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cubes.py
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cubes.py
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import os
import numpy as np
from mpl_toolkits.mplot3d import art3d
from matplotlib import pyplot as plt
from matplotlib import colors
from tqdm import tqdm
from utils import create_3d_figure
class Plane:
def __init__(self, point, normal, xx=None, yy=None, zz=None, d=None,
face_colors=None):
self.point = np.array(point).astype(float) # [x_0, y_0, z_0]
self.normal = np.array(normal).astype(float) # [a, b, c]
self.xx, self.yy, self.zz, self.d = xx, yy, zz, d
self.face_colors = face_colors
@staticmethod
def _rotate_array_elements(array, n):
""" Rotate elements of array n times clockwise """
start_part, end_part = array[:-n], array[-n:]
if isinstance(array, list):
return end_part + start_part
elif isinstance(array, np.ndarray):
return np.concatenate((end_part, start_part))
def calculate_coords(self, min_val, max_val, grid_size=5.0):
# Calculate d = -(a*x_0 + b*y_0 + c*z_0)
self.d = (-self.point * self.normal).sum()
# Rotate dimensions if needed to avoid division by zero
norm = self.normal
times_rotated = 0
while norm[2] == 0:
times_rotated += 1
norm = self._rotate_array_elements(norm, 1)
step = np.abs(max_val-min_val)/np.float(grid_size)
coordinate_matrix_1, coordinate_matrix_2 = np.array(np.meshgrid(
np.arange(min_val, max_val+step, step),
np.arange(min_val, max_val+step, step))).astype(float)
coordinate_matrix_3 = 1. * (
-norm[0] * coordinate_matrix_1 -
norm[1] * coordinate_matrix_2 - self.d) / norm[2]
self.xx, self.yy, self.zz = self._rotate_array_elements(
[coordinate_matrix_1, coordinate_matrix_2, coordinate_matrix_3],
times_rotated)
@staticmethod
def _rotate_point_around_xyz(x, y, z, x_rot, y_rot, z_rot, center):
# Degrees to radians
x_rot = x_rot / 180.0 * np.pi
y_rot = y_rot / 180.0 * np.pi
z_rot = z_rot / 180.0 * np.pi
# Pre-calculate cosines and sines
cos_x, sin_x = np.cos(x_rot), np.sin(x_rot)
cos_y, sin_y = np.cos(y_rot), np.sin(y_rot)
cos_z, sin_z = np.cos(z_rot), np.sin(z_rot)
# Build rotation matrix
# http://tinyurl.com/zpgddsa
a11 = cos_y * cos_z
a12 = cos_x * sin_z + sin_x * sin_y * cos_z
a13 = sin_x * sin_z - cos_x * sin_y * cos_z
a21 = -cos_y * sin_z
a22 = cos_x * cos_z - sin_x * sin_y * sin_z
a23 = sin_x * cos_z + cos_x * sin_y * sin_z
a31 = sin_y
a32 = -sin_x * cos_y
a33 = cos_x * cos_y
# Matrix multiplication
return np.dot(np.array([x, y, z]) - center,
[[a11, a12, a13],
[a21, a22, a23],
[a31, a32, a33]]) + center
def rotate_around_xyz(self, x_rot, y_rot, z_rot, center):
for (ix, x), (_, y), (_, z) in zip(np.ndenumerate(self.xx),
np.ndenumerate(self.yy),
np.ndenumerate(self.zz)):
self.xx[ix], self.yy[ix], self.zz[ix] = \
self._rotate_point_around_xyz(
x, y, z, x_rot, y_rot, z_rot, center)
@staticmethod
def _rotate_point_around_arbitrary_axis(x, y, z, ux, uy, uz, angle):
"""
point = x, y, z
unit vector of an arbitrary axis = ux, uy, uz
"""
# Degrees to radians
angle = angle / 180.0 * np.pi
# Pre-calculate cosine and sine
cos, sin = np.cos(angle), np.sin(angle)
