647 lines
24 KiB
Python
647 lines
24 KiB
Python
"""
|
|
Polygon module
|
|
SPDX - License - Identifier: LGPL - 3.0 - or -later
|
|
Copyright © 2020 Project Author Pilar Monsalvete Alvarez de Uribarri pilar.monsalvete@concordia.ca
|
|
"""
|
|
|
|
|
|
from __future__ import annotations
|
|
import math
|
|
import sys
|
|
from typing import List
|
|
import numpy as np
|
|
from trimesh import Trimesh
|
|
import trimesh.intersections
|
|
from city_model_structure.attributes.point import Point
|
|
|
|
|
|
class Polygon:
|
|
"""
|
|
Polygon class
|
|
"""
|
|
|
|
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
|
|
|
|
@property
|
|
def points(self) -> List[Point]:
|
|
"""
|
|
List of points belonging to the polygon [[x, y, z],...]
|
|
:return: List[Point]
|
|
"""
|
|
if self._points is None:
|
|
self._points = []
|
|
for coordinate in self.coordinates:
|
|
self._points.append(Point(coordinate))
|
|
return self._points
|
|
|
|
@property
|
|
def coordinates(self) -> List[np.ndarray]:
|
|
"""
|
|
List of points in the shape of its coordinates belonging to the polygon [[x, y, z],...]
|
|
:return: [np.ndarray]
|
|
"""
|
|
return self._coordinates
|
|
|
|
@property
|
|
def points_list(self) -> np.ndarray:
|
|
"""
|
|
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):
|
|
"""
|
|
Polygon edges list
|
|
"""
|
|
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):
|
|
"""
|
|
Surface area in square meters
|
|
:return: float
|
|
"""
|
|
# New method to calculate area
|
|
if self._area is None:
|
|
if len(self.points) < 3:
|
|
sys.stderr.write('Warning: the area of a line or point cannot be calculated 1. Area = 0\n')
|
|
return 0
|
|
alpha = 0
|
|
vec_1 = self.points[1].coordinates - self.points[0].coordinates
|
|
for i in range(2, len(self.points)):
|
|
vec_2 = self.points[i].coordinates - self.points[0].coordinates
|
|
alpha += self._angle_between_vectors(vec_1, vec_2)
|
|
if alpha == 0:
|
|
sys.stderr.write('Warning: the area of a line or point cannot be calculated 2. Area = 0\n')
|
|
return 0
|
|
horizontal_points = self._points_rotated_to_horizontal
|
|
area = 0
|
|
for i in range(0, len(horizontal_points)-1):
|
|
point = horizontal_points[i]
|
|
next_point = horizontal_points[i+1]
|
|
area += (next_point[1] + point[1]) / 2 * (next_point[0] - point[0])
|
|
next_point = horizontal_points[0]
|
|
point = horizontal_points[len(horizontal_points)-1]
|
|
area += (next_point[1] + point[1]) / 2 * (next_point[0] - point[0])
|
|
self._area = abs(area)
|
|
return self._area
|
|
|
|
@property
|
|
def _points_rotated_to_horizontal(self):
|
|
"""
|
|
polygon points rotated to horizontal
|
|
:return: [float]
|
|
"""
|
|
z_vector = [0, 0, 1]
|
|
normal_vector = self.normal
|
|
horizontal_points = []
|
|
x = normal_vector[0]
|
|
y = normal_vector[1]
|
|
|
|
if x == 0 and y == 0:
|
|
# Already horizontal
|
|
for point in self.points:
|
|
horizontal_points.append([point.coordinates[0], point.coordinates[1], 0])
|
|
else:
|
|
alpha = self._angle_between_vectors(normal_vector, z_vector)
|
|
rotation_line = np.cross(normal_vector, z_vector)
|
|
third_axis = np.cross(normal_vector, rotation_line)
|
|
w_1 = rotation_line / np.linalg.norm(rotation_line)
|
|
w_2 = normal_vector
|
|
w_3 = third_axis / np.linalg.norm(third_axis)
|
|
rotation_matrix = np.array([[1, 0, 0],
|
|
[0, np.cos(alpha), -np.sin(alpha)],
|
|
[0, np.sin(alpha), np.cos(alpha)]])
|
|
base_matrix = np.array([w_1, w_2, w_3])
|
|
rotation_base_matrix = np.matmul(base_matrix.transpose(), rotation_matrix.transpose())
|
|
rotation_base_matrix = np.matmul(rotation_base_matrix, base_matrix)
|
|
|
|
if rotation_base_matrix is None:
|
|
sys.stderr.write('Warning: rotation base matrix returned None\n')
|
|
else:
|
|
for point in self.points:
|
|
new_point = np.matmul(rotation_base_matrix, point.coordinates)
|
|
horizontal_points.append(new_point)
|
|
return horizontal_points
|
|
|
|
@property
|
|
def normal(self) -> np.ndarray:
|
|
"""
|
|
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
|
|
|
|
def triangulate(self) -> List[Polygon]:
|
|
"""
|
|
triangulates a polygon following the ear clipping methodology
|
|
:return: list[triangles]
|
|
"""
