451 lines
14 KiB
Python
451 lines
14 KiB
Python
"""
|
|
Polygon module
|
|
SPDX - License - Identifier: LGPL - 3.0 - or -later
|
|
Copyright © 2022 Concordia CERC group
|
|
Project Coder Pilar Monsalvete Alvarez de Uribarri pilar.monsalvete@concordia.ca
|
|
"""
|
|
|
|
from __future__ import annotations
|
|
import math
|
|
import sys
|
|
from typing import List
|
|
from hub.hub_logger import logger
|
|
import numpy as np
|
|
from trimesh import Trimesh
|
|
import trimesh.intersections
|
|
import trimesh.creation
|
|
import trimesh.geometry
|
|
from shapely.geometry.polygon import Polygon as shapley_polygon
|
|
|
|
from hub.city_model_structure.attributes.plane import Plane
|
|
from hub.city_model_structure.attributes.point import Point
|
|
import hub.helpers.constants as cte
|
|
|
|
|
|
class Polygon:
|
|
"""
|
|
Polygon class
|
|
"""
|
|
# todo: review with @Guille: Points, Coordinates, Vertices, Faces
|
|
|
|
def __init__(self, coordinates):
|
|
self._area = None
|
|
self._points = None
|
|
self._points_list = None
|
|
self._normal = None
|
|
self._inverse = None
|
|
self._edges = None
|
|
self._coordinates = coordinates
|
|
self._triangles = None
|
|
self._vertices = None
|
|
self._faces = None
|
|
self._plane = None
|
|
|
|
@property
|
|
def points(self) -> List[Point]:
|
|
"""
|
|
Get the points belonging to the polygon [[x, y, z],...]
|
|
:return: [Point]
|
|
"""
|
|
if self._points is None:
|
|
self._points = []
|
|
for coordinate in self.coordinates:
|
|
self._points.append(Point(coordinate))
|
|
return self._points
|
|
|
|
@property
|
|
def plane(self) -> Plane:
|
|
"""
|
|
Get the polygon plane
|
|
:return: Plane
|
|
"""
|
|
if self._plane is None:
|
|
self._plane = Plane(normal=self.normal, origin=self.points[0])
|
|
return self._plane
|
|
|
|
@property
|
|
def coordinates(self) -> List[np.ndarray]:
|
|
"""
|
|
Get the points in the shape of its coordinates belonging to the polygon [[x, y, z],...]
|
|
:return: [np.ndarray]
|
|
"""
|
|
return self._coordinates
|
|
|
|
def contains_point(self, point):
|
|
"""
|
|
Determines if the given point is contained by the current polygon
|
|
:return: boolean
|
|
"""
|
|
# fixme: This method doesn't seems to work.
|
|
n = len(self.vertices)
|
|
angle_sum = 0
|
|
for i in range(0, n):
|
|
vector_0 = self.vertices[i]
|
|
vector_1 = self.vertices[(i+1) % n]
|
|
# set to origin
|
|
vector_0[0] = vector_0[0] - point.coordinates[0]
|
|
vector_0[1] = vector_0[1] - point.coordinates[1]
|
|
vector_0[2] = vector_0[2] - point.coordinates[2]
|
|
vector_1[0] = vector_1[0] - point.coordinates[0]
|
|
vector_1[1] = vector_1[1] - point.coordinates[1]
|
|
vector_1[2] = vector_1[2] - point.coordinates[2]
|
|
module = np.linalg.norm(vector_0) * np.linalg.norm(vector_1)
|
|
|
|
scalar_product = np.dot(vector_0, vector_1)
|
|
angle = np.pi/2
|
|
if module != 0:
|
|
angle = abs(np.arcsin(scalar_product / module))
|
|
angle_sum += angle
|
|
return abs(angle_sum - math.pi*2) < cte.EPSILON
|
|
|
|
def contains_polygon(self, polygon):
|
|
"""
|
|
Determines if the given polygon is contained by the current polygon
|
|
:return: boolean
|
|
"""
|
|
|
|
for point in polygon.points:
|
|
if not self.contains_point(point):
|
|
return False
|
|
return True
|
|
|
|
@property
|
|
def points_list(self) -> np.ndarray:
|
|
"""
|
|
Get the solid surface point coordinates list [x, y, z, x, y, z,...]