# Build rotation matrix
# http://tinyurl.com/ka74357
a11 = cos + (ux ** 2) * (1.0 - cos)
a12 = ux * uy * (1.0 - cos) - uz * sin
a13 = ux * uz * (1.0 - cos) + uy * sin
a21 = uy * ux * (1.0 - cos) + uz * sin
a22 = cos + (uy ** 2) * (1.0 - cos)
a23 = uy * uz * (1.0 - cos) - ux * sin
a31 = uz * ux * (1.0 - cos) - uy * sin
a32 = uz * uy * (1.0 - cos) + ux * sin
a33 = cos + (uz ** 2) * (1.0 - cos)
# Matrix multiplication
return np.dot(np.array([x, y, z]),
[[a11, a12, a13],
[a21, a22, a23],
[a31, a32, a33]])
def rotate_around_arbitrary_axis(self, ux, uy, uz, angle):
for (ix, x), (_, y), (_, z) in zip(np.ndenumerate(self.xx),
np.ndenumerate(self.yy),
np.ndenumerate(self.zz)):
self.xx[ix], self.yy[ix], self.zz[ix] = \
self._rotate_point_around_arbitrary_axis(
x, y, z, ux, uy, uz, angle)
def get_cube(min_val, max_val, center, grid_size):
# Define the 6 square faces of cube using
# point-normal form of the equation of a plane.
# Points are in the centers of square faces.
square_faces = [Plane(point=[center, center, min_val], # xy-plane 1
normal=[0, 0, 1]),
Plane(point=[center, center, max_val], # xy-plane 2
normal=[0, 0, 1]),
Plane(point=[center, min_val, center], # xz-plane 1
normal=[0, 1, 0]),
Plane(point=[center, max_val, center], # xz-plane 2
normal=[0, 1, 0]),
Plane(point=[min_val, center, center], # yz-plane 1
normal=[1, 0, 0]),
Plane(point=[max_val, center, center], # yz-plane 2
normal=[1, 0, 0])]
for face in square_faces:
face.calculate_coords(min_val, max_val, grid_size=grid_size)
return square_faces
def colomapped_wireframe(plane, ax, stride, norm, colormap='hsv'):
# Source: http://stackoverflow.com/a/24958192/5524090
wire = ax.plot_wireframe(
X=plane.xx, Y=plane.yy, Z=plane.zz, rstride=stride, cstride=stride)
# Retrieve data from internal storage of plot_wireframe, then delete it
nx, ny, _ = np.shape(wire._segments3d)
wire_x = np.array(wire._segments3d)[:, :, 0].ravel()
wire_y = np.array(wire._segments3d)[:, :, 1].ravel()
wire_z = np.array(wire._segments3d)[:, :, 2].ravel()
wire.remove()
# Create data for a LineCollection
wire_x1 = np.vstack([wire_x, np.roll(wire_x, 1)])
wire_y1 = np.vstack([wire_y, np.roll(wire_y, 1)])
wire_z1 = np.vstack([wire_z, np.roll(wire_z, 1)])
to_delete = np.arange(0, nx * ny, ny)
wire_x1 = np.delete(wire_x1, to_delete, axis=1)
wire_y1 = np.delete(wire_y1, to_delete, axis=1)
wire_z1 = np.delete(wire_z1, to_delete, axis=1)
scalars = np.delete(wire_z, to_delete)
segs = [list(zip(xl, yl, zl)) for xl, yl, zl in
zip(wire_x1.T, wire_y1.T, wire_z1.T)]
# Plot the wireframe by a line3DCollection
my_wire = art3d.Line3DCollection(segs, cmap=colormap, norm=norm,
linewidths=2.0)
my_wire.set_array(scalars)
ax.add_collection(my_wire)
return my_wire
def draw_cubes(ax, face_big, face_small, norm_small):
return [
ax.plot_wireframe(X=face_big.xx, Y=face_big.yy, Z=face_big.zz,
rstride=1, cstride=1, color='#465563', alpha=0.5,
linewidth=1.0),
ax.scatter(face_big.xx, face_big.yy, face_big.zz, s=30,
c='#465563', lw=0, alpha=0.5),
colomapped_wireframe(plane=face_small, ax=ax, stride=50,
norm=norm_small, colormap='cool')]
def save_image(fig, output_folder, frame, max_frame_digits):