|
|
# todo: review triangulate_polygon in
|
|
# https://github.com/mikedh/trimesh/blob/dad11126742e140ef46ba12f8cb8643c83356467/trimesh/creation.py#L415,
|
|
# it had a problem with a class called 'triangle', but, if solved,
|
|
# it could be a very good substitute of this method
|
|
# this method is very dirty and has an infinite loop solved with a counter!!
|
|
if self._triangles is None:
|
|
points_list = self.points_list
|
|
normal = self.normal
|
|
if np.linalg.norm(normal) == 0:
|
|
sys.stderr.write('Not able to triangulate polygon\n')
|
|
return [self]
|
|
# are points concave or convex?
|
|
total_points_list, concave_points, convex_points = self._starting_lists(points_list, normal)
|
|
|
|
# list of ears
|
|
ears = []
|
|
j = 0
|
|
while (len(concave_points) > 3 or len(convex_points) != 0) and j < 100:
|
|
j += 1
|
|
for i in range(0, len(concave_points)):
|
|
ear = self._triangle(points_list, total_points_list, concave_points[i])
|
|
rest_points = []
|
|
for points in total_points_list:
|
|
rest_points.append(list(self.coordinates[points]))
|
|
if self._is_ear(ear, rest_points):
|
|
ears.append(ear)
|
|
point_to_remove = concave_points[i]
|
|
previous_point_in_list, next_point_in_list = self._enveloping_points(point_to_remove, total_points_list)
|
|
total_points_list.remove(point_to_remove)
|
|
concave_points.remove(point_to_remove)
|
|
# Was any of the adjacent points convex? -> check if changed status to concave
|
|
for convex_point in convex_points:
|
|
if convex_point == previous_point_in_list:
|
|
concave_points, convex_points, end_loop = self._if_concave_change_status(normal, points_list,
|
|
convex_point,
|
|
total_points_list,
|
|
concave_points, convex_points,
|
|
previous_point_in_list)
|
|
if end_loop:
|
|
break
|
|
continue
|
|
if convex_point == next_point_in_list:
|
|
concave_points, convex_points, end_loop = self._if_concave_change_status(normal, points_list,
|
|
convex_point,
|
|
total_points_list,
|
|
concave_points, convex_points,
|
|
next_point_in_list)
|
|
if end_loop:
|
|
break
|
|
continue
|
|
break
|
|
if len(total_points_list) <= 3 and len(convex_points) > 0:
|
|
sys.stderr.write('Not able to triangulate polygon\n')
|
|
return [self]
|
|
if j >= 100:
|
|
sys.stderr.write('Not able to triangulate polygon\n')
|
|
return [self]
|
|
last_ear = self._triangle(points_list, total_points_list, concave_points[1])
|
|
ears.append(last_ear)
|
|
self._triangles = ears
|
|
return self._triangles
|
|
|
|
@staticmethod
|
|
def _starting_lists(points_list, normal) -> [List[float], List[float], List[float]]:
|
|
"""
|
|
creates the list of vertices (points) that define the polygon (total_points_list), together with other two lists
|
|
separating points between convex and concave
|
|
:param points_list: points_list
|
|
:param normal: normal
|
|
:return: list[point], list[point], list[point]
|
|
"""
|
|
concave_points = []
|
|
convex_points = []
|
|
# lists of concave and convex points
|
|
# case 1: first point
|
|
point = points_list[0:3]
|
|
previous_point = points_list[len(points_list) - 3:]
|
|
next_point = points_list[3:6]
|
|
index = 0
|
|
total_points_list = [index]
|
|
if Polygon._point_is_concave(normal, point, previous_point, next_point):
|
|
concave_points.append(index)
|
|
else:
|
|
convex_points.append(index)
|
|
# case 2: all points except first and last
|
|
for i in range(0, int((len(points_list)-6)/3)):
|
|
point = points_list[(i+1)*3:(i+2)*3]
|
|
previous_point = points_list[i*3:(i+1)*3]
|
|
next_point = points_list[(i+2)*3:(i+3)*3]
|
|
index = i+1
|
|
total_points_list.append(index)
|
|
if Polygon._point_is_concave(normal, point, previous_point, next_point):
|
|
concave_points.append(index)
|
|
else:
|
|
convex_points.append(index)
|
|
# case 3: last point
|
|
point = points_list[len(points_list) - 3:]
|
|
previous_point = points_list[len(points_list) - 6:len(points_list) - 3]
|
|
next_point = points_list[0:3]
|
|
index = int(len(points_list)/3) - 1
|
|
total_points_list.append(index)
|
|
if Polygon._point_is_concave(normal, point, previous_point, next_point):
|
|
concave_points.append(index)
|
|
else:
|
|
convex_points.append(index)
|
|
return total_points_list, concave_points, convex_points
|
|
|
|
@staticmethod
