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

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 <MESH-NAME>_<OP>.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 or http://mit-license.org

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This code was written as a part of my independent study in Differential Geometry with Dr. Kaushik Kalyanaraman at IIIT Delhi during Winter 2019 Semester.

For bugs in the code, please write to: aditya16217 [at] iiitd [dot] ac [dot] in