file_name = os.path.join(output_folder, 'frame_%s.png' %
str(frame).zfill(max_frame_digits))
plt.savefig(file_name, format='png', facecolor=fig.get_facecolor())
def ease_out_quad(t, b, c, d):
# Source: http://gizma.com/easing/
# t = current time or frame
# b = start value
# c = change in value
# d = duration in time or frames
t /= d
return -c * t*(t-2) + b
def ease_in_quad(t, b, c, d):
# Source: http://gizma.com/easing/
t /= d
return c*t*t + b
def create_animation_frames(gif_frames_output_folder: str) -> None:
# Settings
big_cube_min, big_cube_max = 20, 80 # For x, y, z
center = big_cube_min + (big_cube_max - big_cube_min) / 2.0
small_cube_min, small_cube_max = (big_cube_min + (center-big_cube_min)*0.5,
big_cube_max - (center-big_cube_min)*0.5)
elev, azim = 35.3, 45 # Initial camera position
# Initialize cubes
big_cube = get_cube(big_cube_min, big_cube_max, center, grid_size=2.0)
small_cube = get_cube(small_cube_min, small_cube_max, center,
grid_size=50.0)
# Initialize figure
fig, ax = create_3d_figure(figsize=(5, 5),
xlim=(big_cube_min, big_cube_max),
ylim=(big_cube_min, big_cube_max),
zlim=(big_cube_min, big_cube_max),
background_color="#131919",
elev=elev,
azim=azim,
# Disable perspective
proj_type="ortho")
# Initialize color normalizer
norm_small = colors.Normalize(vmin=small_cube_min, vmax=small_cube_max)
print("Creating frames of the cubes GIF...")
# Rotate cubes standing on their corners
max_frames_rot1 = 61
max_frames_rot2 = 254
for frame in tqdm(range(max_frames_rot1)):
drawn_shapes = []
for face_big, face_small in zip(big_cube, small_cube):
if frame > 0:
face_small.rotate_around_arbitrary_axis(
ux=1/np.sqrt(3), uy=1/np.sqrt(3), uz=1/np.sqrt(3), angle=2)
face_big.rotate_around_arbitrary_axis(
ux=1/np.sqrt(3), uy=1/np.sqrt(3), uz=1/np.sqrt(3), angle=2)
drawn_shapes += draw_cubes(ax, face_big, face_small, norm_small)
save_image(fig, gif_frames_output_folder, frame, 3)
# Remove last drawn shapes
[shape.remove() for shape in drawn_shapes]
# Rotate small cube around x and z axis
frames_accelerate = 70
for frame in tqdm(np.arange(1, max_frames_rot2, 1)):
drawn_shapes = []
for face_big, face_small in zip(big_cube, small_cube):
drawn_shapes += draw_cubes(ax, face_big, face_small, norm_small)
if frame <= frames_accelerate:
# Start rotating slowly in the beginning
face_small.rotate_around_xyz(
ease_in_quad(float(frame)+1, 0, 2, frames_accelerate), 0.0,
ease_in_quad(float(frame)+1, 0, -1, frames_accelerate),
center=center)
elif max_frames_rot2-frame <= frames_accelerate:
# Slow down rotating in the end
face_small.rotate_around_xyz(
ease_out_quad(
frames_accelerate-float(max_frames_rot2-frame)+1,
2, -2, frames_accelerate),
0.0,
ease_out_quad(
frames_accelerate-float(max_frames_rot2-frame)+1,
-1, 1, frames_accelerate),
center=center)
else:
# Rotation with steady speed
face_small.rotate_around_xyz(2.0, 0.0, -1.0, center=center)
# Rotate camera 360 degrees during the loop
if frame > 0:
ax.view_init(elev=elev,
azim=azim + (frame / float(max_frames_rot2) * 360))
save_image(fig, gif_frames_output_folder, max_frames_rot1 + frame, 3)
# Remove last drawn shapes
[shape.remove() for shape in drawn_shapes]