|
|
def _triangle(points_list, total_points_list, point_position) -> Polygon:
|
|
"""
|
|
creates a triangular polygon out of three points
|
|
:param points_list: points_list
|
|
:param total_points_list: [point]
|
|
:param point_position: int
|
|
:return: polygon
|
|
"""
|
|
index = point_position * 3
|
|
previous_point_index, next_point_index = Polygon._enveloping_points_indices(point_position, total_points_list)
|
|
points = points_list[previous_point_index:previous_point_index + 3]
|
|
points = np.append(points, points_list[index:index + 3])
|
|
points = np.append(points, points_list[next_point_index:next_point_index + 3])
|
|
rows = points.size // 3
|
|
points = points.reshape(rows, 3)
|
|
triangle = Polygon(points)
|
|
return triangle
|
|
|
|
@staticmethod
|
|
def _enveloping_points_indices(point_position, total_points_list):
|
|
"""
|
|
due to the fact that the lists are not circular, a method to find the previous and next points
|
|
of an specific one is needed
|
|
:param point_position: int
|
|
:param total_points_list: [point]
|
|
:return: int, int
|
|
"""
|
|
previous_point_index = None
|
|
next_point_index = None
|
|
if point_position == total_points_list[0]:
|
|
previous_point_index = total_points_list[len(total_points_list) - 1] * 3
|
|
next_point_index = total_points_list[1] * 3
|
|
if point_position == total_points_list[len(total_points_list) - 1]:
|
|
previous_point_index = total_points_list[len(total_points_list) - 2] * 3
|
|
next_point_index = total_points_list[0] * 3
|
|
for i in range(1, len(total_points_list)-1):
|
|
if point_position == total_points_list[i]:
|
|
previous_point_index = total_points_list[i - 1] * 3
|
|
next_point_index = total_points_list[i + 1] * 3
|
|
return previous_point_index, next_point_index
|
|
|
|
@staticmethod
|
|
def _enveloping_points(point_to_remove, total_points_list):
|
|
"""
|
|
due to the fact that the lists are not circular, a method to find the previous and next points
|
|
of an specific one is needed
|
|
:param point_to_remove: point
|
|
:param total_points_list: [point]
|
|
:return: point, point
|
|
"""
|
|
index = total_points_list.index(point_to_remove)
|
|
if index == 0:
|
|
previous_point_in_list = total_points_list[len(total_points_list) - 1]
|
|
next_point_in_list = total_points_list[1]
|
|
elif index == len(total_points_list) - 1:
|
|
previous_point_in_list = total_points_list[len(total_points_list) - 2]
|
|
next_point_in_list = total_points_list[0]
|
|
else:
|
|
previous_point_in_list = total_points_list[index - 1]
|
|
next_point_in_list = total_points_list[index + 1]
|
|
return previous_point_in_list, next_point_in_list
|
|
|
|
@staticmethod
|
|
def _is_ear(ear, points) -> bool:
|
|
"""
|
|
finds whether a triangle is an ear of the polygon
|
|
:param ear: polygon
|
|
:param points: [point]
|
|
:return: boolean
|
|
"""
|
|
area_ear = ear.area
|
|
for point in points:
|
|
area_points = 0
|
|
point_is_not_vertex = True
|
|
for i in range(0, 3):
|
|
if abs(np.linalg.norm(point) - np.linalg.norm(ear.coordinates[i])) < 0.0001:
|
|
point_is_not_vertex = False
|
|
break
|
|
if point_is_not_vertex:
|
|
for i in range(0, 3):
|
|
if i != 2:
|
|
new_points = ear.coordinates[i][:]
|
|
new_points = np.append(new_points, ear.coordinates[i + 1][:])
|
|
new_points = np.append(new_points, point[:])
|
|
else:
|
|
new_points = ear.coordinates[i][:]
|
|
new_points = np.append(new_points, point[:])
|
|
new_points = np.append(new_points, ear.coordinates[0][:])
|
|
rows = new_points.size // 3
|
|
new_points = new_points.reshape(rows, 3)
|
|
new_triangle = Polygon(new_points)
|
|
area_points += new_triangle.area
|
|
if abs(area_points - area_ear) < 1e-6:
|
|
# point_inside_ear = True
|
|
return False
|
|
return True
|
|
|
|
@staticmethod
|
|
def _if_concave_change_status(normal, points_list, convex_point, total_points_list,
|
|
concave_points, convex_points, point_in_list) -> [List[float], List[float], bool]:
|
|
"""
|
|
checks whether an convex specific point change its status to concave after removing one ear in the polygon
|
|
returning the new convex and concave points lists together with a flag advising that the list of total points
|
|
already 3 and, therefore, the triangulation must be finished.