|
|
:return: np.ndarray
|
|
"""
|
|
if self._points_list is None:
|
|
s = self.coordinates
|
|
self._points_list = np.reshape(s, len(s) * 3)
|
|
return self._points_list
|
|
|
|
@property
|
|
def edges(self) -> List[List[Point]]:
|
|
"""
|
|
Get polygon edges list
|
|
:return: [[Point]]
|
|
"""
|
|
if self._edges is None:
|
|
self._edges = []
|
|
for i in range(0, len(self.points) - 1):
|
|
point_1 = self.points[i]
|
|
point_2 = self.points[i + 1]
|
|
self._edges.append([point_1, point_2])
|
|
self._edges.append([self.points[len(self.points) - 1], self.points[0]])
|
|
return self._edges
|
|
|
|
@property
|
|
def area(self):
|
|
"""
|
|
Get surface area in square meters
|
|
:return: float
|
|
"""
|
|
if self._area is None:
|
|
self._area = 0
|
|
for triangle in self.triangles:
|
|
ab = np.zeros(3)
|
|
ac = np.zeros(3)
|
|
for i in range(0, 3):
|
|
ab[i] = triangle.coordinates[1][i] - triangle.coordinates[0][i]
|
|
ac[i] = triangle.coordinates[2][i] - triangle.coordinates[0][i]
|
|
self._area += np.linalg.norm(np.cross(ab, ac)) / 2
|
|
return self._area
|
|
|
|
@property
|
|
def normal(self) -> np.ndarray:
|
|
"""
|
|
Get surface normal vector
|
|
:return: np.ndarray
|
|
"""
|
|
if self._normal is None:
|
|
points = self.coordinates
|
|
# todo: IF THE FIRST ONE IS 0, START WITH THE NEXT
|
|
point_origin = points[len(points) - 2]
|
|
vector_1 = points[len(points) - 1] - point_origin
|
|
vector_2 = points[0] - point_origin
|
|
vector_3 = points[1] - point_origin
|
|
cross_product = np.cross(vector_1, vector_2)
|
|
if np.linalg.norm(cross_product) != 0:
|
|
cross_product = cross_product / np.linalg.norm(cross_product)
|
|
alpha = self._angle_between_vectors(vector_1, vector_2)
|
|
else:
|
|
cross_product = [0, 0, 0]
|
|
alpha = 0
|
|
if len(points) == 3:
|
|
return cross_product
|
|
if np.linalg.norm(cross_product) == 0:
|
|
return cross_product
|
|
alpha += self._angle(vector_2, vector_3, cross_product)
|
|
for i in range(0, len(points) - 4):
|
|
vector_1 = points[i + 1] - point_origin
|
|
vector_2 = points[i + 2] - point_origin
|
|
alpha += self._angle(vector_1, vector_2, cross_product)
|
|
vector_1 = points[len(points) - 1] - point_origin
|
|
vector_2 = points[0] - point_origin
|
|
if alpha < 0:
|
|
cross_product = np.cross(vector_2, vector_1)
|
|
else:
|
|
cross_product = np.cross(vector_1, vector_2)
|
|
self._normal = cross_product / np.linalg.norm(cross_product)
|
|
return self._normal
|
|
|
|
@staticmethod
|
|
def _angle(vector_1, vector_2, cross_product):
|
|
"""
|
|
alpha angle in radians
|
|
:param vector_1: [float]
|
|
:param vector_2: [float]
|
|
:param cross_product: [float]
|
|
:return: float
|
|
"""
|
|
accepted_normal_difference = 0.01
|
|
cross_product_next = np.cross(vector_1, vector_2)
|
|
if np.linalg.norm(cross_product_next) != 0:
|
|
cross_product_next = cross_product_next / np.linalg.norm(cross_product_next)
|
|
alpha = Polygon._angle_between_vectors(vector_1, vector_2)
|
|
else:
|
|
cross_product_next = [0, 0, 0]
|
|
alpha = 0
|
|
delta_normals = 0
|
|
for j in range(0, 3):
|
|
delta_normals += cross_product[j] - cross_product_next[j]
|
|
if np.abs(delta_normals) < accepted_normal_difference:
|
|
return alpha
|
|
return -alpha
|
|
|
|
@staticmethod
|
|
def triangle_mesh(vertices, normal):
|
|
min_x = 1e16
|
|
min_y = 1e16
|
|
min_z = 1e16
|
|
for vertex in vertices:
|
|
if vertex[0] < min_x:
|
|
min_x = vertex[0]
|
|
if vertex[1] < min_y:
|
|
min_y = vertex[1]
|
|
if vertex[2] < min_z:
|
|
min_z = vertex[2]
|
|
|
|
new_vertices = []
|
|
for vertex in vertices:
|
|
