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shapes_2d.py
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shapes_2d.py
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import numpy as np
from periodic_functions import sin, cos
from rotation import rotate_2d
def circle(n_points, radius=1, phase_shift=0, origin=(0, 0)):
x = cos(n_points, amplitude=radius, phase_shift=phase_shift)
y = sin(n_points, amplitude=radius, phase_shift=phase_shift)
x = x + origin[0]
y = y + origin[0]
return x, y
def regular_polygon(n_sides, size=1, phase_shift=0):
x, y = circle(n_points=n_sides, phase_shift=phase_shift + (np.pi / 2))
for dim in x, y:
dim = dim * size
return x, y
def linspace_shift(start, stop, n_points, phase_shift):
v = np.linspace(0, 2 * np.pi, n_points + 1)[:-1]
v += phase_shift
v = np.mod(v, 2 * np.pi)
range = np.ptp((start, stop))
v = (v / (2 * np.pi)) * range
v += start
return v
def length(x, y):
l = np.sqrt(x**2 + y**2)
return l
# def points_along_polygon(x, y, n_points, phase_shift=0):
# n_points = np.asarray(x).shape[0]
# total_length = 0
# for idx in range(n_points):
# if idx == n_points - 1:
# current_segment_start = np.asarray((x[idx], y[idx]))
# current_segment_end = np.asarray(x[0], y[0])
# else:
# current_segment_start = np.asarray((x[idx], y[idx]))
# current_segment_end = np.asarray(x[idx + 1], y[idx + 1])
#
# def points_along_regular_polygon(n_points, n_sides, phase_shift_points=0, phase_shift_polygon=0):
# theta_points = linspace_shift(0, 2*np.pi, n_points=n_points, phase_shift=phase_shift_points)
# theta_corners = linspace_shift(0, 2 * np.pi, n_points=n_sides, phase_shift=phase_shift_polygon)
#
# corners_x, corners_y = regular_polygon(n_sides, phase_shift_polygon)
#
# edges = np.zeros((n_sides, 2, 2))
# for edge_idx in range(n_sides):
def edges_from_corners(x, y):
"""
computes edges from x, y vectors describing corners of a polygon
:param x: x position of corner
:param y: y position of corner
:return: x_edges, y_edges, (n_edges, 2, 2), dim 1 = edge, dim2 = start,end, dim3 = x, y
"""
x = np.asarray(x)
y = np.asarray(y)
n_edges = np.asarray(x).shape[0]
edges = np.zeros((n_edges, 2, 2))
for edge_idx in range(n_edges):
if edge_idx == n_edges - 1:
edges[edge_idx, 0, :] = [x[edge_idx], y[edge_idx]]
edges[edge_idx, 1, :] = [x[0], y[0]]
else:
edges[edge_idx, 0, :] = [x[edge_idx], y[edge_idx]]
edges[edge_idx, 1, :] = [x[edge_idx + 1], y[edge_idx + 1]]
return edges
# import matplotlib.pyplot as plt
#
# x, y = regular_polygon(13, 3.14 / 2 )
# x2, y2, e = edges_from_corners(x, y)
# fig, ax = plt.subplots()
#
# ax.plot(x2-2,y2-2)
# for idx, edge in enumerate(e):
# x = edge[:, 0]
# y = edge[:, 1]
# ax.plot(x,y, label=f'edge {idx}')
# ax.set_aspect('equal')
# ax.legend()
class RegularPolygon:
def __init__(self, n_edges, size=1, origin=(0,0)):
corners_x, corners_y = regular_polygon(n_edges, size=size, phase_shift=0)
self.corners = corners_x + origin[0], corners_y + origin[1]
self.origin = origin
self.edges = edges_from_corners(self.corners[0], self.corners[1])
self.n_edges = self.edges.shape[0]
def get_edges_from_corners(self):
x_edges = np.zeros(self.n_edges + 1)
y_edges = np.zeros(self.n_edges + 1)
x_edges[:-1] = self.corners[0]
x_edges[-1] = x_edges[0]
y_edges[:-1] = self.corners[1]
y_edges[-1] = y_edges[0]
return x_edges, y_edges
def get_all_edges(self):
edges = [self.get_edge(edge_idx) for edge_idx in range(self.n_edges)]
return edges
def get_edge(self, edge_index):
edge = self.edges[edge_index]
x = edge[:, 0]
y = edge[:, 1]
return x, y
def set_edge(self, edge_index, x, y):
self.edges[edge_index][:, 0] = x
self.edges[edge_index][:, 1] = y
return None
def get_edge_center(self, edge_index):
edge_x, edge_y = self.get_edge(edge_index)
x = np.mean(edge_x)
y = np.mean(edge_y)
return x, y
def get_all_corners(self):
x = self.corners[0]
y = self.corners[1]
return x, y
def get_corner(self, corner_index):
x = self.corners[0][corner_index]
