# -*- coding: utf-8 -*-
"""
This module contains the Branch class (one branch of the tree) and the Nodes class
"""
import numpy as np
from multiprocessing.dummy import Pool as ThreadPool
from operator import itemgetter
from scipy.spatial import cKDTree
pool = ThreadPool(16)
[docs]class Branch:
"""Class that contains a branch of the fractal tree.
Args:
mesh: an object of the mesh class, where the fractal tree will grow
init_node (int): initial node to grow the branch. This is an index that refers to a node in the nodes.nodes array.
init_dir (array): initial direction to grow the branch. In general, it refers to the direction of the last segment of the mother brach.
init_tri (int): the index of triangle of the mesh where the init_node sits.
l (float): total length of the branch
angle (float): angle (rad) with respect to the init_dir in the plane of the init_tri triangle
w (float): repulsitivity parameter. Controls how much the branches repel each other.
nodes: the object of the class nodes that contains all the nodes of the existing branches.
brother_nodes (list): the nodes of the brother and mother branches, to be excluded from the collision detection between branches.
Nsegments (int): number of segments to divide the branch.
Attributes:
child (list): contains the indexes of the child branches. It is not assigned when created.
dir (array): vector direction of the last segment of the branch.
nodes (list): contains the node indices of the branch. The node coordinates can be retrieved using nodes.nodes[i]
triangles (list): contains the indices of the triangles from the mesh where every node of the branch lies.
tri (int): triangle index where last node sits.
growing (bool): False if the branch collide or is out of the surface. True otherwise.
"""
def __init__(self,mesh,init_node,init_dir,init_tri,l,angle,w,nodes,brother_nodes,Nsegments):
# self.nnodes=0
self.child = [0,0]
self.dir = np.array([0.0,0.0,0.0])
self.nodes=[]
self.triangles=[]
# self.normal=np.array([0.0,0.0,0.0])
self.queue=[]
self.growing=True
shared_node=-1
init_normal=mesh.normals[init_tri]
nodes.update_collision_tree(brother_nodes)
# global_nnodes=len(nodes.nodes)
# R=np.array([[np.cos(angle),-np.sin(angle)],[ np.sin(angle), np.cos(angle)]])
inplane=-np.cross(init_dir,init_normal)
dir=np.cos(angle)*init_dir+np.sin(angle)*inplane
dir=dir/np.linalg.norm(dir)
self.nodes.append(init_node)
self.queue.append(nodes.nodes[init_node])
self.triangles.append(init_tri)
grad=nodes.gradient(self.queue[0])
dir=(dir+w*grad)/np.linalg.norm(dir+w*grad)
# print nodes.nodes[init_node]+dir*l/Nsegments
for i in range(1,Nsegments):
intriangle=self.add_node_to_queue(mesh,self.queue[i-1],dir*l/Nsegments)
#print 'intriangle',intriangle
if not intriangle:
print 'Point not in triangle',i
# print self.queue[i-1]+dir*l/50.
self.growing=False
break
collision=nodes.collision(self.queue[i])
if collision[1]<l/5.:
print "Collision",i, collision
self.growing=False
self.queue.pop()
self.triangles.pop()
shared_node=collision[0]
break
grad=nodes.gradient(self.queue[i])
normal=mesh.normals[self.triangles[i],:]
#Project the gradient to the surface
grad=grad-(np.dot(grad,normal))*normal
dir=(dir+w*grad)/np.linalg.norm(dir+w*grad)
nodes_id=nodes.add_nodes(self.queue[1:])
[self.nodes.append(x) for x in nodes_id]
if not self.growing:
nodes.end_nodes.append(self.nodes[-1])
self.dir=dir
# #print self.triangles
self.tri=self.triangles[-1]
#Uncomment the following lines for a closed network
# if shared_node is not -1:
# self.nodes.append(shared_node)
[docs] def add_node_to_queue(self,mesh,init_node,dir):
"""Functions that projects a node in the mesh surface and it to the queue is it lies in the surface.
Args:
mesh: an object of the mesh class, where the fractal tree will grow
init_node (array): vector that contains the coordinates of the last node added in the branch.
dir (array): vector that contains the direction from the init_node to the node to project.
Return:
success (bool): true if the new node is in the triangle.