vertex = [vertex[0]-min_x, vertex[1]-min_y, vertex[2]-min_z]
|
|
new_vertices.append(vertex)
|
|
|
|
transformation_matrix = trimesh.geometry.plane_transform(origin=new_vertices[0], normal=normal)
|
|
|
|
coordinates = []
|
|
for vertex in vertices:
|
|
transformed_vertex = [vertex[0]-min_x, vertex[1]-min_y, vertex[2]-min_z, 1]
|
|
transformed_vertex = np.dot(transformation_matrix, transformed_vertex)
|
|
coordinate = [transformed_vertex[0], transformed_vertex[1]]
|
|
coordinates.append(coordinate)
|
|
|
|
polygon = shapley_polygon(coordinates)
|
|
|
|
try:
|
|
vertices_2d, faces = trimesh.creation.triangulate_polygon(polygon, engine='triangle')
|
|
mesh = Trimesh(vertices=vertices, faces=faces)
|
|
|
|
# check orientation
|
|
normal_sum = 0
|
|
for i in range(0, 3):
|
|
normal_sum += normal[i] + mesh.face_normals[0][i]
|
|
|
|
if abs(normal_sum) <= 1E-10:
|
|
new_faces = []
|
|
for face in faces:
|
|
new_face = []
|
|
for i in range(0, len(face)):
|
|
new_face.append(face[len(face)-i-1])
|
|
new_faces.append(new_face)
|
|
mesh = Trimesh(vertices=vertices, faces=new_faces)
|
|
|
|
return mesh
|
|
|
|
except ValueError:
|
|
logger.error(f'Not able to triangulate polygon\n')
|
|
sys.stderr.write(f'Not able to triangulate polygon\n')
|
|
_vertices = [[0, 0, 0], [0, 0, 1], [0, 1, 0]]
|
|
_faces = [[0, 1, 2]]
|
|
return Trimesh(vertices=_vertices, faces=_faces)
|
|
|
|
@property
|
|
def triangles(self) -> List[Polygon]:
|
|
if self._triangles is None:
|
|
self._triangles = []
|
|
_mesh = self.triangle_mesh(self.coordinates, self.normal)
|
|
for face in _mesh.faces:
|
|
points = []
|
|
for vertex in face:
|
|
points.append(self.coordinates[vertex])
|
|
polygon = Polygon(points)
|
|
self._triangles.append(polygon)
|
|
return self._triangles
|
|
|
|
@staticmethod
|
|
def _angle_between_vectors(vec_1, vec_2):
|
|
"""
|
|
angle between vectors in radians
|
|
:param vec_1: vector
|
|
:param vec_2: vector
|
|
:return: float
|
|
"""
|
|
if np.linalg.norm(vec_1) == 0 or np.linalg.norm(vec_2) == 0:
|
|
sys.stderr.write("Warning: impossible to calculate angle between planes' normal. Return 0\n")
|
|
return 0
|
|
cosine = np.dot(vec_1, vec_2) / np.linalg.norm(vec_1) / np.linalg.norm(vec_2)
|
|
if cosine > 1 and cosine - 1 < 1e-5:
|
|
cosine = 1
|
|
elif cosine < -1 and cosine + 1 > -1e-5:
|
|
cosine = -1
|
|
alpha = math.acos(cosine)
|
|
return alpha
|
|
|
|
@property
|
|
def inverse(self):
|
|
"""
|
|
Get the polygon coordinates in reversed order
|
|
:return: [np.ndarray]
|
|
"""
|
|
if self._inverse is None:
|
|
self._inverse = self.coordinates[::-1]
|
|
return self._inverse
|
|
|
|
def divide(self, plane):
|
|
"""
|
|
Divides the polygon in two by a plane
|
|
:param plane: plane that intersects with self to divide it in two parts (Plane)
|
|
:return: Polygon, Polygon, [Point]
|
|
"""
|
|
tri_polygons = Trimesh(vertices=self.vertices, faces=self.faces)
|
|
intersection = trimesh.intersections.mesh_plane(tri_polygons, plane.normal, plane.origin.coordinates)
|
|
polys_1 = trimesh.intersections.slice_mesh_plane(tri_polygons, plane.opposite_normal, plane.origin.coordinates)
|
|
polys_2 = trimesh.intersections.slice_mesh_plane(tri_polygons, plane.normal, plane.origin.coordinates)
|
|
triangles_1 = []
|
|
for triangle in polys_1.triangles:
|
|
triangles_1.append(Polygon(triangle))
|
|
polygon_1 = self._reshape(triangles_1)
|
|
triangles_2 = []
|
|
for triangle in polys_2.triangles:
|
|
triangles_2.append(Polygon(triangle))
|
|
polygon_2 = self._reshape(triangles_2)
|
|
return polygon_1, polygon_2, intersection
|
|
|
|
def _reshape(self, triangles) -> Polygon:
