121 lines
4.2 KiB
Python
121 lines
4.2 KiB
Python
from math import sqrt, inf
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import numpy as np
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class Point2D:
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def __init__(self, x, y):
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self.x = x
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self.y = y
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def __repr__(self):
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return f"({self.x} {self.y})"
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def copy(self):
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return Point2D(self.x, self.y)
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def get_coordinates(self):
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return (self.x, self.y)
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def coordinates_to_vectors(coordinates):
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vectors = []
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for coordinate in coordinates:
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vectors.append(np.array(coordinate.get_coordinates()))
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if (len(vectors) == 1):
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return vectors[0]
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else:
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return vectors
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class Polyline:
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def __init__(self, points):
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self.points = coordinates_to_vectors(points)
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self.length_polyline = len(points)
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self.vectors = [None] * self.length_polyline
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self.lengths = [None] * self.length_polyline
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self.unit_vectors = [None] * self.length_polyline
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self.tangente = [None] * self.length_polyline
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self.alpha_radii = [None] * self.length_polyline
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self.compute_requirements()
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self.compute_alpha_radii()
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def compute_requirements(self):
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# Between two points, there is only one segment
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for j in range(self.length_polyline-1):
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self.vectors[j] = self.points[j+1] - self.points[j]
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self.lengths[j] = np.linalg.norm(self.vectors[j])
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self.unit_vectors[j] = self.vectors[j]/self.lengths[j]
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# print("\n\n", vectors, "\n\n", lengths, "\n\n", unit_vectors, "\n\n")
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# Between two segments, there is only one angle
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for k in range(1, self.length_polyline-1):
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cross = np.dot(self.unit_vectors[k], self.unit_vectors[k-1])
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self.tangente[k] = sqrt((1+cross)/(1-cross))
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def compute_alpha_radii(self):
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self.alpha_radii[0] = 0
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self.alpha_radii[self.length_polyline-1] = 0
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for i in range(1, self.length_polyline-2):
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self.alpha_radii[i] = min(self.lengths[i-1] - self.alpha_radii[i-1], (self.lengths[i]
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* self.tangente[i+1])/(self.tangente[i]+self.tangente[i+1]))
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def radius_balance(self, i):
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"""
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Returns the radius that balances the radii on either end segement i.
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"""
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alpha_a = min(self.lengths[i-1], (self.lengths[i]*self.tangente[i+1]) /
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(self.tangente[i] + self.tangente[i+1]))
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alpha_b = min(self.lengths[i+1], self.lengths[i]-alpha_a)
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return alpha_a, alpha_b, max(self.tangente[i]*alpha_a, self.tangente[i+1]*alpha_b)
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def alpha_assign(self, start_index, end_index):
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"""
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The Alpha-assign procedure assigning radii based on a polyline.
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"""
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minimum_radius, minimum_index = inf, end_index
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if start_index + 1 >= end_index:
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return
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alpha_b = min(
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self.lengths[start_index] - self.alpha_radii[start_index], self.lengths[start_index + 1])
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current_radius = max(self.tangente[start_index] * self.alpha_radii[start_index],
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self.tangente[start_index + 1] * alpha_b) # Radis at initial segment
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if current_radius < minimum_radius:
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minimum_radius, minimum_index = current_radius, start_index
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alpha_low, alpha_high = self.alpha_radii[start_index], alpha_b
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for i in range(start_index + 1, end_index - 2): # Radii for internal segments
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alpha_a, alpha_b, current_radius = self.radius_balance(i)
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if current_radius < minimum_radius:
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alpha_low, alpha_high = alpha_a, self.alpha_radii[end_index]
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# Assign alphas at ends of selected segment
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self.alpha_radii[minimum_index] = alpha_low
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self.alpha_radii[minimum_index+1] = alpha_high
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print(alpha_low, alpha_high)
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# Recur on lower segments
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self.alpha_assign(start_index, minimum_index)
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# Recur on higher segments
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self.alpha_assign(minimum_index + 1, end_index)
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polyline = Polyline((Point2D(0, 0), Point2D(0, 10), Point2D(
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10, 10), Point2D(10, 20), Point2D(20, 20), Point2D(20, 30), Point2D(60, 60), Point2D(60, 0)))
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# print(polyline.radius_balance(2))
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polyline.alpha_assign(1, polyline.length_polyline-1)
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print(polyline.alpha_radii)
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