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geometry.py
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geometry.py
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# ~*~ coding:utf-8 ~*~
import math
import numpy as np
class Geometry:
"""
Класс для математики - хранение точек, матриц, совершение преобразований
"""
def __init__(self):
self.clear_points = []
self.points = [] # Точки
self.edges = [] # Рёбра
self.faces = [] # Грани
# Углы поворота
self.x_rotate_angle = 0
self.y_rotate_angle = 0
self.z_rotate_angle = 0
# Координаты перемещения
self.x_move = 0
self.y_move = 0
self.z_move = 0
# Коэффициенты масштабирования
self.x_scale = 1
self.y_scale = 1
self.z_scale = 1
# Углы аксонометрической проекции
self.axonometric_angle_fi = 0
self.axonometric_angle_psi = 0
# Параметры косоугольной проекции
self.oblique_angle_alpha = 0
self.oblique_L = 0
# Параметры перспективной проекции
self.perspective_angle_teta = 0
self.perspective_angle_fi = 0
self.perspective_ro = 0
self.perspective_d = 0
self.m_rotate_x = np.zeros(0)
self.m_rotate_y = np.zeros(0)
self.m_rotate_z = np.zeros(0)
self.m_move = np.zeros(0)
self.m_scale = np.zeros(0)
self.m_horizontal = np.zeros(0)
self.m_frontal = np.zeros(0)
self.m_profile = np.zeros(0)
self.m_axonometric = np.zeros(0)
self.m_oblique = np.zeros(0)
self.m_perspective = np.zeros(0)
self.m_perspective_view = np.zeros(0)
def clear(self):
self.clear_points = []
self.points = []
self.edges = []
self.faces = []
def apply_projection(self, name):
# Конвертируем список точек в матрицу
self.clear_points = np.array(self.points)
self.points = np.array(self.points)
self.prepare_matrix()
if name == "default":
# Поворот, перемещение и масштаб только для проекции по умолчанию
self.points = self.multiplication_matrix(self.points, self.m_rotate_x)
self.points = self.multiplication_matrix(self.points, self.m_rotate_y)
self.points = self.multiplication_matrix(self.points, self.m_rotate_z)
self.points = self.multiplication_matrix(self.points, self.m_move)
self.points = self.multiplication_matrix(self.points, self.m_scale)
self.points = self.multiplication_matrix(self.points, self.m_frontal)
if name == "front":
self.points = self.multiplication_matrix(self.points, self.m_frontal)
elif name == "horizontal":
self.points = self.multiplication_matrix(self.points, self.m_horizontal)
elif name == "profile":
self.points = self.multiplication_matrix(self.points, self.m_profile)
elif name == "axonometric":
self.points = self.multiplication_matrix(self.points, self.m_axonometric)
elif name == "oblique":
self.points = self.multiplication_matrix(self.points, self.m_oblique)
elif name == "perspective":
self.points = self.multiplication_matrix(self.points, self.m_perspective_view)
self.points = self.multiplication_matrix(self.points, self.m_perspective)
for point in self.points:
if point[3] == 0:
point[3] = 0.00001
point[0] /= point[3]
point[1] /= point[3]
point[2] /= point[3]
point[3] /= point[3]
@staticmethod
def from_polar(radius, angle, z_axis):
"""
Конвертирует координату из двумерной полярной системы координат в декартову трёхмерную
:param radius: Радиус до точке в полярной системе координат
:param angle: Угол до точки в полярной системе координат
:param z_axis: Ось z, передаётся напрямую
:return: Список координат точки
"""
x = radius * math.cos(angle)
y = radius * math.sin(angle)
z = z_axis
return x, y, z, 1
