227 lines
9.9 KiB
Python
227 lines
9.9 KiB
Python
from math import inf, sqrt
|
|
from typing import List, Tuple, Union
|
|
|
|
import numpy as np
|
|
|
|
from networks.geometry.Circle import Circle
|
|
from networks.geometry.Point2D import Point2D
|
|
from networks.geometry.Segment2D import Segment2D
|
|
|
|
|
|
class Polyline:
|
|
def __init__(self, points: List[Point2D]):
|
|
"""A polyline with smooth corners, only composed of segments and circle arc.
|
|
|
|
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.
|
|
|
|
Args:
|
|
points (List[Point2D]): List of 2d-points in order describing the polyline.
|
|
|
|
Raises:
|
|
ValueError: At least 4 points required.
|
|
|
|
>>> Polyline((Point2D(0, 0), Point2D(0, 10), Point2D(50, 10), Point2D(20, 20)))
|
|
"""
|
|
self.output_points = points
|
|
self.points_array = Point2D.to_arrays(
|
|
self._remove_collinear_points(points))
|
|
self.length_polyline = len(self.points_array)
|
|
|
|
if self.length_polyline < 4:
|
|
raise ValueError("The list must contain at least 4 elements.")
|
|
|
|
self.vectors = [None] * self.length_polyline # v
|
|
self.lengths = [0] * (self.length_polyline - 1) # l
|
|
self.unit_vectors = [None] * self.length_polyline # n
|
|
self.tangente = [0] * self.length_polyline # f
|
|
|
|
# alpha, maximum radius factor
|
|
self.alpha_radii = [0] * self.length_polyline
|
|
|
|
# Useful outputs. In order to not break indexation, each list has the same length, even if for n points, there is n-2 radius.
|
|
# Lists will start and end with None.
|
|
self.radii = [0] * self.length_polyline # r, list of points
|
|
self.centers = [None] * self.length_polyline # c, list of points
|
|
# list of tuple of points (first intersection, corresponding corner, last intersection)
|
|
self.acrs_intersections = [None] * self.length_polyline
|
|
self.arcs = [[] for _ in range(self.length_polyline)] # list of points
|
|
# self.bisectors = [None] * self.length_polyline
|
|
|
|
# For n points, there is n-1 segments. Last element should stays None.
|
|
self.segments = [None] * \
|
|
self.length_polyline # list of segments
|
|
|
|
# Run procedure
|
|
self._compute_requirements()
|
|
self._compute_alpha_radii()
|
|
|
|
self._alpha_assign(0, self.length_polyline-1)
|
|
self.get_radii()
|
|
self.get_centers()
|
|
self.get_arcs_intersections()
|
|
self.get_arcs()
|
|
self.get_segments()
|
|
|
|
self.total_line_output = []
|
|
for i in range(1, self.length_polyline-1):
|
|
self.total_line_output.extend(self.segments[i].segment())
|
|
self.total_line_output.extend(self.arcs[i])
|
|
|
|
def __repr__(self):
|
|
return str(self.alpha_radii)
|
|
|
|
def get_radii(self) -> List[Union[int]]:
|
|
for i in range(1, self.length_polyline-1):
|
|
self.radii[i] = round(self.alpha_radii[i] * self.tangente[i])
|
|
return self.radii
|
|
|
|
def get_centers(self) -> List[Union[Point2D, None]]:
|
|
for i in range(1, self.length_polyline-1):
|
|
bisector = (self.unit_vectors[i] - self.unit_vectors[i-1]) / (
|
|
np.linalg.norm(self.unit_vectors[i] - self.unit_vectors[i-1]))
|
|
|
|
array = self.points_array[i] + sqrt((self.radii[i]
|
|
** 2) + (self.alpha_radii[i] ** 2)) * bisector
|
|
self.centers[i] = Point2D(array[0], array[1]).round()
|
|
return self.centers
|
|
|
|
def get_arcs_intersections(self) -> List[Tuple[Point2D]]:
|
|
"""Get arcs intersections points.
|
|
|
|
First and last elements elements of the list should be None. For n points, there are n-1 segments, and n-2 angle.
|
|
|
|
Returns:
|
|
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.
|
|
"""
|
|
for i in range(1, self.length_polyline-1):
|
|
point_1 = Point2D.from_arrays(self.points_array[i] -
|
|
self.alpha_radii[i] * self.unit_vectors[i-1])
|
|
point_2 = Point2D.from_arrays(self.points_array[i] +
|
|
self.alpha_radii[i] * self.unit_vectors[i])
|
|
self.acrs_intersections[i] = point_1.round(), Point2D.from_arrays(
|
|
self.points_array[i]), point_2.round()
|
|
return self.acrs_intersections
|
|
|
|
def get_arcs(self) -> List[Point2D]:
|
|
for i in range(1, self.length_polyline-1):
|
|
points = Circle(self.centers[i]).circle(self.radii[i])
|
|
|
|
# Better to do here than drawing circle arc inside big triangle!
|
|
double_point_a = Point2D.from_arrays(Point2D.to_arrays(self.acrs_intersections[i][0]) + 5 * (Point2D.to_arrays(
|
|
self.acrs_intersections[i][0]) - Point2D.to_arrays(self.centers[i])))
|
|
double_point_b = Point2D.from_arrays(Point2D.to_arrays(self.acrs_intersections[i][2]) + 5 * (Point2D.to_arrays(
|
|
self.acrs_intersections[i][2]) - Point2D.to_arrays(self.centers[i])))
|
|
|
|
for j in range(len(points)):
|
|
if points[j].is_in_triangle(double_point_a, self.centers[i], double_point_b):
|
|
self.arcs[i].append(points[j])
|
|
return self.arcs
|
|
|
|
def get_segments(self) -> List[Segment2D]:
|
|
"""Get the segments between the circle arcs and at the start and end.