|
|
edges_list = []
|
|
for i in range(0, len(triangles)):
|
|
for edge in triangles[i].edges:
|
|
if not self._edge_in_edges_list(edge, edges_list):
|
|
edges_list.append(edge)
|
|
else:
|
|
edges_list = self._remove_from_list(edge, edges_list)
|
|
points = self._order_points(edges_list)
|
|
return Polygon(points)
|
|
|
|
@staticmethod
|
|
def _edge_in_edges_list(edge, edges_list):
|
|
for edge_element in edges_list:
|
|
if (edge_element[0].distance_to_point(edge[0]) == 0 and edge_element[1].distance_to_point(edge[1]) == 0) or \
|
|
(edge_element[1].distance_to_point(edge[0]) == 0 and edge_element[0].distance_to_point(
|
|
edge[1]) == 0):
|
|
return True
|
|
return False
|
|
|
|
@staticmethod
|
|
def _order_points(edges_list):
|
|
# todo: not sure that this method works for any case -> RECHECK
|
|
points = edges_list[0]
|
|
for _ in range(0, len(points)):
|
|
for i in range(1, len(edges_list)):
|
|
point_1 = edges_list[i][0]
|
|
point_2 = points[len(points) - 1]
|
|
if point_1.distance_to_point(point_2) == 0:
|
|
points.append(edges_list[i][1])
|
|
points.remove(points[len(points) - 1])
|
|
array_points = []
|
|
for point in points:
|
|
array_points.append(point.coordinates)
|
|
return np.array(array_points)
|
|
|
|
@staticmethod
|
|
def _remove_from_list(edge, edges_list):
|
|
new_list = []
|
|
for edge_element in edges_list:
|
|
if not ((edge_element[0].distance_to_point(edge[0]) == 0 and edge_element[1].distance_to_point(
|
|
edge[1]) == 0) or
|
|
(edge_element[1].distance_to_point(edge[0]) == 0 and edge_element[0].distance_to_point(
|
|
edge[1]) == 0)):
|
|
new_list.append(edge_element)
|
|
return new_list
|
|
|
|
@property
|
|
def vertices(self) -> np.ndarray:
|
|
"""
|
|
Get polygon vertices
|
|
:return: np.ndarray(int)
|
|
"""
|
|
if self._vertices is None:
|
|
vertices, self._vertices = [], []
|
|
_ = [vertices.extend(s.coordinates) for s in self.triangles]
|
|
for vertex_1 in vertices:
|
|
found = False
|
|
for vertex_2 in self._vertices:
|
|
found = False
|
|
power = 0
|
|
for dimension in range(0, 3):
|
|
power += math.pow(vertex_2[dimension] - vertex_1[dimension], 2)
|
|
distance = math.sqrt(power)
|
|
if distance == 0:
|
|
found = True
|
|
break
|
|
if not found:
|
|
self._vertices.append(vertex_1)
|
|
self._vertices = np.asarray(self._vertices)
|
|
return self._vertices
|
|
|
|
@property
|
|
def faces(self) -> List[List[int]]:
|
|
"""
|
|
Get polygon triangular faces
|
|
:return: [face]
|
|
"""
|
|
if self._faces is None:
|
|
self._faces = []
|
|
|
|
for polygon in self.triangles:
|
|
face = []
|
|
points = polygon.coordinates
|
|
if len(points) != 3:
|
|
sub_polygons = polygon.triangles
|
|
# todo: I modified this! To be checked @Guille
|
|
if len(sub_polygons) >= 1:
|
|
for sub_polygon in sub_polygons:
|
|
face = []
|
|
points = sub_polygon.coordinates
|
|
for point in points:
|
|
face.append(self._position_of(point, face))
|
|
self._faces.append(face)
|
|
else:
|
|
for point in points:
|
|
face.append(self._position_of(point, face))
|
|
self._faces.append(face)
|
|
return self._faces
|
|
|
|
def _position_of(self, point, face):
|
|
"""
|
|
position of a specific point in the list of points that define a face
|
|
:return: int
|
|
"""
|
|
vertices = self.vertices
|
|
for i in range(len(vertices)):
|
|
# ensure not duplicated vertex
|
|
power = 0
|
|
vertex2 = vertices[i]
|
|
for dimension in range(0, 3):
|
|
power += math.pow(vertex2[dimension] - point[dimension], 2)
|
|
distance = math.sqrt(power)
|
|
if i not in face and distance == 0:
|
|
return i
|
|
return -1
|