def face_flatness(self, fkey, maxdev=0.02):
"""Compute the flatness of the mesh face.
Parameters
----------
fkey : int
The identifier of the face.
maxdev : float, optional
A maximum value for the allowed deviation from flatness.
Default is ``0.02``.
Returns
-------
float
The flatness.
Notes
-----
Flatness is computed as the ratio of the distance between the diagonals
of the face to the average edge length. A practical limit on this value
realted to manufacturing is 0.02 (2%).
Warnings
--------
This method only makes sense for quadrilateral faces.
"""
vertices = self.face_vertices(fkey)
f = len(vertices)
points = self.vertices_attributes('xyz', keys=vertices)
lengths = [distance_point_point(a, b) for a, b in pairwise(points + points[:1])]
length = sum(lengths) / f
d = distance_line_line((points[0], points[2]), (points[1], points[3]))
return (d / length) / maxdev
def flatness(vertices, faces, maxdev=0.02):
"""Compute mesh flatness per face.
Parameters
----------
vertices : list
The vertex coordinates.
faces : list
The face vertices.
maxdev : float, optional
A maximum value for the allowed deviation from flatness.
Default is ``0.02``.
Returns
-------
dict
For each face, a deviation from *flatness*.
Notes
-----
The "flatness" of a face is expressed as the ratio of the distance between
the diagonals to the average edge length. For the fabrication of glass panels,
for example, ``0.02`` could be a reasonable maximum value.
Warning
-------
This function only works as expected for quadrilateral faces.
See Also
--------
* :func:`compas.geometry.mesh_flatness`
"""
dev = []
for face in faces:
points = [vertices[index] for index in face]
lengths = [
distance_point_point(a, b)
for a, b in window(points + points[0:1], 2)
]
l = sum(lengths) / len(lengths)
d = distance_line_line((points[0], points[2]), (points[1], points[3]))
dev.append((d / l) / maxdev)
return dev
def mesh_flatness(mesh, maxdev=1.0):
"""Compute mesh flatness per face.
Parameters
----------
mesh : Mesh
A mesh object.
maxdev : float, optional
A maximum value for the allowed deviation from flatness.
Default is ``1.0``.
Returns
-------
dict
For each face, a deviation from *flatness*.
Notes
-----
The "flatness" of a face is expressed as the ratio of the distance between
the diagonals to the average edge length. For the fabrication of glass panels,
for example, ``0.02`` could be a reasonable maximum value.
Warnings
--------
This function only works as expected for quadrilateral faces.
"""
dev = []
for fkey in mesh.faces():
points = mesh.face_coordinates(fkey)
if len(points) == 3:
dev.append(0.0)
else:
lengths = [
distance_point_point(a, b)
for a, b in window(points + points[0:1], 2)
]
length = sum(lengths) / len(lengths)
d = distance_line_line((points[0], points[2]),
(points[1], points[3]))
dev.append((d / length) / maxdev)
return dev
def face_curvatures(mesh):
"""Curvatures of the mesh quad faces as dict face: face curvature.
Curvature of a face = distance between diagonals / mean diagonal length.
Parameters
----------
mesh : Mesh
A mesh.
Returns
-------
face_curvature_dict: dict
Dictionary of curvatures per face {face: face curvature}. None if vertex is not a quad.
Raises
------
-
"""
face_curvature_dict = {}
for fkey in mesh.faces():
if len(mesh.face_vertices(fkey)) == 4:
u, v, w, x = [
mesh.vertex_coordinates(vkey)
for vkey in mesh.face_vertices(fkey)
]
face_curvature_dict[fkey] = distance_line_line(
(u, w), (v, x)) / (distance_point_point(u, w) +
distance_point_point(v, x)) * 2
elif len(mesh.face_vertices(fkey)) == 3:
face_curvature_dict[fkey] = 0
else:
face_curvature_dict[fkey] = None
return face_curvature_dict
