import random
import numpy as np
from yt.visualization.volume_rendering.create_spline import create_spline
[docs]
class Keyframes:
def __init__(
self,
x,
y,
z=None,
north_vectors=None,
up_vectors=None,
times=None,
niter=50000,
init_temp=10.0,
alpha=0.999,
fixed_start=False,
):
r"""Keyframes for camera path generation.
From a set of keyframes with position and optional up and
north vectors, an interpolated camera path is generated.
Parameters
----------
x : array_like
The x positions of the keyframes
y : array_like
The y positions of the keyframes
z : array_like, optional
The z positions of the keyframes. Default: 0.0
north_vectors : array_like, optional
The north vectors of the keyframes. Default: None
up_vectors : array_like, optional
The up vectors of the keyframes. Default: None
times : array_like, optional
The times of the keyframes. Default: arange(N)
niter : integer, optional
Maximum number of iterations to find solution. Default: 50000
init_temp : float, optional
Initial temperature for simulated annealing when finding a
solution. Lower initial temperatures result in an initial solution
in first several iterations that changes more rapidly. Default: 10.0
alpha : float, optional
Exponent in cooling function in simulated annealing. Must be < 1.
In each iteration, the temperature_new = temperature_old * alpha.
Default: 0.999
fixed_start: boolean, optional
If true, the first point never changes when searching for shortest
path. Default: False
Examples
--------
>>> import matplotlib.pyplot as plt
... import numpy as np
... from yt.visualization.volume_rendering.camera_path import *
>>> # Make a camera path from 10 random (x, y, z) keyframes
>>> data = np.random.random(10, 3)
>>> kf = Keyframes(data[:, 0], data[:, 1], data[:, 2])
>>> path = kf.create_path(250, shortest_path=False)
>>> # Plot the keyframes in the x-y plane and camera path
>>> plt.plot(kf.pos[:, 0], kf.pos[:, 1], "ko")
>>> plt.plot(path["position"][:, 0], path["position"][:, 1])
>>> plt.savefig("path.png")
"""
Nx = len(x)
Ny = len(y)
if z is not None:
Nz = len(z)
ndims = 3
else:
Nz = 1
ndims = 2
if Nx * Ny * Nz != Nx**ndims:
print("Need Nx (%d) == Ny (%d) == Nz (%d)" % (Nx, Ny, Nz))
raise RuntimeError
self.nframes = Nx
self.pos = np.zeros((Nx, 3))
self.pos[:, 0] = x
self.pos[:, 1] = y
if z is not None:
self.pos[:, 2] = z
else:
self.pos[:, 2] = 0.0
self.north_vectors = north_vectors
self.up_vectors = up_vectors
if times is None:
self.times = np.arange(self.nframes)
else:
self.times = times
self.cartesian_matrix()
self.setup_tsp(niter, init_temp, alpha, fixed_start)
[docs]
def setup_tsp(self, niter=50000, init_temp=10.0, alpha=0.999, fixed_start=False):
r"""Setup parameters for Travelling Salesman Problem.
Parameters
----------
niter : integer, optional
Maximum number of iterations to find solution. Default: 50000
init_temp : float, optional
Initial temperature for simulated annealing when finding a
solution. Lower initial temperatures result in an initial solution
in first several iterations that changes more rapidly. Default: 10.0
alpha : float, optional
Exponent in cooling function in simulated annealing. Must be < 1.
In each iteration, the temperature_new = temperature_old * alpha.
Default: 0.999
fixed_start: boolean, optional
If true, the first point never changes when searching for shortest
path. Default: False
"""
# randomize tour
self.tour = list(range(self.nframes))
np.random.shuffle(self.tour)
if fixed_start:
first = self.tour.index(0)
self.tour[0], self.tour[first] = self.tour[first], self.tour[0]
self.max_iterations = niter
self.initial_temp = init_temp
self.alpha = alpha
self.fixed_start = fixed_start
self.best_score = None
self.best = None
[docs]
def set_times(self, times):
self.times = times
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def rand_seq(self):
r"""
Generates values in random order, equivalent to using shuffle
in random without generation all values at once.
"""
values = list(range(self.nframes))
for i in range(self.nframes):
# pick a random index into remaining values
j = i + int(random.random() * (self.nframes - i))
# swap the values
values[j], values[i] = values[i], values[j]
# return the swapped value
yield values[i]
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def all_pairs(self):
r"""
Generates all (i,j) pairs for (i,j) for 0-size
"""
for i in self.rand_seq():
for j in self.rand_seq():
yield (i, j)
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def reversed_sections(self, tour):
r"""
Generator to return all possible variations where a section
between two cities are swapped.
