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dijkstra_algorithm.py
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dijkstra_algorithm.py
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# -*- coding: utf-8 -*-
"""
/***************************************************************************
ForestRoads
A QGIS plugin
Create a network of forest roads based on zones to access, roads to connect
them to, and a cost matrix.
The code of the plugin is based on the "LeastCostPath" plugin available on
https://github.com/Gooong/LeastCostPath. We thank their team for the template.
Generated by Plugin Builder: http://g-sherman.github.io/Qgis-Plugin-Builder/
-------------------
begin : 10-07-2019
copyright : (C) 2019 by Clement Hardy
email : [email protected]
***************************************************************************/
/***************************************************************************
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
***************************************************************************/
This script describes the A* algorithm used to find the least cost path between two given
node, both described by a row and a column of the cost raster.
"""
from math import sqrt
import math
import queue
import random
from qgis.core import (
QgsFeature,
QgsGeometry,
QgsPoint,
QgsPointXY,
QgsField,
QgsFields,
QgsWkbTypes,
QgsProcessing,
QgsFeatureSink,
QgsProcessingException,
QgsProcessingAlgorithm,
QgsProcessingParameterFeatureSource,
QgsProcessingParameterFeatureSink,
QgsProcessingParameterRasterLayer,
QgsProcessingParameterBand,
QgsProcessingParameterBoolean
)
def dijkstra(start_row_col, end_row_cols, block, angle_considered, punisherAngleDictionnary,feedback=None):
sqrt2 = sqrt(2)
# The grid class is used to both contain the matrix of the values
# of the cost raster, but also to have usefull function for the
# pathfinding algorithm used here.
class Grid:
def __init__(self, matrix):
self.map = matrix
# h is the height of the matrix/raster
self.h = len(matrix)
# w is the width of the matrix/raster
self.w = len(matrix[0])
# Function to test if a coordinate is in the bounds of the matrix/raster
# In the code, self.h is used to invert the y axis of the coordinates of rows
# because I used cartesian coordinates, and the raster have raster coordinates
# (inverted y axis). Self.h is diminished by one because it starts at 1, while
# the rows start at 0.
def _in_bounds(self, id):
row, col = id
return 0 <= col < self.w and 0 <= row < (self.h-1)
# Function to test if the raster value of this coordinate is not empty (has a cost to pass it)
def _passable(self, id):
row, col = id
return self.map[(self.h-1)-row][col] is not None
# Function to test a coordinate is both in bound and passable
def is_valid(self, id):
return self._in_bounds(id) and self._passable(id)
# Function to get the eight neighbours of a given cell. They are filtered to get only the valid ones.
def neighbors(self, id):
row, col = id
results = [(row + 1, col), (row, col - 1), (row - 1, col), (row, col + 1),
(row + 1, col - 1), (row + 1, col + 1), (row - 1, col - 1), (row - 1, col + 1)]
results = filter(self.is_valid, results)
return results
# Static function to calculate the manhattan distance between two cells.
@staticmethod
def manhattan_distance(id1, id2):
x1, y1 = id1
x2, y2 = id2
return abs(x1 - x2) + abs(y1 - y2)
# Function to calculate the minimum manhattan distance between nodes that have been explored yet and the ending
# nodes for feedback purposes.
def min_manhattan(self, curr_node, end_nodes):
return min(map(lambda node: self.manhattan_distance(curr_node, node), end_nodes))
def getAngle(self, a, b, c):
"""Function to get the angle between three coordinates."""
ang = math.degrees(math.atan2(c[1]-b[1], c[0]-b[0]) - math.atan2(a[1]-b[1], a[0]-b[0]))
return ang + 360 if ang < 0 else ang
# Function to get the cost associated for passing from a node to another (current, next)
def simple_cost(self, cur, nex, predecessorDictionnary, angle_considered, punisherAngleDictionnary):
# Coordinates of current
crow, ccol = cur
# Coordinates of next
nrow, ncol = nex
# Get the value associated with the current node
currV = self.map[(self.h-1) - crow][ccol]
# Get the value associated with the next node
offsetV = self.map[(self.h-1) - nrow][ncol]