@staticmethod
def multiplication_matrix(first, second):
"""
Умножение матриц, аналог функции np.dot(a,b)
:param first: Левая матрица
:param second: Правая матрица
:return: Произведение матриц
"""
tmp = np.zeros(first.shape)
for i in range(first.shape[0]):
for l in range(second.shape[1]):
tmp[i][l] = 0
for j in range(second.shape[0]):
tmp[i][l] += first[i][j] * second[j][l]
return tmp
def prepare_matrix(self):
"""
Подготавливает матрицы различных преобразований
"""
# Матрицы поворота по осям
x_rotate_cos = math.cos(self.x_rotate_angle * math.pi / 180)
x_rotate_sin = math.sin(self.x_rotate_angle * math.pi / 180)
self.m_rotate_x = np.array([[1, 0, 0, 0],
[0, x_rotate_cos, x_rotate_sin, 0],
[0, -x_rotate_sin, x_rotate_cos, 0],
[0, 0, 0, 1]])
y_rotate_cos = math.cos(self.y_rotate_angle * math.pi / 180)
y_rotate_sin = math.sin(self.y_rotate_angle * math.pi / 180)
self.m_rotate_y = np.array([[y_rotate_cos, 0, -y_rotate_sin, 0],
[0, 1, 0, 0],
[y_rotate_sin, 0, y_rotate_cos, 0],
[0, 0, 0, 1]])
z_rotate_cos = math.cos(self.z_rotate_angle * math.pi / 180)
z_rotate_sin = math.sin(self.z_rotate_angle * math.pi / 180)
self.m_rotate_z = np.array([[z_rotate_cos, z_rotate_sin, 0, 0],
[-z_rotate_sin, z_rotate_cos, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
# Матрицы перемещения
self.m_move = np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[self.x_move, self.y_move, self.z_move, 1]])
# Матрица масштабирования
self.m_scale = np.array([[self.x_scale, 0, 0, 0],
[0, self.y_scale, 0, 0],
[0, 0, self.z_scale, 0],
[0, 0, 0, 1]])
# Матрицы ортографических проекций
self.m_horizontal = np.array([[1, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
self.m_frontal = np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])
self.m_profile = np.array([[0, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
# Матрица аксонометрической проекции
angle_fi_sin = math.sin(self.axonometric_angle_fi * math.pi / 180)
angle_psi_sin = math.sin(self.axonometric_angle_psi * math.pi / 180)
angle_fi_cos = math.cos(self.axonometric_angle_fi * math.pi / 180)
angle_psi_cos = math.cos(self.axonometric_angle_psi * math.pi / 180)
self.m_axonometric = np.array([[angle_psi_cos, angle_fi_sin * angle_psi_sin, 0, 0],
[0, angle_fi_cos, 0, 0],
[angle_psi_sin, -angle_fi_sin*angle_psi_cos, 0, 0],
[0, 0, 0, 1]])
# Матрица косоугольной проекции
angle_alpha_sin = math.sin(self.oblique_angle_alpha * math.pi / 180)
angle_alpha_cos = math.cos(self.oblique_angle_alpha * math.pi / 180)
self.m_oblique = np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[self.oblique_L * angle_alpha_cos, self.oblique_L * angle_alpha_sin, 0, 0],
[0, 0, 0, 1]])
# Матрицы перспективной проекции
angle_teta_sin = math.sin(self.perspective_angle_teta*math.pi / 180)
angle_teta_cos = math.cos(self.perspective_angle_teta*math.pi / 180)
angle_fi_sin = math.sin(self.perspective_angle_fi*math.pi / 180)
angle_fi_cos = math.cos(self.perspective_angle_fi*math.pi / 180)
if self.perspective_d == 0:
self.perspective_d = 1
self.m_perspective = np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 1/self.perspective_d],
[0, 0, 0, 0]])
self.m_perspective_view = np.array([[-angle_teta_sin, -angle_fi_cos * angle_teta_cos, -angle_fi_sin * angle_teta_cos, 0],
[angle_teta_cos, -angle_fi_cos * angle_teta_sin, -angle_fi_sin * angle_teta_sin, 0],
[0, angle_fi_sin, -angle_fi_cos, 0],
[0, 0, self.perspective_ro, 1]])