# -*- coding: utf-8 -*-
# Author: Yikun Zhang
# Last Editing: July 03, 2022
# Description: This script contains code for detecting the knots (or intersection
# points) and computing the length of a given filament/web-like structure.
import numpy as np
from sklearn.cluster import AgglomerativeClustering
from numpy import linalg as LA
[docs]def DetectKnot(x, r_in, r_out, fila_map):
'''
Detecting if a point on the filament is a knot/intersection
(Metric Graph Method).
Parameters
----------
x: (D,)-array
The coordinate of the point of interest.
r_in: float
The radius of the inner ball around the point of interest.
r_out: float
The radius of the outer ball around the point of interest.
fila_map : (N,D)-array
The coordinates of all the filament points.
Returns
-------
'Knot'/'Non-Knot': str
The indicator of whether the point of interest is a knot/intersection
on the input filament.
'''
dist = LA.norm(fila_map - x.values, axis=1)
can_pts = fila_map[(dist >= r_in) & (dist <= r_out)]
if can_pts.shape[0] < 3:
return 'Non-Knot'
clustering = AgglomerativeClustering(n_clusters=None, affinity='euclidean',
linkage='average', distance_threshold=(r_in + r_out)/2)
clustering.fit_predict(can_pts)
if len(np.unique(clustering.labels_)) >= 3:
return 'Knot'
else:
return 'Non-Knot'