157 lines
6.1 KiB
Python
157 lines
6.1 KiB
Python
from networks.geometry.Point2D import Point2D
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from math import sqrt, inf
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import numpy as np
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class Polyline:
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def __init__(self, points: list["Point2D"]):
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"""A polyline with smooth corners, only composed of segments and circle arc.
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Mathematics and algorithms behind this can be found here: https://cdr.lib.unc.edu/concern/dissertations/pz50gw814?locale=en, E2 Construction of arc roads from polylines, page 210.
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Args:
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points (List[Point2D]): List of 2d-points in order describing the polyline.
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Raises:
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ValueError: At least 4 points required.
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>>> Polyline((Point2D(0, 0), Point2D(0, 10), Point2D(50, 10), Point2D(20, 20)))
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"""
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self.points = Point2D.to_vectors(self._remove_collinear_points(points))
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self.length_polyline = len(points)
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if self.length_polyline < 4:
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raise ValueError("The list must contain at least 4 elements.")
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self.vectors = [None] * self.length_polyline # v
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self.lengths = [None] * (self.length_polyline - 1) # l
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self.unit_vectors = [None] * self.length_polyline # n
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self.tangente = [0] * self.length_polyline # f
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self.alpha_radii = [None] * self.length_polyline # alpha
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self.radii = [None] * self.length_polyline # r
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self.centers = [None] * self.length_polyline # c
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self.connections = [None] * self.length_polyline
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self._compute_requirements()
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self._compute_alpha_radii()
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self._alpha_assign(0, self.length_polyline-1)
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self.output_points = points
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def __repr__(self):
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return str(self.alpha_radii)
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def get_radii(self):
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for i in range(1, self.length_polyline-1):
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self.radii[i] = round(self.alpha_radii[i] * self.tangente[i])
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return self.radii
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def get_centers(self):
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if self.radii == [None] * self.length_polyline:
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raise ValueError("No radii found. Run get_radii before.")
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for i in range(1, self.length_polyline-1):
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bisector = (self.unit_vectors[i] - self.unit_vectors[i-1]) / (
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np.linalg.norm(self.unit_vectors[i] - self.unit_vectors[i-1]))
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array = self.points[i] + sqrt((self.radii[i]
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** 2) + (self.alpha_radii[i] ** 2)) * bisector
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self.centers[i] = Point2D(array[0], array[1]).round()
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return self.centers
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def get_arcs(self):
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for i in range(1, self.length_polyline-1):
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point_1 = self.points[i] - \
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self.alpha_radii[i] * self.unit_vectors[i-1]
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point_2 = self.points[i] + \
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self.alpha_radii[i] * self.unit_vectors[i]
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self.connections[i] = (point_1, point_2)
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return self.connections
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def _alpha_assign(self, start_index: int, end_index: int):
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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) # Radius 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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# 0, 8
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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 - 1): # 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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minimum_radius, minimum_index = current_radius, i
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alpha_low, alpha_high = alpha_a, alpha_b
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alpha_a = min(self.lengths[end_index-2],
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self.lengths[end_index-1]-self.alpha_radii[end_index])
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current_radius = max(self.tangente[end_index-1]*alpha_a, self.tangente[end_index]
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* self.alpha_radii[end_index]) # Radius at final segment
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if current_radius < minimum_radius:
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minimum_radius, minimum_index = current_radius, end_index - 1
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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/1.5
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self.alpha_radii[minimum_index+1] = alpha_high/1.5
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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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def _radius_balance(self, i: int):
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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, min(self.tangente[i]*alpha_a, self.tangente[i+1]*alpha_b)
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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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# 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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dot = np.dot(self.unit_vectors[k], self.unit_vectors[k-1])
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self.tangente[k] = sqrt((1+dot)/(1-dot))
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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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@staticmethod
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def _remove_collinear_points(points):
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output_points = [points[0]]
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for i in range(1, len(points) - 1):
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if not Point2D.collinear(
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points[i-1], points[i], points[i+1]):
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output_points.append(points[i])
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output_points.append(points[-1])
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return output_points
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