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479from __future__ import annotations
import itertools as it
import numpy as np
from scipy.integrate import solve_ivp
from manimlib.constants import FRAME_HEIGHT, FRAME_WIDTH
from manimlib.constants import DEFAULT_MOBJECT_COLOR
from manimlib.animation.indication import VShowPassingFlash
from manimlib.mobject.types.vectorized_mobject import VGroup
from manimlib.mobject.types.vectorized_mobject import VMobject
from manimlib.utils.bezier import interpolate
from manimlib.utils.bezier import inverse_interpolate
from manimlib.utils.color import get_colormap_list
from manimlib.utils.color import get_color_map
from manimlib.utils.iterables import cartesian_product
from manimlib.utils.rate_functions import linear
from manimlib.utils.space_ops import get_norm
from typing import TYPE_CHECKING
if TYPE_CHECKING:
from typing import Callable, Iterable, Sequence, TypeVar, Tuple, Optional
from manimlib.typing import ManimColor, Vect3, VectN, VectArray, Vect3Array, Vect4Array
from manimlib.mobject.coordinate_systems import CoordinateSystem
from manimlib.mobject.mobject import Mobject
T = TypeVar("T")
#### Delete these two ###
def get_vectorized_rgb_gradient_function(
min_value: T,
max_value: T,
color_map: str
) -> Callable[[VectN], Vect3Array]:
rgbs = np.array(get_colormap_list(color_map))
def func(values):
alphas = inverse_interpolate(
min_value, max_value, np.array(values)
)
alphas = np.clip(alphas, 0, 1)
scaled_alphas = alphas * (len(rgbs) - 1)
indices = scaled_alphas.astype(int)
next_indices = np.clip(indices + 1, 0, len(rgbs) - 1)
inter_alphas = scaled_alphas % 1
inter_alphas = inter_alphas.repeat(3).reshape((len(indices), 3))
result = interpolate(rgbs[indices], rgbs[next_indices], inter_alphas)
return result
return func
def get_rgb_gradient_function(
min_value: T,
max_value: T,
color_map: str
) -> Callable[[float], Vect3]:
vectorized_func = get_vectorized_rgb_gradient_function(min_value, max_value, color_map)
return lambda value: vectorized_func(np.array([value]))[0]
####
def ode_solution_points(function, state0, time, dt=0.01):
solution = solve_ivp(
lambda t, state: function(state),
t_span=(0, time),
y0=state0,
t_eval=np.arange(0, time, dt)
)
return solution.y.T
def move_along_vector_field(
mobject: Mobject,
func: Callable[[Vect3], Vect3]
) -> Mobject:
mobject.add_updater(
lambda m, dt: m.shift(
func(m.get_center()) * dt
)
)
return mobject
def move_submobjects_along_vector_field(
mobject: Mobject,
func: Callable[[Vect3], Vect3]
) -> Mobject:
def apply_nudge(mob, dt):
for submob in mob:
x, y = submob.get_center()[:2]
if abs(x) < FRAME_WIDTH and abs(y) < FRAME_HEIGHT:
submob.shift(func(submob.get_center()) * dt)
mobject.add_updater(apply_nudge)
return mobject
def move_points_along_vector_field(
mobject: Mobject,
func: Callable[[float, float], Iterable[float]],
coordinate_system: CoordinateSystem
) -> Mobject:
cs = coordinate_system
origin = cs.get_origin()
def apply_nudge(mob, dt):
mob.apply_function(
lambda p: p + (cs.c2p(*func(*cs.p2c(p))) - origin) * dt
)
mobject.add_updater(apply_nudge)
return mobject
def get_sample_coords(
coordinate_system: CoordinateSystem,
density: float = 1.0
) -> it.product[tuple[Vect3, ...]]:
ranges = []
for range_args in coordinate_system.get_all_ranges():
_min, _max, step = range_args
step /= density
ranges.append(np.arange(_min, _max + step, step))
return np.array(list(it.product(*ranges)))
def vectorize(pointwise_function: Callable[[Tuple], Tuple]):
def v_func(coords_array: VectArray) -> VectArray:
return np.array([pointwise_function(*coords) for coords in coords_array])
return v_func
# Mobjects
class VectorField(VMobject):
