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333 lines
11 KiB
Python
333 lines
11 KiB
Python
from __future__ import annotations
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import itertools as it
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import numpy as np
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from manimlib.constants import FRAME_HEIGHT, FRAME_WIDTH
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from manimlib.constants import WHITE
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from manimlib.animation.indication import VShowPassingFlash
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from manimlib.mobject.geometry import Arrow
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from manimlib.mobject.types.vectorized_mobject import VGroup
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from manimlib.mobject.types.vectorized_mobject import VMobject
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from manimlib.utils.bezier import interpolate
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from manimlib.utils.bezier import inverse_interpolate
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from manimlib.utils.color import get_colormap_list
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from manimlib.utils.color import rgb_to_color
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from manimlib.utils.dict_ops import merge_dicts_recursively
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from manimlib.utils.rate_functions import linear
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from manimlib.utils.simple_functions import sigmoid
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from manimlib.utils.space_ops import get_norm
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from typing import TYPE_CHECKING
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if TYPE_CHECKING:
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from typing import Callable, Iterable, Sequence, TypeVar, Tuple
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from manimlib.typing import ManimColor, Vect3, VectN, Vect3Array
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from manimlib.mobject.coordinate_systems import CoordinateSystem
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from manimlib.mobject.mobject import Mobject
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T = TypeVar("T")
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def get_vectorized_rgb_gradient_function(
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min_value: T,
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max_value: T,
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color_map: str
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) -> Callable[[VectN], Vect3Array]:
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rgbs = np.array(get_colormap_list(color_map))
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def func(values):
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alphas = inverse_interpolate(
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min_value, max_value, np.array(values)
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)
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alphas = np.clip(alphas, 0, 1)
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scaled_alphas = alphas * (len(rgbs) - 1)
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indices = scaled_alphas.astype(int)
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next_indices = np.clip(indices + 1, 0, len(rgbs) - 1)
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inter_alphas = scaled_alphas % 1
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inter_alphas = inter_alphas.repeat(3).reshape((len(indices), 3))
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result = interpolate(rgbs[indices], rgbs[next_indices], inter_alphas)
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return result
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return func
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def get_rgb_gradient_function(
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min_value: T,
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max_value: T,
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color_map: str
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) -> Callable[[float], Vect3]:
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vectorized_func = get_vectorized_rgb_gradient_function(min_value, max_value, color_map)
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return lambda value: vectorized_func(np.array([value]))[0]
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def move_along_vector_field(
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mobject: Mobject,
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func: Callable[[Vect3], Vect3]
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) -> Mobject:
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mobject.add_updater(
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lambda m, dt: m.shift(
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func(m.get_center()) * dt
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)
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)
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return mobject
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def move_submobjects_along_vector_field(
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mobject: Mobject,
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func: Callable[[Vect3], Vect3]
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) -> Mobject:
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def apply_nudge(mob, dt):
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for submob in mob:
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x, y = submob.get_center()[:2]
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if abs(x) < FRAME_WIDTH and abs(y) < FRAME_HEIGHT:
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submob.shift(func(submob.get_center()) * dt)
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mobject.add_updater(apply_nudge)
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return mobject
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def move_points_along_vector_field(
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mobject: Mobject,
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func: Callable[[float, float], Iterable[float]],
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coordinate_system: CoordinateSystem
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) -> Mobject:
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cs = coordinate_system
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origin = cs.get_origin()
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def apply_nudge(self, dt):
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mobject.apply_function(
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lambda p: p + (cs.c2p(*func(*cs.p2c(p))) - origin) * dt
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)
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mobject.add_updater(apply_nudge)
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return mobject
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def get_sample_points_from_coordinate_system(
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coordinate_system: CoordinateSystem,
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step_multiple: float
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) -> it.product[tuple[Vect3, ...]]:
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ranges = []
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for range_args in coordinate_system.get_all_ranges():
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_min, _max, step = range_args
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step *= step_multiple
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ranges.append(np.arange(_min, _max + step, step))
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return it.product(*ranges)
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# Mobjects
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class VectorField(VGroup):
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def __init__(
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self,
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func: Callable[[float, float], Sequence[float]],
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coordinate_system: CoordinateSystem,
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step_multiple: float = 0.5,
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magnitude_range: Tuple[float, float] = (0, 2),
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color_map: str = "3b1b_colormap",
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# Takes in actual norm, spits out displayed norm
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length_func: Callable[[float], float] = lambda norm: 0.45 * sigmoid(norm),
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opacity: float = 1.0,
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vector_config: dict = dict(),
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**kwargs
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):
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super().__init__(**kwargs)
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self.func = func
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self.coordinate_system = coordinate_system
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self.step_multiple = step_multiple
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self.magnitude_range = magnitude_range
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self.color_map = color_map
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self.length_func = length_func
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self.opacity = opacity
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self.vector_config = dict(vector_config)
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self.value_to_rgb = get_rgb_gradient_function(
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*self.magnitude_range, self.color_map,
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)
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samples = get_sample_points_from_coordinate_system(
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coordinate_system, self.step_multiple
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)
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self.add(*(
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self.get_vector(coords)
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for coords in samples
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))
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def get_vector(self, coords: Iterable[float], **kwargs) -> Arrow:
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vector_config = merge_dicts_recursively(
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self.vector_config,
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kwargs
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)
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output = np.array(self.func(*coords))
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norm = get_norm(output)
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if norm > 0:
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output *= self.length_func(norm) / norm
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origin = self.coordinate_system.get_origin()
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_input = self.coordinate_system.c2p(*coords)
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_output = self.coordinate_system.c2p(*output)
