def face_matrix(self):
face_vertices = [None] * self.mesh.number_of_faces()
for fkey in self.mesh.faces():
face_vertices[self.fkey_index[fkey]] = [
self.key_index[key] for key in self.mesh.face_vertices(fkey)
]
return face_matrix(face_vertices, rtype='csr', normalize=True)
def mesh_face_matrix(mesh, rtype='array'):
r"""Construct the face matrix from a Mesh datastructure.
Parameters
----------
mesh : compas.datastructures.Mesh
Instance of mesh.
rtype : {'array', 'csc', 'csr', 'coo', 'list'}
Format of the result.
Returns
-------
array-like
Constructed mesh face matrix.
Notes
-----
The face matrix represents the relationship between faces and vertices.
Each row of the matrix represents a face. Each column represents a vertex.
The matrix is filled with zeros except where a relationship between a vertex
and a face exist.
.. math::
F_{ij} =
\begin{cases}
1 & \text{if vertex j is part of face i} \\
0 & \text{otherwise}
\end{cases}
The face matrix can for example be used to compute the centroids of all
faces of a mesh.
Examples
--------
>>> from compas.datastructures import Mesh
>>> mesh = Mesh.from_polyhedron(6)
>>> F = mesh_face_matrix(mesh)
>>> type(F)
<class 'numpy.ndarray'>
>>> F = mesh_face_matrix(mesh, rtype='csr')
>>> type(F)
<class 'scipy.sparse.csr.csr_matrix'>
>>> from numpy import allclose
>>> xyz = asarray(mesh.vertices_attributes('xyz'))
>>> F = mesh_face_matrix(mesh, rtype='csr')
>>> c1 = F.dot(xyz) / F.sum(axis=1)
>>> c2 = [mesh.face_centroid(fkey) for fkey in mesh.faces()]
>>> allclose(c1, c2)
True
"""
key_index = {key: index for index, key in enumerate(mesh.vertices())}
face_vertices = [[key_index[key] for key in mesh.face_vertices(fkey)]
for fkey in mesh.faces()]
return face_matrix(face_vertices, rtype=rtype)
def mesh_face_matrix(mesh, rtype='csr'):
r"""Construct the face matrix from a Mesh datastructure.
Parameters
----------
mesh : obj
Mesh datastructure object to get data from.
rtype : {'array', 'csc', 'csr', 'coo', 'list'}
Format of the result.
Returns
-------
array-like
Constructed mesh face matrix.
Notes
-----
The face matrix represents the relationship between faces and vertices.
Each row of the matrix represents a face. Each column represents a vertex.
The matrix is filled with zeros except where a relationship between a vertex
and a face exist.
.. math::
F_{ij} =
\begin{cases}
1 & \text{if vertex j is part of face i} \\
0 & \text{otherwise}
\end{cases}
The face matrix can for example be used to compute the centroids of all
faces of a mesh.
Examples
--------
.. code-block:: python
import compas
from compas.datastructures import Mesh
from compas.datastructures import mesh_face_matrix
mesh = Mesh.from_obj(compas.get('faces.obj'))
F = mesh_face_matrix(mesh)
xyz = array([mesh.vertex_coordinates(key) for key in mesh.vertices()])
c = F.dot(xyz) / normrow(F)
"""
key_index = {key: index for index, key in enumerate(mesh.vertices())}
face_vertices = [[key_index[key] for key in mesh.face_vertices(fkey)]
for fkey in mesh.faces()]
return face_matrix(face_vertices, rtype=rtype)