"""
for i, j in self.all_pairs():
if i == j:
continue
copy = tour[:]
if i < j:
copy[i : j + 1] = reversed(tour[i : j + 1])
else:
copy[i + 1 :] = reversed(tour[:j])
copy[:j] = reversed(tour[i + 1 :])
if self.fixed_start:
ind = copy.index(0)
copy[0], copy[ind] = copy[ind], copy[0]
if copy != tour: # no point return the same tour
yield copy
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def cartesian_matrix(self):
r"""
Create a distance matrix for the city coords that uses
straight line distance
"""
self.dist_matrix = np.zeros((self.nframes, self.nframes))
xmat = np.zeros((self.nframes, self.nframes))
xmat[:, :] = self.pos[:, 0]
dx = xmat - xmat.T
ymat = np.zeros((self.nframes, self.nframes))
ymat[:, :] = self.pos[:, 1]
dy = ymat - ymat.T
zmat = np.zeros((self.nframes, self.nframes))
zmat[:, :] = self.pos[:, 2]
dz = zmat - zmat.T
self.dist_matrix = np.sqrt(dx * dx + dy * dy + dz * dz)
[docs]
def tour_length(self, tour):
r"""
Calculate the total length of the tour based on the distance
matrix
"""
total = 0
num_cities = len(tour)
for i in range(num_cities):
j = (i + 1) % num_cities
city_i = tour[i]
city_j = tour[j]
total += self.dist_matrix[city_i, city_j]
return -total
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def cooling(self):
T = self.initial_temp
while True:
yield T
T = self.alpha * T
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def prob(self, prev, next, temperature):
if next > prev:
return 1.0
else:
return np.exp(-abs(next - prev) / temperature)
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def get_shortest_path(self):
"""
Determine shortest path between all keyframes.
"""
# this obviously doesn't work. When someone fixes it, remove the NOQA
self.setup_tsp(niter, init_temp, alpha, fixed_start) # NOQA
num_eval = 1
cooling_schedule = self.cooling()
current = self.tour
current_score = self.tour_length(current)
for temperature in cooling_schedule:
done = False
# Examine moves around the current position
for next in self.reversed_sections(current):
if num_eval >= self.max_iterations:
done = True
break
next_score = self.tour_length(next)
num_eval += 1
# Anneal. Accept new solution if a random number is
# greater than our "probability".
p = self.prob(current_score, next_score, temperature)
if random.random() < p:
current = next
self.current_score = next_score
if self.current_score > self.best_score:
# print(num_eval, self.current_score, self.best_score, current)
self.best_score = self.current_score
self.best = current
break
if done:
break
self.pos = self.pos[self.tour, :]
if self.north_vectors is not None:
self.north_vectors = self.north_vectors[self.tour]
if self.up_vectors is not None:
self.up_vectors = self.up_vectors[self.tour]
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def create_path(self, npoints, path_time=None, tension=0.5, shortest_path=False):
r"""Create a interpolated camera path from keyframes.
Parameters
----------
npoints : integer
Number of points to interpolate from keyframes
path_time : array_like, optional
Times of interpolated points. Default: Linearly spaced
tension : float, optional
Controls how sharp of a curve the spline takes. A higher tension
allows for more sharp turns. Default: 0.5
shortest_path : boolean, optional
If true, estimate the shortest path between the keyframes.
Default: False
Returns
-------
path : dict
Dictionary (time, position, north_vectors, up_vectors) of camera
path. Also saved to self.path.
"""
self.npoints = npoints
self.path = {
"time": np.zeros(npoints),
"position": np.zeros((npoints, 3)),
"north_vectors": np.zeros((npoints, 3)),
"up_vectors": np.zeros((npoints, 3)),
}
if shortest_path:
self.get_shortest_path()
if path_time is None:
path_time = np.linspace(0, self.nframes, npoints)
self.path["time"] = path_time
for dim in range(3):
self.path["position"][:, dim] = create_spline(
self.times, self.pos[:, dim], path_time, tension=tension
)
if self.north_vectors is not None:
self.path["north_vectors"][:, dim] = create_spline(
self.times, self.north_vectors[:, dim], path_time, tension=tension
)
if self.up_vectors is not None:
self.path["up_vectors"][:, dim] = create_spline(
self.times, self.up_vectors[:, dim], path_time, tension=tension
)
return self.path
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def write_path(self, filename="path.dat"):
r"""Writes camera path to ASCII file
Parameters
----------
filename : string, optional
Filename containing the camera path. Default: path.dat
"""
fp = open(filename, "w")
fp.write(
"#%11s %12s %12s %12s %12s %12s %12s %12s %12s\n"
% ("x", "y", "z", "north_x", "north_y", "north_z", "up_x", "up_y", "up_z")
)
for i in range(self.npoints):
fp.write(
"{:.12f} {:.12f} {:.12f} {:.12f} {:.12f} {:.12f} {:.12f} {:.12f} {:.12f}\n".format(
self.path["position"][i, 0],
self.path["position"][i, 1],
self.path["position"][i, 2],
self.path["north_vectors"][i, 0],
self.path["north_vectors"][i, 1],
self.path["north_vectors"][i, 2],
self.path["up_vectors"][i, 0],
self.path["up_vectors"][i, 1],
self.path["up_vectors"][i, 2],
)
)
fp.close()