def __init__(
self,
# Vectorized function: Takes in an array of coordinates, returns an array of outputs.
func: Callable[[VectArray], VectArray],
# Typically a set of Axes or NumberPlane
coordinate_system: CoordinateSystem,
sample_coords: Optional[VectArray] = None,
density: float = 2.0,
magnitude_range: Optional[Tuple[float, float]] = None,
color: Optional[ManimColor] = None,
color_map_name: Optional[str] = "3b1b_colormap",
color_map: Optional[Callable[[Sequence[float]], Vect4Array]] = None,
stroke_opacity: float = 1.0,
stroke_width: float = 3,
tip_width_ratio: float = 4,
tip_len_to_width: float = 0.01,
max_vect_len: float | None = None,
max_vect_len_to_step_size: float = 0.8,
flat_stroke: bool = False,
norm_to_opacity_func=None, # TODO, check on this
**kwargs
):
self.func = func
self.coordinate_system = coordinate_system
self.stroke_width = stroke_width
self.tip_width_ratio = tip_width_ratio
self.tip_len_to_width = tip_len_to_width
self.norm_to_opacity_func = norm_to_opacity_func
# Search for sample_points
if sample_coords is not None:
self.sample_coords = sample_coords
else:
self.sample_coords = get_sample_coords(coordinate_system, density)
self.update_sample_points()
if max_vect_len is None:
step_size = get_norm(self.sample_points[1] - self.sample_points[0])
self.max_displayed_vect_len = max_vect_len_to_step_size * step_size
else:
self.max_displayed_vect_len = max_vect_len * coordinate_system.x_axis.get_unit_size()
# Prepare the color map
if magnitude_range is None:
max_value = max(map(get_norm, func(self.sample_coords)))
magnitude_range = (0, max_value)
self.magnitude_range = magnitude_range
if color is not None:
self.color_map = None
else:
self.color_map = color_map or get_color_map(color_map_name)
self.init_base_stroke_width_array(len(self.sample_coords))
super().__init__(
stroke_opacity=stroke_opacity,
flat_stroke=flat_stroke,
**kwargs
)
self.set_stroke(color, stroke_width)
self.update_vectors()
def init_points(self):
n_samples = len(self.sample_coords)
self.set_points(np.zeros((8 * n_samples - 1, 3)))
self.set_joint_type('no_joint')
def get_sample_points(
self,
center: np.ndarray,
width: float,
height: float,
depth: float,
x_density: float,
y_density: float,
z_density: float
) -> np.ndarray:
to_corner = np.array([width / 2, height / 2, depth / 2])
spacings = 1.0 / np.array([x_density, y_density, z_density])
to_corner = spacings * (to_corner / spacings).astype(int)
lower_corner = center - to_corner
upper_corner = center + to_corner + spacings
return cartesian_product(*(
np.arange(low, high, space)
for low, high, space in zip(lower_corner, upper_corner, spacings)
))
def init_base_stroke_width_array(self, n_sample_points):
arr = np.ones(8 * n_sample_points - 1)
arr[4::8] = self.tip_width_ratio
arr[5::8] = self.tip_width_ratio * 0.5
arr[6::8] = 0
arr[7::8] = 0
self.base_stroke_width_array = arr
def set_sample_coords(self, sample_coords: VectArray):
self.sample_coords = sample_coords
return self
def set_stroke(self, color=None, width=None, opacity=None, behind=None, flat=None, recurse=True):
super().set_stroke(color, None, opacity, behind, flat, recurse)
if width is not None:
self.set_stroke_width(float(width))
return self
def set_stroke_width(self, width: float):
if self.get_num_points() > 0:
self.get_stroke_widths()[:] = width * self.base_stroke_width_array
self.stroke_width = width
return self
def update_sample_points(self):
self.sample_points = self.coordinate_system.c2p(*self.sample_coords.T)
def update_vectors(self):
tip_width = self.tip_width_ratio * self.stroke_width
tip_len = self.tip_len_to_width * tip_width
# Outputs in the coordinate system
outputs = self.func(self.sample_coords)
output_norms = np.linalg.norm(outputs, axis=1)[:, np.newaxis]
# Corresponding vector values in global coordinates
out_vects = self.coordinate_system.c2p(*outputs.T) - self.coordinate_system.get_origin()
out_vect_norms = np.linalg.norm(out_vects, axis=1)[:, np.newaxis]
unit_outputs = np.zeros_like(out_vects)
np.true_divide(out_vects, out_vect_norms, out=unit_outputs, where=(out_vect_norms > 0))
# How long should the arrows be drawn, in global coordinates
max_len = self.max_displayed_vect_len
if max_len < np.inf:
drawn_norms = max_len * np.tanh(out_vect_norms / max_len)
else:
drawn_norms = out_vect_norms
# What's the distance from the base of an arrow to
# the base of its head?
dist_to_head_base = np.clip(drawn_norms - tip_len, 0, np.inf) # Mixing units!
