def area_normalize(points, faces, spectrum):
"""
Normalize a spectrum using areas as suggested in Reuter et al. (2006)
Parameters
------------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
spectrum : list of floats
LB spectrum of a given shape defined by _points_ and _faces_
Returns
-----------
new_spectrum : list of floats
LB spectrum normalized by area
"""
from mindboggle.guts.mesh import area_of_faces
area = area_of_faces(points, faces)
total_area = sum(area)
new_spectrum = [x/total_area for x in spectrum]
return new_spectrum
def area_normalize(points, faces, spectrum):
"""
Normalize a spectrum using areas as suggested in Reuter et al. (2006)
Parameters
------------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
spectrum : list of floats
LB spectrum of a given shape defined by _points_ and _faces_
Returns
-----------
new_spectrum : list of floats
LB spectrum normalized by area
"""
from mindboggle.guts.mesh import area_of_faces
area = area_of_faces(points, faces)
total_area = sum(area)
new_spectrum = [x / total_area for x in spectrum]
return new_spectrum
def area_normalize(points, faces, spectrum):
"""
Normalize a spectrum using areas as suggested in Reuter et al. (2006)
Parameters
----------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
spectrum : list of floats
LB spectrum of a given shape defined by _points_ and _faces_
Returns
-------
new_spectrum : list of floats
LB spectrum normalized by area
Examples
--------
>>> import numpy as np
>>> from mindboggle.shapes.laplace_beltrami import area_normalize
>>> from mindboggle.shapes.laplace_beltrami import fem_laplacian
>>> # Define a cube:
>>> points = [[0,0,0], [0,1,0], [1,1,0], [1,0,0],
... [0,0,1], [0,1,1], [1,1,1], [1,0,1]]
>>> faces = [[0,1,2], [2,3,0], [4,5,6], [6,7,4], [0,4,7], [7,3,0],
... [0,4,5], [5,1,0], [1,5,6], [6,2,1], [3,7,6], [6,2,3]]
>>> spectrum = fem_laplacian(points, faces, spectrum_size=3,
... normalization=None)
>>> print(np.array_str(np.array(spectrum[1::]),
... precision=5, suppress_small=True))
[ 4.58359 4.8 ]
>>> new_spectrum = area_normalize(points, faces, spectrum)
>>> print(np.array_str(np.array(new_spectrum[1::]),
... precision=5, suppress_small=True))
[ 27.50155 28.8 ]
"""
from mindboggle.guts.mesh import area_of_faces
area = area_of_faces(points, faces)
total_area = sum(area)
new_spectrum = [x*total_area for x in spectrum]
return new_spectrum
def area_normalize(points, faces, spectrum):
"""
Normalize a spectrum using areas as suggested in Reuter et al. (2006)
Parameters
----------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
spectrum : list of floats
LB spectrum of a given shape defined by _points_ and _faces_
Returns
-------
new_spectrum : list of floats
LB spectrum normalized by area
Examples
--------
>>> import numpy as np
>>> from mindboggle.shapes.laplace_beltrami import area_normalize
>>> from mindboggle.shapes.laplace_beltrami import fem_laplacian
>>> # Define a cube:
>>> points = [[0,0,0], [0,1,0], [1,1,0], [1,0,0],
... [0,0,1], [0,1,1], [1,1,1], [1,0,1]]
>>> faces = [[0,1,2], [2,3,0], [4,5,6], [6,7,4], [0,4,7], [7,3,0],
... [0,4,5], [5,1,0], [1,5,6], [6,2,1], [3,7,6], [6,2,3]]
>>> spectrum = fem_laplacian(points, faces, spectrum_size=3,
... normalization=None)
>>> print(np.array_str(np.array(spectrum[1::]),
... precision=5, suppress_small=True))
[ 4.58359 4.8 ]
>>> new_spectrum = area_normalize(points, faces, spectrum)
>>> print(np.array_str(np.array(new_spectrum[1::]),
... precision=5, suppress_small=True))
[ 27.50155 28.8 ]
"""
from mindboggle.guts.mesh import area_of_faces
area = area_of_faces(points, faces)
total_area = sum(area)
new_spectrum = [x * total_area for x in spectrum]
return new_spectrum