y = self.corners[1][corner_index]
return x, y
def rotate(self, theta, origin=None):
if origin is not None:
self.rotate_all_edge_extremities(theta)
self.rotate_all_edge_centers(theta, origin=origin)
self.rotate_all_corners(theta, origin=origin)
else:
self.rotate(theta, origin=self.origin)
return None
def rotate_all_corners(self, theta, origin=None):
corners_x = self.corners[0]
corners_y = self.corners[1]
if origin is not None:
self.corners = rotate_2d(corners_x, corners_y, theta=theta, origin=origin)
else:
self.corners = rotate_2d(corners_x, corners_y, theta=theta, origin=self.origin)
return None
def rotate_corner(self, corner_index, theta, origin=None):
corner_x, corner_y = self.get_corner(corner_index)
if origin is not None:
corner_x_rotated = rotate_2d(corner_x, corner_y, theta=theta, origin=origin)
else:
corner_y_rotated = rotate_2d(corner_x, corner_y, theta=theta, origin=self.origin)
return None
def rotate_all_edge_centers(self, theta, origin=None):
for edge_idx in range(self.n_edges):
if origin is not None:
self.rotate_edge_center(edge_idx, theta=theta, origin=origin)
else:
self.rotate_edge_center(edge_idx, theta=theta, origin=self.origin)
return None
def rotate_all_edge_extremities(self, theta, origin=None):
for edge_idx in range(self.n_edges):
self.rotate_edge_extremities(edge_idx, theta, origin=origin)
return None
def rotate_edge_extremities(self, edge_index, theta, origin=None):
edge_x, edge_y = self.get_edge(edge_index)
if origin is None:
origin = self.get_edge_center(edge_index)
edge_x_rotated, edge_y_rotated = rotate_2d(edge_x, edge_y, theta, origin=origin)
self.set_edge(edge_index, edge_x_rotated, edge_y_rotated)
return None
def rotate_edge_center(self, edge_index, theta, origin=None):
edge_x, edge_y = self.get_edge(edge_index)
edge_center_x, edge_center_y = self.get_edge_center(edge_index)
edge_dx = edge_x - edge_center_x
edge_dy = edge_y - edge_center_y
if origin is None:
origin = self.get_edge_center(edge_index)
edge_center_rotated_x, edge_center_rotated_y = rotate_2d(edge_center_x,
edge_center_y,
theta=theta,
origin=origin)
x = edge_center_rotated_x + edge_dx
y = edge_center_rotated_y + edge_dy
self.set_edge(edge_index, x, y)
return None
def rotate_edge_around_start(self, edge_index, theta):
edge_x, edge_y = self.get_edge(edge_index)
rotation_center = (edge_x[0], edge_y[0])
edge_x_rotated, edge_y_rotated = rotate_2d(edge_x, edge_y, theta=theta, origin=rotation_center)
self.set_edge(edge_index, edge_x_rotated, edge_y_rotated)
return None
def rotate_edge_around_end(self, edge_index, theta):
edge_x, edge_y = self.get_edge(edge_index)
rotation_center = (edge_x[-1], edge_y[-1])
edge_x_rotated, edge_y_rotated = rotate_2d(edge_x, edge_y, theta=theta, origin=rotation_center)
self.set_edge(edge_index, edge_x_rotated, edge_y_rotated)
return None
def rotate_all_edges_around_start(self, theta):
for edge_idx in range(self.n_edges):
self.rotate_edge_around_start(edge_idx, theta=theta)
return None
def rotate_all_edges_around_end(self, theta):
for edge_idx in range(self.n_edges):
self.rotate_edge_around_end(edge_idx, theta=theta)
return None
#
# class Square(regular_polygon):
# def __init__(self, size, phase_shift=0):
# import matplotlib.pyplot as plt
#
#
# def plot_square(ax):
# x, y = square.get_all_corners()
# ax.scatter(x,y)
# for idx, edge in enumerate(square.edges):
# edge_x = edge[:, 0]
# edge_y = edge[:, 1]
# ax.plot(edge_x, edge_y, label=f'edge {idx}')
# ax.set_aspect('equal')
# ax.set_xlim(-1.5, 1.5)
# ax.set_ylim(-1.5, 1.5)
# return None
#
# square = RegularPolygon(4)
# fig, axes = plt.subplots(5)
# plot_square(axes[0])
# square.rotate_all_edge_extremities(np.deg2rad(45))
# plot_square(axes[1])
# square.rotate_all_edge_centers(np.deg2rad(45))
# plot_square(axes[2])
# square.rotate_all_corners(np.deg2rad(45))
# plot_square(axes[3])
#
# square = RegularPolygon(4)
# square.rotate_object(np.deg2rad(45))
# plot_square(axes[4])
#