"""
# print 'node trying to project', init_node+dir
point, triangle=mesh.project_new_point(init_node+dir)
# print 'Projected point', point, 'dist', np.linalg.norm(point-init_node)
if triangle>=0:
self.queue.append(point)
self.triangles.append(triangle)
success=True
else:
# print point, triangle
success=False
#print 'Success? ',success
return success
[docs]class Nodes:
"""A class containing the nodes of the branches plus some fuctions to compute distance related quantities.
Args:
init_node (array): an array with the coordinates of the initial node of the first branch.
Attributes:
nodes (list): list of arrays containing the coordinates of the nodes
last_node (int): last added node.
end_nodes (list): a list containing the indices of all end nodes (nodes that are not connected) of the tree.
tree (scipy.spatial.cKDTree): a k-d tree to compute the distance from any point to the closest node in the tree. It is updated once a branch is finished.
collision_tree (scipy.spatial.cKDTree): a k-d tree to compute the distance from any point to the closest node in the tree, except from the brother and mother branches. It is used to check collision between branches.
"""
def __init__(self,init_node):
self.nodes=[]
self.nodes.append(init_node)
self.last_node=0
self.end_nodes=[]
self.tree=cKDTree(self.nodes)
[docs] def add_nodes(self,queue):
"""This function stores a list of nodes of a branch and returns the node indices. It also updates the tree to compute distances.
Args:
queue (list): a list of arrays containing the coordinates of the nodes of one branch.
Returns:
nodes_id (list): the indices of the added nodes.
"""
nodes_id=[]
for point in queue:
self.nodes.append(point)
self.last_node+=1
nodes_id.append(self.last_node)
self.tree=cKDTree(self.nodes)
return nodes_id
[docs] def distance_from_point(self,point):
"""This function returns the distance from any point to the closest node in the tree.
Args:
point (array): the coordinates of the point to calculate the distance from.
Returns:
d (float): the distance between point and the closest node in the tree.
"""
d,node=self.tree.query(point)
# distance=pool.map(lambda a: np.linalg.norm(a-point),self.nodes.values())
return d
[docs] def distance_from_node(self,node):
"""This function returns the distance from any node to the closest node in the tree.
Args:
node (int): the index of the node to calculate the distance from.
Returns:
d (float): the distance between specified node and the closest node in the tree.
"""
d, node = self.tree.query(self.nodes[node])
# distance=pool.map(lambda a: np.linalg.norm(a-self.nodes[node]),self.nodes.values())
return d
[docs] def update_collision_tree(self,nodes_to_exclude):
"""This function updates the collision_tree excluding a list of nodes from all the nodes in the tree. If all the existing nodes are excluded, one distant node is added.
Args:
nodes_to_exclude (list): contains the nodes to exclude from the tree. Usually it should be the mother and the brother branch nodes.
Returns:
none
"""
nodes=set(range(len(self.nodes)))
nodes=nodes.difference(nodes_to_exclude)
nodes_to_consider=[self.nodes[x] for x in nodes]
self.nodes_to_consider_keys=[x for x in nodes]
if len(nodes_to_consider)==0:
nodes_to_consider=[np.array([-100000000000.0,-100000000000.0,-100000000000.0])]
self.nodes_to_consider_keys=[100000000]
print "no nodes to consider"
self.collision_tree=cKDTree(nodes_to_consider)
[docs] def collision(self,point):
"""This function returns the distance between one point and the closest node in the tree and the index of the closest node using the collision_tree.
Args:
point (array): the coordinates of the point to calculate the distance from.
Returns:
collision (tuple): (distance to the closest node, index of the closest node)
"""
d,node=self.collision_tree.query(point)
collision=(self.nodes_to_consider_keys[node],d)
return collision
[docs] def gradient(self,point):
"""This function returns the gradient of the distance from the existing points of the tree from any point. It uses a central finite difference approximation.
Args:
point (array): the coordinates of the point to calculate the gradient of the distance from.
Returns:
grad (array): (x,y,z) components of gradient of the distance.
"""
delta=0.01
dx=np.array([delta,0,0])
dy=np.array([0.0,delta,0.0])
dz=np.array([0.0,0.0,delta])
distx_m=self.distance_from_point(point-dx)
distx_p=self.distance_from_point(point+dx)
disty_m=self.distance_from_point(point-dy)
disty_p=self.distance_from_point(point+dy)
distz_m=self.distance_from_point(point-dz)
distz_p=self.distance_from_point(point+dz)
grad=np.array([(distx_p-distx_m)/(2*delta),(disty_p-disty_m)/(2*delta),(distz_p-distz_m)/(2*delta)])
return grad