# Set all points
points = self.get_points()
points[0::8] = self.sample_points
points[2::8] = self.sample_points + dist_to_head_base * unit_outputs
points[4::8] = points[2::8]
points[6::8] = self.sample_points + drawn_norms * unit_outputs
for i in (1, 3, 5):
points[i::8] = 0.5 * (points[i - 1::8] + points[i + 1::8])
points[7::8] = points[6:-1:8]
# Adjust stroke widths
width_arr = self.stroke_width * self.base_stroke_width_array
width_scalars = np.clip(drawn_norms / tip_len, 0, 1)
width_scalars = np.repeat(width_scalars, 8)[:-1]
self.get_stroke_widths()[:] = width_scalars * width_arr
# Potentially adjust opacity and color
if self.color_map is not None:
self.get_stroke_colors() # Ensures the array is updated to appropriate length
low, high = self.magnitude_range
self.data['stroke_rgba'][:, :3] = self.color_map(
inverse_interpolate(low, high, np.repeat(output_norms, 8)[:-1])
)[:, :3]
if self.norm_to_opacity_func is not None:
self.get_stroke_opacities()[:] = self.norm_to_opacity_func(
np.repeat(output_norms, 8)[:-1]
)
self.note_changed_data()
return self
class TimeVaryingVectorField(VectorField):
def __init__(
self,
# Takes in an array of points and a float for time
time_func: Callable[[VectArray, float], VectArray],
coordinate_system: CoordinateSystem,
**kwargs
):
self.time = 0
def func(coords):
return time_func(coords, self.time)
super().__init__(func, coordinate_system, **kwargs)
self.add_updater(lambda m, dt: m.increment_time(dt))
self.always.update_vectors()
def increment_time(self, dt):
self.time += dt
class StreamLines(VGroup):
def __init__(
self,
func: Callable[[VectArray], VectArray],
coordinate_system: CoordinateSystem,
density: float = 1.0,
n_repeats: int = 1,
noise_factor: float | None = None,
# Config for drawing lines
solution_time: float = 3,
dt: float = 0.05,
arc_len: float = 3,
max_time_steps: int = 200,
n_samples_per_line: int = 10,
cutoff_norm: float = 15,
# Style info
stroke_width: float = 1.0,
stroke_color: ManimColor = DEFAULT_MOBJECT_COLOR,
stroke_opacity: float = 1,
color_by_magnitude: bool = True,
magnitude_range: Tuple[float, float] = (0, 2.0),
taper_stroke_width: bool = False,
color_map: str = "3b1b_colormap",
**kwargs
):
super().__init__(**kwargs)
self.func = func
self.coordinate_system = coordinate_system
self.density = density
self.n_repeats = n_repeats
self.noise_factor = noise_factor
self.solution_time = solution_time
self.dt = dt
self.arc_len = arc_len
self.max_time_steps = max_time_steps
self.n_samples_per_line = n_samples_per_line
self.cutoff_norm = cutoff_norm
self.stroke_width = stroke_width
self.stroke_color = stroke_color
self.stroke_opacity = stroke_opacity
self.color_by_magnitude = color_by_magnitude
self.magnitude_range = magnitude_range
self.taper_stroke_width = taper_stroke_width
self.color_map = color_map
self.draw_lines()
self.init_style()
def point_func(self, points: Vect3Array) -> Vect3:
in_coords = np.array(self.coordinate_system.p2c(points)).T
out_coords = self.func(in_coords)
origin = self.coordinate_system.get_origin()
return self.coordinate_system.c2p(*out_coords.T) - origin
def draw_lines(self) -> None:
lines = []
# Todo, it feels like coordinate system should just have
# the ODE solver built into it, no?
lines = []
for coords in self.get_sample_coords():
solution_coords = ode_solution_points(self.func, coords, self.solution_time, self.dt)
line = VMobject()
line.set_points_smoothly(self.coordinate_system.c2p(*solution_coords.T))
# TODO, account for arc length somehow?
line.virtual_time = self.solution_time
lines.append(line)
self.set_submobjects(lines)
def get_sample_coords(self):
cs = self.coordinate_system
sample_coords = get_sample_coords(cs, self.density)
noise_factor = self.noise_factor
if noise_factor is None:
noise_factor = (cs.x_axis.get_unit_size() / self.density) * 0.5
return np.array([
coords + noise_factor * np.random.random(coords.shape)
for n in range(self.n_repeats)
for coords in sample_coords
])
def init_style(self) -> None:
if self.color_by_magnitude:
values_to_rgbs = get_vectorized_rgb_gradient_function(
*self.magnitude_range, self.color_map,
)
cs = self.coordinate_system
for line in self.submobjects:
norms = [
get_norm(self.func(cs.p2c(point)))
for point in line.get_points()
]
rgbs = values_to_rgbs(norms)
rgbas = np.zeros((len(rgbs), 4))
rgbas[:, :3] = rgbs
rgbas[:, 3] = self.stroke_opacity
line.set_rgba_array(rgbas, "stroke_rgba")
else:
self.set_stroke(self.stroke_color, opacity=self.stroke_opacity)
if self.taper_stroke_width:
width = [0, self.stroke_width, 0]
else:
width = self.stroke_width
self.set_stroke(width=width)
class AnimatedStreamLines(VGroup):
def __init__(
self,
stream_lines: StreamLines,
lag_range: float = 4,
rate_multiple: float = 1.0,
line_anim_config: dict = dict(
rate_func=linear,
time_width=1.0,
),
**kwargs
):
super().__init__(**kwargs)
self.stream_lines = stream_lines
for line in stream_lines:
line.anim = VShowPassingFlash(
line,
run_time=line.virtual_time / rate_multiple,
**line_anim_config,
)
line.anim.begin()
line.time = -lag_range * np.random.random()
self.add(line.anim.mobject)
self.add_updater(lambda m, dt: m.update(dt))
def update(self, dt: float = 0) -> None:
stream_lines = self.stream_lines
for line in stream_lines:
line.time += dt
adjusted_time = max(line.time, 0) % line.anim.run_time
line.anim.update(adjusted_time / line.anim.run_time)