# Copyright (c) 2015, Ecole Polytechnique Federale de Lausanne, Blue Brain Project
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'''Section functions and functional tools'''
from neurom import morphmath as mm
from neurom._compat import range
[docs]def section_path_length(section):
'''Path length from section to root'''
return sum(s.length for s in section.iupstream())
[docs]def section_volume(section):
'''Volume of a section'''
return section.volume
[docs]def section_area(section):
'''Surface area of a section'''
return section.area
[docs]def section_tortuosity(section):
'''Tortuosity of a section
The tortuosity is defined as the ratio of the path length of a section
and the euclidian distnce between its end points.
The path length is the sum of distances between consecutive points.
If the section contains less than 2 points, the value 1 is returned.
'''
pts = section.points
return 1 if len(pts) < 2 else mm.section_length(pts) / mm.point_dist(pts[-1], pts[0])
[docs]def section_end_distance(section):
'''End to end distance of a section
The end to end distance of a section is defined as
the euclidian distnce between its end points.
If the section contains less than 2 points, the value 0 is returned.
'''
pts = section.points
return 0 if len(pts) < 2 else mm.point_dist(pts[-1], pts[0])
[docs]def branch_order(section):
'''Branching order of a tree section
The branching order is defined as the depth of the tree section.
Note:
The first level has branch order 1.
'''
return sum(1 for _ in section.iupstream()) - 1
[docs]def section_radial_distance(section, origin):
'''Return the radial distances of a tree section to a given origin point
The radial distance is the euclidian distance between the
end-point point of the section and the origin point in question.
Parameters:
section: neurite section object
origin: point to which distances are measured. It must have at least 3\
components. The first 3 components are (x, y, z).
'''
return mm.point_dist(section.points[-1], origin)
[docs]def section_meander_angles(section):
'''Inter-segment opening angles in a section'''
p = section.points
return [mm.angle_3points(p[i - 1], p[i - 2], p[i])
for i in range(2, len(p))]
[docs]def strahler_order(section):
'''Branching order of a tree section
The strahler order is the inverse of the branch order,
since this is computed from the tips of the tree
towards the root.
This implementation is a translation of the three steps described in
Wikipedia (https://en.wikipedia.org/wiki/Strahler_number):
- If the node is a leaf (has no children), its Strahler number is one.
- If the node has one child with Strahler number i, and all other children
have Strahler numbers less than i, then the Strahler number of the node
is i again.
- If the node has two or more children with Strahler number i, and no
children with greater number, then the Strahler number of the node is
i + 1.
No efforts have been invested in making it computationnaly efficient, but
it computes acceptably fast on tested morphologies (i.e., no waiting time).
'''
if section.children:
child_orders = [strahler_order(child) for child in section.children]
max_so_children = max(child_orders)
it = iter(co == max_so_children for co in child_orders)
# check if there are *two* or more children w/ the max_so_children
any(it)
if any(it):
return max_so_children + 1
return max_so_children
return 1
[docs]def locate_segment_position(section, fraction):
'''
Segment ID / offset corresponding to a given fraction of section length.
'''
return mm.path_fraction_id_offset(section.points, fraction)