:
- 0: For computation
- 1: For Plotting
--ops OPS number to denote all the operations to be
performed on each file.
--mesh MESH mesh on which curvatures were calculated (redundant in computation mode)
--save flag for saving the plot (redundant in computation mode)
--title TITLE title of plot (redundant in computation mode)
```
First you need to provide a 3D mesh as an input to the code with `--mode 0` for computation. The mesh should be in Object File Format (.off). Then use the command with `--mode 1` for plotting. For more explaination, see Example Usage.
### Example Usage
```
$ # Calculating Gaussian Curvature of a Torus mesh
$ python3 DiffGeoOps.py --mode 0 --op 2 torus.off
$ # Plotting the generated values. The file generated will be _.npy
$ python3 DiffGeoOps.py --mode 1 --mesh torus.off torus_KG.npy
```
You can also provide multiple files as input for `--mode 0` now:
```
$ # Calculating Mean and Gaussian curvatures for 2 meshes
$ python DiffGeoOps.py --mode 0 --op 12 example_meshes/torus.off example_meshes/moebius.off
[DiffGeoOps]: Mean Curvature for example_meshes/torus.off saved to ./example_meshes/torus_KH.npy
[DiffGeoOps]: Gaussian Curvature for example_meshes/torus.off saved to ./example_meshes/torus_KG.npy
[DiffGeoOps]: Mean Curvature for example_meshes/moebius.off saved to ./example_meshes/moebius_KH.npy
[DiffGeoOps]: Gaussian Curvature for example_meshes/moebius.off saved to ./example_meshes/moebius_KG.npy
```
**Note**: The plot mode does not yet support multiple inputs
## Some results
- Plot of Gaussian curvature for Torus
- Plot of Mean curvature for the Mother-son mesh
## License
Copyright (c) 2019 Aditya Chetan
For license information, see [LICENSE](LICENSE) or http://mit-license.org
- - -
This code was written as a part of my independent study in **Differential Geometry** with [Dr. Kaushik Kalyanaraman](https://www.iiitd.ac.in/kaushik) at IIIT Delhi during Winter 2019 Semester.
For bugs in the code, please write to: aditya16217 [at] iiitd [dot] ac [dot] in