# Check if the nodes are horizontal/vertical neighbours, or diagonals.
# Adjust the cost to go from one to the other accordingly.
if ccol == ncol or crow == nrow:
cost = (currV + offsetV) / 2
else:
cost = sqrt2 * (currV + offsetV) / 2
# Then, we adjust the cost according to the angle formed between the predecessor of current and next.
if angle_considered and predecessorDictionnary[cur] is not None:
pred = predecessorDictionnary[cur]
angle = self.getAngle(pred, cur, nex)
# Case of 45 degrees
if angle == 180 - 45 or angle == 180 + 45:
cost = cost * punisherAngleDictionnary[45]
elif angle == 180 - 90 or angle == 180 + 90:
cost = cost * punisherAngleDictionnary[90]
elif angle == 180 - 135 or angle == 180 + 135:
cost = cost * punisherAngleDictionnary[135]
# Case of a flat angle (0 degrees) : we do nothing.
# Case of a full turn (180 degrees) : impossible with the dijkstra algorithm.
return cost
# We create the grid object containing the values of the cost raster
grid = Grid(block)
# We create a set of nodes to reach (multiple goal possible)
end_row_cols = set(end_row_cols)
# We create a priority Queue which contains the nodes that are opened but
# not closed (see functioning of dijkstra algorithm; nodes are opened to
# initialize their remaining distance, then closed)
frontier = queue.PriorityQueue()
# In the frontier, we put tuples containing distance from start, and the node)
frontier.put((0, start_row_col))
# We initialize a dictionary of predecessors. For a given node, we'll know
# which node is his predecessor.
came_from = {}
# A dictionary to know what is the distance from a given node to the start.
cost_so_far = {}
# If the starting node is invalid, we return nothing
if not grid.is_valid(start_row_col):
return None, None, None
# If the starting node is also an ending node, we return nothing
if start_row_col in end_row_cols:
# feedback.pushInfo("Starting node seem to coincide with a ending node")
return None, None, None
# We initialize the beginning of the loop
came_from[start_row_col] = None
cost_so_far[start_row_col] = 0
current_node = None
# feedback.pushInfo("Dijkstra loop initialized.")
# We launch the loop. It will end when there are no more cell to
# check (impossible to reach an end node), or will be broken when
# a end node is reached
while not frontier.empty():
# We get the node with the smallest distance to start
# First node will be the start node, of course
# By using this function, the current node is removed
# from the frontier.
current_cost, current_node = frontier.get()
# update the progress bar if feedback is activated.
if feedback:
# The algorithm is canceled if users told it to feedback.
if feedback.isCanceled():
return None, None, None
# We break the loop if the current node is a goal to reach
if current_node in end_row_cols:
break
# If not, we look at each neighbour of the node
for nex in grid.neighbors(current_node):
# We calculate the distance to goal from this neighbour (which is the one
# from the current node + the move from current node to neighbour)
new_cost = cost_so_far[current_node] + grid.simple_cost(current_node, nex, came_from, angle_considered,
punisherAngleDictionnary)
# If the neighbour is not in the dictionary of opened nodes, or if
# the cost of passing by this neighbour is cheaper than the previous
# predecessor that this node had
if nex not in cost_so_far or new_cost < cost_so_far[nex]:
# We put the current node as predecessor of this neighbour,
# we put the neighbour in the frontier, and we register
# the cost to start
cost_so_far[nex] = new_cost
frontier.put((new_cost, nex))
came_from[nex] = current_node
# When the loop ends, if we did indeed found an end goal :
if current_node in end_row_cols:
# We calculate the cost from this end goal to the start
end_node = current_node
# We initialize the path object that we are going to return : it is a list.
# We also make a list of costs.
path = []
costs = []
# From the end node, we add the current node,
# we register the cost to go to it from the goal,
# and we take the predecessor as the current node.
# We stop when there are no more predecessors
# (meaning current node = starting node)
while current_node is not None:
path.append(current_node)
costs.append(cost_so_far[current_node])
current_node = came_from[current_node]
# We reverse the order of the list to start from the start
path.reverse()
costs.reverse()
# We return the path
return path, costs, end_node
# If we did not reached a end goal, it was unreachable.
# We return nothing.
else:
return None, None, None