This repository contains a Python implementation of the paper:
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
$ 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.
$ # 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
- Plot of Gaussian curvature for Torus
- Plot of Mean curvature for the Mother-son mesh
Copyright (c) 2019 Aditya Chetan
For license information, see LICENSE or http://mit-license.org
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