The purpose of this library is to provide tools for the study of the most beautiful discipline of mathematics: geometry and geometric analysis. In doing so, we restrict ourselves to 2-manifolds. For a mathematician, this may initially seem like a major restriction. However, it allows us, in a relatively simple way, to represent 2-manifolds as 'meshes' and to develop powerful tools to study them. The abstraction hardly needs to be restricted at all, because the proposed calculus for meshes makes it possible to develop new geometries with comparatively little effort. Properties of these meshes can then be examined using maniflow. For example, we provide tools to break down meshes into their connected components. You can also use maniflow to determine the orientability of a mesh. It is also possible to run a geometric flow, such as the mean curvature flow, on a mesh. This means that maniflow can also be used to examine meshes with regard to curvature (Gaussian curvature, mean curvature). maniflow also provides the option of creating images of the meshes. This makes it possible, for example, to create animations of geometric flows etc.
Make sure that you have installed the packages from requirements.txt
To install the libarary, use
pip install maniflow-1.0-py2.py3-none-any.whl
For builing the libarary one uses the command
python setup.py bdist_wheel --universal
In the doc/ folder you will find a detailed documentation of maniflow in the file doc/maniflow.pdf. The examples/ folder also contains some jupyter notebooks that describe a few applications of maniflow.
The example given here will create a moebius strip. We'll demonstrate this using the following code:
from maniflow.mesh.parameterized import *
from maniflow.mesh.obj import OBJFile
@VertexFunction
def moebius(vertex):
x = vertex[0]
y = vertex[1]
x0 = np.cos(x) * (1 + (y / 2) * np.cos(x / 2))
x1 = np.sin(x) * (1 + (y / 2) * np.cos(x / 2))
x2 = (y / 2) * np.sin(x / 2)
return np.array([x0, x1, x2])
u = Grid((0, 2 * np.pi), (-1, 1), 30, 10) # create a high resolution grid
moebiusMesh = moebius(u) # mapping the vertices from the grid according to the parametrisation
coincidingVertices(moebiusMesh) # remove the redundant vertices at the joint after making the moebius band
print(eulerCharacteristic(moebiusMesh)) # verify it is a real moebius band (expected value 0)
OBJFile.write(moebiusMesh, "moebius.obj") # writing the mesh data to the file 'moebius.obj'The .obj file created by this code can be loaded into Blender:
The following are some images and animations created using maniflow