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vect = Arrow(
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origin, _output, buff=0,
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**vector_config
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)
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vect.shift(_input - origin)
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vect.set_color(
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rgb_to_color(self.value_to_rgb(norm)),
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opacity=self.opacity,
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)
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return vect
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class StreamLines(VGroup):
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def __init__(
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self,
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func: Callable[[float, float], Sequence[float]],
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coordinate_system: CoordinateSystem,
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step_multiple: float = 0.5,
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n_repeats: int = 1,
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noise_factor: float | None = None,
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# Config for drawing lines
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dt: float = 0.05,
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arc_len: float = 3,
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max_time_steps: int = 200,
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n_samples_per_line: int = 10,
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cutoff_norm: float = 15,
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# Style info
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stroke_width: float = 1.0,
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stroke_color: ManimColor = WHITE,
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stroke_opacity: float = 1,
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color_by_magnitude: bool = True,
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magnitude_range: Tuple[float, float] = (0, 2.0),
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taper_stroke_width: bool = False,
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color_map: str = "3b1b_colormap",
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**kwargs
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):
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super().__init__(**kwargs)
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self.func = func
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self.coordinate_system = coordinate_system
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self.step_multiple = step_multiple
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self.n_repeats = n_repeats
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self.noise_factor = noise_factor
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self.dt = dt
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self.arc_len = arc_len
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self.max_time_steps = max_time_steps
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self.n_samples_per_line = n_samples_per_line
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self.cutoff_norm = cutoff_norm
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self.stroke_width = stroke_width
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self.stroke_color = stroke_color
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self.stroke_opacity = stroke_opacity
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self.color_by_magnitude = color_by_magnitude
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self.magnitude_range = magnitude_range
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self.taper_stroke_width = taper_stroke_width
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self.color_map = color_map
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self.draw_lines()
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self.init_style()
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def point_func(self, point: Vect3) -> Vect3:
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in_coords = self.coordinate_system.p2c(point)
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out_coords = self.func(*in_coords)
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return self.coordinate_system.c2p(*out_coords)
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def draw_lines(self) -> None:
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lines = []
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origin = self.coordinate_system.get_origin()
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for point in self.get_start_points():
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points = [point]
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total_arc_len = 0
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time = 0
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for x in range(self.max_time_steps):
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time += self.dt
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last_point = points[-1]
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new_point = last_point + self.dt * (self.point_func(last_point) - origin)
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points.append(new_point)
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total_arc_len += get_norm(new_point - last_point)
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if get_norm(last_point) > self.cutoff_norm:
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break
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if total_arc_len > self.arc_len:
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break
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line = VMobject()
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line.virtual_time = time
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step = max(1, int(len(points) / self.n_samples_per_line))
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line.set_points_as_corners(points[::step])
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line.make_smooth(approx=True)
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lines.append(line)
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self.set_submobjects(lines)
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def get_start_points(self) -> Vect3Array:
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cs = self.coordinate_system
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sample_coords = get_sample_points_from_coordinate_system(
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cs, self.step_multiple,
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)
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noise_factor = self.noise_factor
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if noise_factor is None:
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noise_factor = cs.x_range[2] * self.step_multiple * 0.5
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return np.array([
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cs.c2p(*coords) + noise_factor * np.random.random(3)
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for n in range(self.n_repeats)
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for coords in sample_coords
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])
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def init_style(self) -> None:
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if self.color_by_magnitude:
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values_to_rgbs = get_vectorized_rgb_gradient_function(
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*self.magnitude_range, self.color_map,
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)
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cs = self.coordinate_system
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for line in self.submobjects:
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norms = [
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get_norm(self.func(*cs.p2c(point)))
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for point in line.get_points()
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]
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rgbs = values_to_rgbs(norms)
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rgbas = np.zeros((len(rgbs), 4))
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rgbas[:, :3] = rgbs
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rgbas[:, 3] = self.stroke_opacity
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line.set_rgba_array(rgbas, "stroke_rgba")
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else:
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self.set_stroke(self.stroke_color, opacity=self.stroke_opacity)
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if self.taper_stroke_width:
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width = [0, self.stroke_width, 0]
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else:
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width = self.stroke_width
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self.set_stroke(width=width)
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class AnimatedStreamLines(VGroup):
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def __init__(
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self,
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stream_lines: StreamLines,
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lag_range: float = 4,
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line_anim_config: dict = dict(
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rate_func=linear,
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time_width=1.0,
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),
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**kwargs
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):
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super().__init__(**kwargs)
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self.stream_lines = stream_lines
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for line in stream_lines:
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line.anim = VShowPassingFlash(
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line,
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run_time=line.virtual_time,
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**line_anim_config,
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)
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line.anim.begin()
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line.time = -lag_range * np.random.random()
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self.add(line.anim.mobject)
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self.add_updater(lambda m, dt: m.update(dt))
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def update(self, dt: float) -> None:
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stream_lines = self.stream_lines
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for line in stream_lines:
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line.time += dt
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adjusted_time = max(line.time, 0) % line.anim.run_time
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line.anim.update(adjusted_time / line.anim.run_time)
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