|
|
:param normal: normal
|
|
:param points_list: points_list
|
|
:param convex_point: int
|
|
:param total_points_list: [point]
|
|
:param concave_points: [point]
|
|
:param convex_points: [point]
|
|
:param point_in_list: int
|
|
:return: list[points], list[points], boolean
|
|
"""
|
|
end_loop = False
|
|
point = points_list[point_in_list * 3:(point_in_list + 1) * 3]
|
|
pointer = total_points_list.index(point_in_list) - 1
|
|
if pointer < 0:
|
|
pointer = len(total_points_list) - 1
|
|
previous_point = points_list[total_points_list[pointer] * 3:total_points_list[pointer] * 3 + 3]
|
|
pointer = total_points_list.index(point_in_list) + 1
|
|
if pointer >= len(total_points_list):
|
|
pointer = 0
|
|
next_point = points_list[total_points_list[pointer] * 3:total_points_list[pointer] * 3 + 3]
|
|
if Polygon._point_is_concave(normal, point, previous_point, next_point):
|
|
if concave_points[0] > convex_point:
|
|
concave_points.insert(0, convex_point)
|
|
elif concave_points[len(concave_points) - 1] < convex_point:
|
|
concave_points.append(convex_point)
|
|
else:
|
|
for point_index in range(0, len(concave_points) - 1):
|
|
if concave_points[point_index] < convex_point < concave_points[point_index + 1]:
|
|
concave_points.insert(point_index + 1, convex_point)
|
|
convex_points.remove(convex_point)
|
|
end_loop = True
|
|
return concave_points, convex_points, end_loop
|
|
|
|
@staticmethod
|
|
def _point_is_concave(normal, point, previous_point, next_point) -> bool:
|
|
"""
|
|
returns whether a point is concave
|
|
:param normal: normal
|
|
:param point: point
|
|
:param previous_point: point
|
|
:param next_point: point
|
|
:return: boolean
|
|
"""
|
|
is_concave = False
|
|
accepted_error = 0.1
|
|
points = np.append(previous_point, point)
|
|
points = np.append(points, next_point)
|
|
rows = points.size // 3
|
|
points = points.reshape(rows, 3)
|
|
triangle = Polygon(points)
|
|
error_sum = 0
|
|
for i in range(0, len(normal)):
|
|
error_sum += triangle.normal[i] - normal[i]
|
|
if np.abs(error_sum) < accepted_error:
|
|
is_concave = True
|
|
return is_concave
|
|
|
|
@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):
|
|
"""
|
|
Flips the order of the coordinates
|
|
: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:
|
|
"""
|
|
Polyhedron vertices
|
|
:return: np.ndarray(int)
|
|
"""
|
|
if self._vertices is None:
|
|
vertices, self._vertices = [], []
|
|
_ = [vertices.extend(s.coordinates) for s in self.triangulate()]
|
|
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]]:
|
|
"""
|
|
Polyhedron triangular faces
|
|
:return: [face]
|
|
"""
|
|
if self._faces is None:
|
|
self._faces = []
|
|
|
|
for polygon in self.triangulate():
|
|
face = []
|
|
points = polygon.coordinates
|
|
if len(points) != 3:
|
|
sub_polygons = polygon.triangulate()
|
|
# 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
|