235 lines
10 KiB
Python
235 lines
10 KiB
Python
from math import inf, sqrt
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from typing import List, Tuple, Union
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import numpy as np
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from networks.geometry.Circle import Circle
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from networks.geometry.Point2D import Point2D
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from networks.geometry.Segment2D import Segment2D
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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.output_points = points
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self.points_array = Point2D.to_arrays(
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self._remove_collinear_points(points))
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self.length_polyline = len(self.points_array)
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if self.length_polyline < 4:
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print(self.length_polyline)
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print(self.points_array)
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print(self.output_points)
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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 = [0] * (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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# alpha, maximum radius factor
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self.alpha_radii = [0] * self.length_polyline
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# Useful outputs. In order to not break indexation, each list has the same length, even if for n points, there is n-2 radius.
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# Lists will start and end with None.
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self.radii = [0] * self.length_polyline # r, list of points
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self.centers = [None] * self.length_polyline # c, list of points
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# list of tuple of points (first intersection, corresponding corner, last intersection)
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self.acrs_intersections = [None] * self.length_polyline
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self.arcs = [[] for _ in range(self.length_polyline)] # list of points
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# self.bisectors = [None] * self.length_polyline
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# For n points, there is n-1 segments. Last element should stays None.
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self.segments = [None] * \
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self.length_polyline # list of segments
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# Run procedure
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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.get_radii()
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self.get_centers()
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self.get_arcs_intersections()
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self.get_arcs()
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self.get_segments()
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self.total_line_output = []
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for i in range(1, self.length_polyline-1):
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self.total_line_output.extend(self.segments[i].segment())
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self.total_line_output.extend(self.arcs[i])
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self.total_line_output.extend(
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self.segments[self.length_polyline-1].segment())
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self.total_line_output = self.total_line_output[0].optimized_path(
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self.total_line_output)
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def __repr__(self):
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return str(self.alpha_radii)
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def get_radii(self) -> List[Union[int]]:
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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) -> List[Union[Point2D, None]]:
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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_array[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_intersections(self) -> List[Tuple[Point2D]]:
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"""Get arcs intersections points.
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First and last elements elements of the list should be None. For n points, there are n-1 segments, and n-2 angle.
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Returns:
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list[tuple(Point2D)]: List of tuples composed - in order - of the first arc points, the corner points, the last arc points. The corresponding arc circle is inside this triangle.
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"""
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for i in range(1, self.length_polyline-1):
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point_1 = Point2D.from_arrays(self.points_array[i] -
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self.alpha_radii[i] * self.unit_vectors[i-1])
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point_2 = Point2D.from_arrays(self.points_array[i] +
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self.alpha_radii[i] * self.unit_vectors[i])
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self.acrs_intersections[i] = point_1.round(), Point2D.from_arrays(
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self.points_array[i]), point_2.round()
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return self.acrs_intersections
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def get_arcs(self) -> List[Point2D]:
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for i in range(1, self.length_polyline-1):
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points = Circle(self.centers[i]).circle(self.radii[i])
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# Better to do here than drawing circle arc inside big triangle!
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double_point_a = Point2D.from_arrays(Point2D.to_arrays(self.acrs_intersections[i][0]) + 5 * (Point2D.to_arrays(
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self.acrs_intersections[i][0]) - Point2D.to_arrays(self.centers[i])))
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double_point_b = Point2D.from_arrays(Point2D.to_arrays(self.acrs_intersections[i][2]) + 5 * (Point2D.to_arrays(
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self.acrs_intersections[i][2]) - Point2D.to_arrays(self.centers[i])))
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for j in range(len(points)):
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if points[j].is_in_triangle(double_point_a, self.centers[i], double_point_b):
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self.arcs[i].append(points[j])
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return self.arcs
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def get_segments(self) -> List[Segment2D]:
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"""Get the segments between the circle arcs and at the start and end.
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Last list element should be None, and last usable index is -2 or self.length_polyline - 2. For n points, there are n-1 segments.
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Returns:
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list[Segment2D]: List of segments in order.
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"""
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# Get first segment.
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# First arc index is 1 because index 0 is None due to fix list lenght. Is it a good choice?
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self.segments[1] = Segment2D(Point2D.from_arrays(
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self.points_array[0]), self.acrs_intersections[1][0])
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# Get segments between arcs
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for i in range(2, self.length_polyline - 1):
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self.segments[i] = Segment2D(Point2D(self.acrs_intersections[i][0].x, self.acrs_intersections[i][0].y), Point2D(
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self.acrs_intersections[i-1][-1].x, self.acrs_intersections[i-1][-1].y))
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# Why -3?
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# For n points, there are n-1 segments.
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self.segments[-1] = Segment2D(self.acrs_intersections[-2][2], Point2D.from_arrays(
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self.points_array[-1]))
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return self.segments
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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(
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self.lengths[end_index-2], 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
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self.alpha_radii[minimum_index+1] = 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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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] *
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self.tangente[i+1])/(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_array[j+1] - self.points_array[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 i in range(1, self.length_polyline-1):
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dot = np.dot(self.unit_vectors[i], self.unit_vectors[i-1])
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self.tangente[i] = sqrt((1+dot)/(1-dot))
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# self.bisectors[i] = (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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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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