114 lines
3.8 KiB
Python
114 lines
3.8 KiB
Python
from math import sqrt, inf
|
|
import numpy as np
|
|
|
|
|
|
class Point2D:
|
|
def __init__(self, x, y):
|
|
self.x = x
|
|
self.y = y
|
|
|
|
def __repr__(self):
|
|
return f"({self.x} {self.y})"
|
|
|
|
def copy(self):
|
|
return Point2D(self.x, self.y)
|
|
|
|
def get_coordinates(self):
|
|
return (self.x, self.y)
|
|
|
|
|
|
def coordinates_to_vectors(coordinates):
|
|
vectors = []
|
|
for coordinate in coordinates:
|
|
vectors.append(np.array(coordinate.get_coordinates()))
|
|
|
|
if (len(vectors) == 1):
|
|
return vectors[0]
|
|
else:
|
|
return vectors
|
|
|
|
|
|
class Polyline:
|
|
def __init__(self, points):
|
|
self.points = coordinates_to_vectors(points)
|
|
self.length_polyline = len(points)
|
|
|
|
self.vectors = [None] * self.length_polyline
|
|
self.lengths = [None] * self.length_polyline
|
|
self.unit_vectors = [None] * self.length_polyline
|
|
self.tangente = [None] * self.length_polyline
|
|
|
|
self.compute_requirements()
|
|
|
|
def compute_requirements(self):
|
|
|
|
# Between two points, there is only one segment
|
|
for j in range(self.length_polyline-1):
|
|
self.vectors[j] = self.points[j+1] - self.points[j]
|
|
self.lengths[j] = np.linalg.norm(self.vectors[j])
|
|
self.unit_vectors[j] = self.vectors[j]/self.lengths[j]
|
|
|
|
# print("\n\n", vectors, "\n\n", lengths, "\n\n", unit_vectors, "\n\n")
|
|
|
|
# Between two segments, there is only one angle
|
|
for k in range(self.length_polyline-2):
|
|
cross = np.dot(self.unit_vectors[k+1], self.unit_vectors[k])
|
|
self.tangente[k] = sqrt((1+cross)/(1-cross))
|
|
|
|
def radius_balance(self, i):
|
|
"""
|
|
Returns the radius that balances the radii on either end segement i.
|
|
"""
|
|
|
|
alpha_a = min(self.lengths[i], (self.lengths[i+1]*self.tangente[i+1]) /
|
|
(self.tangente[i] + self.tangente[i+1]))
|
|
alpha_b = min(self.lengths[i+2], self.lengths[i+1]-alpha_a)
|
|
|
|
return alpha_a, alpha_b, max(self.tangente[i]*alpha_a, self.tangente[i+1]*alpha_b)
|
|
|
|
def alpha_assign(polyline, alpha_radii, start_index, end_index):
|
|
"""
|
|
The Alpha-assign procedure assigning radii based on a polyline.
|
|
"""
|
|
minimum_radius, minimum_index = inf, end_index
|
|
|
|
if start_index + 1 >= end_index:
|
|
return
|
|
|
|
alpha_b = min(lenghts[start_index] -
|
|
alpha_radii[start_index], lenghts[start_index + 1])
|
|
current_radius = max(tangente[start_index] * alpha_radii[start_index],
|
|
tangente[start_index + 1] * alpha_b) # Radis at initial segment
|
|
|
|
if current_radius < minimum_radius:
|
|
minimum_radius, minimum_index = current_radius, start_index
|
|
alpha_low, alpha_high = alpha_radii[start_index], alpha_b
|
|
|
|
for i in range(start_index + 1, end_index - 2): # Radii for internal segments
|
|
alpha_a, alpha_b, current_radius = radius_balance(polyline, i)
|
|
if current_radius < minimum_radius:
|
|
alpha_low, alpha_high = alpha_a, alpha_radii[end_index]
|
|
|
|
# Assign alphas at ends of selected segment
|
|
alpha_radii[minimum_index] = alpha_low
|
|
alpha_radii[minimum_index+1] = alpha_high
|
|
# Recur on lower segments
|
|
alpha_assign(alpha_radii, start_index, minimum_index)
|
|
alpha_assign(alpha_radii, minimum_index + 1,
|
|
end_index) # Recur on higher segments
|
|
|
|
def compute_alpha_radii(polyline):
|
|
length_array = len(polyline)
|
|
apha_radii = [None] * length_array
|
|
|
|
alpha_radii[0] = 0
|
|
alpha_radii[length_array-1] = 0
|
|
|
|
for i in range(1, length_array-2):
|
|
alpha_radii[i] = min()
|
|
|
|
|
|
polyline = Polyline((Point2D(0, 0), Point2D(
|
|
0, 10), Point2D(10, 10), Point2D(10, 20)))
|
|
print(polyline.radius_balance(0))
|