diode 1.2.2

Get, Build, Install

The simplest way to install Diode as a Python package:

pip install --verbose diode

or from this repository directly:

pip install --verbose git+https://github.com/mrzv/diode.git

Alternatively, you can clone and build everything by hand. To get Diode, either clone its repository:

git clone https://github.com/mrzv/diode.git

or download it as a Zip archive.

To build the project:

mkdir build
cd build
cmake ..
make

To use the Python bindings, either launch Python from .../build/bindings/python or add this directory to your PYTHONPATH variable, by adding:

export PYTHONPATH=.../build/bindings/python:$PYTHONPATH

to your ~/.bashrc or ~/.zshrc.

Usage

NB: a remark below about using exact computation. This issue is especially important when working with degenerate point sets (e.g., repeated copies of a fundamental domain in a periodic point set).

See examples/generate_alpha_shape.cpp and examples/generate_weighted_alpha_shape.cpp for C++ examples.

In Python, use diode.fill_alpha_shapes(...) and diode.fill_weighted_alpha_shapes(...) to fill a list of simplices, together with their alpha values:

>>> import diode
>>> import numpy as np

>>> points = np.random.random((100,3))
>>> simplices = diode.fill_alpha_shapes(points)

>>> print(simplices)
 [([13L], 0.0),
  ([18L], 0.0),
  ([59L], 0.0),
  ([10L], 0.0),
  ([72L], 0.0),
  ...,
  ([91L, 4L, 16L, 49L], 546.991052812204),
  ([49L, 62L], 1933.2257381777533),
  ([62L, 34L, 49L], 1933.2257381777533),
  ([62L, 91L, 49L], 1933.2257381777533),
  ([62L, 91L, 34L, 49L], 1933.2257381777533)]

>>> weighted_points = np.random.random((100,4))
>>> simplices2 = diode.fill_weighted_alpha_shapes(weighted_points)
>>> print(simplices2)
[([24L], -0.987214836816236),
 ([35L], -0.968749877102265),
 ([50L], -0.9673151804059413),
 ([47L], -0.9640549893422644),
 ([71L], -0.9639978806827709),
 ([24L, 50L], -0.9540965704765515),
 ...
 ([54L, 10L], 29223.611044169364),
 ([10L, 54L, 43L], 29223.611044169364),
 ([13L, 10L, 54L], 29223.611044169364),
 ([13L, 10L, 54L, 43L], 29223.611044169364)]

The list can be passed to Dionysus to initialize a filtration:

>>> import dionysus
>>> f = dionysus.Filtration(simplices)
>>> print(f)
Filtration with 2287 simplices

DioDe also includes diode.fill_periodic_alpha_shapes(...), which generates the alpha shape for a point set on a periodic cube, by default [0,0,0] - [1,1,1]. (In the periodic case, it may happen that CGAL reports each simplex multiple times. However, passing the result to dionysus.Filtration will take care of the duplicates.):

>>> simplices_periodic = diode.fill_periodic_alpha_shapes(points)
>>> f_periodic = dionysus.Filtration(simplices_periodic)
>>> print(f_periodic)
Filtration with 2912 simplices

>>> for s in f_periodic: print(s)
<0> 0
<1> 0
<2> 0
<3> 0
...
<77,94,97> 0.0704355
<46,77,94,97> 0.0708062
<30,77,94,97> 0.0708474
<18,65,79> 0.0715833
<18,64,65,79> 0.0715833
<18,65,79,99> 0.0725366

When using CGAL version at least 4.11, DioDe includes diode.fill_weighted_periodic_alpha_shapes(...), which generates the alpha shape for a weighted point set on a periodic cube:

>>> weighted_points[:,3] /= 64
>>> simplices_weighted_periodic = diode.fill_weighted_periodic_alpha_shapes(weighted_points)

diode.circumcenter(...) can be used to compute the circumcenter of a tetrahedron in 3D:

>>> tet = np.random.random((4,3))
>>> center = diode.circumcenter(tet)
>>> print(center)
[-0.00752673  0.14213101  1.0060982 ]

>>> verts_by_dim = diode.fill_delaunay_arrays(points)

>>> vertices, offsets = diode.fill_periodic_delaunay_lifts_arrays(
...     points, bbox_min=[0, 0, 0], bbox_max=[1, 1, 1])