|
|
|
|
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.
|
|
|
|
Returns:
|
|
list[Segment2D]: List of segments in order.
|
|
"""
|
|
# Get first segment.
|
|
# First arc index is 1 because index 0 is None due to fix list lenght. Is it a good choice?
|
|
self.segments[1] = Segment2D(Point2D.from_arrays(
|
|
self.points_array[0]), self.acrs_intersections[1][0])
|
|
|
|
# Get segments between arcs
|
|
for i in range(2, self.length_polyline - 1):
|
|
self.segments[i] = Segment2D(Point2D(self.acrs_intersections[i][0].x, self.acrs_intersections[i][0].y), Point2D(
|
|
self.acrs_intersections[i-1][-1].x, self.acrs_intersections[i-1][-1].y))
|
|
|
|
# Why -3?
|
|
# For n points, there are n-1 segments.
|
|
self.segments[-3] = Segment2D(self.acrs_intersections[-2][2], Point2D.from_arrays(
|
|
self.points_array[-1]))
|
|
|
|
return self.segments
|
|
|
|
def _alpha_assign(self, start_index: int, end_index: int):
|
|
"""
|
|
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(
|
|
self.lengths[start_index] - self.alpha_radii[start_index], self.lengths[start_index + 1])
|
|
current_radius = max(self.tangente[start_index] * self.alpha_radii[start_index],
|
|
self.tangente[start_index + 1] * alpha_b) # Radius at initial segment
|
|
|
|
if current_radius < minimum_radius:
|
|
minimum_radius, minimum_index = current_radius, start_index
|
|
# 0, 8
|
|
alpha_low, alpha_high = self.alpha_radii[start_index], alpha_b
|
|
|
|
for i in range(start_index + 1, end_index - 1): # Radii for internal segments
|
|
alpha_a, alpha_b, current_radius = self._radius_balance(i)
|
|
|
|
if current_radius < minimum_radius:
|
|
minimum_radius, minimum_index = current_radius, i
|
|
alpha_low, alpha_high = alpha_a, alpha_b
|
|
|
|
alpha_a = min(
|
|
self.lengths[end_index-2], self.lengths[end_index-1]-self.alpha_radii[end_index])
|
|
|
|
current_radius = max(self.tangente[end_index-1]*alpha_a, self.tangente[end_index]
|
|
* self.alpha_radii[end_index]) # Radius at final segment
|
|
|
|
if current_radius < minimum_radius:
|
|
minimum_radius, minimum_index = current_radius, end_index - 1
|
|
alpha_low, alpha_high = alpha_a, self.alpha_radii[end_index]
|
|
|
|
# Assign alphas at ends of selected segment
|
|
self.alpha_radii[minimum_index] = alpha_low
|
|
self.alpha_radii[minimum_index+1] = alpha_high
|
|
# Recur on lower segments
|
|
self._alpha_assign(start_index, minimum_index)
|
|
# Recur on higher segments
|
|
self._alpha_assign(minimum_index + 1, end_index)
|
|
|
|
def _radius_balance(self, i: int):
|
|
"""
|
|
Returns the radius that balances the radii on either end segement i.
|
|
"""
|
|
alpha_a = min(self.lengths[i-1], (self.lengths[i] *
|
|
self.tangente[i+1])/(self.tangente[i] + self.tangente[i+1]))
|
|
alpha_b = min(self.lengths[i+1], self.lengths[i]-alpha_a)
|
|
return alpha_a, alpha_b, min(self.tangente[i]*alpha_a, self.tangente[i+1]*alpha_b)
|
|
|
|
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_array[j+1] - self.points_array[j]
|
|
self.lengths[j] = np.linalg.norm(self.vectors[j])
|
|
self.unit_vectors[j] = self.vectors[j]/self.lengths[j]
|
|
|
|
# Between two segments, there is only one angle
|
|
for i in range(1, self.length_polyline-1):
|
|
dot = np.dot(self.unit_vectors[i], self.unit_vectors[i-1])
|
|
self.tangente[i] = sqrt((1+dot)/(1-dot))
|
|
# self.bisectors[i] = (self.unit_vectors[i]+self.unit_vectors[i-1]) / \
|
|
# np.linalg.norm(self.unit_vectors[i]-self.unit_vectors[i-1])
|
|
|
|
def _compute_alpha_radii(self):
|
|
self.alpha_radii[0] = 0
|
|
self.alpha_radii[self.length_polyline-1] = 0
|
|
|
|
@staticmethod
|
|
def _remove_collinear_points(points):
|
|
output_points = [points[0]]
|
|
|
|
for i in range(1, len(points) - 1):
|
|
if not Point2D.collinear(
|
|
points[i-1], points[i], points[i+1]):
|
|
output_points.append(points[i])
|
|
|
|
output_points.append(points[-1])
|
|
return output_points
|