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512 lines
17 KiB
Python
512 lines
17 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 BLUE, WHITE
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from manimlib.constants import ORIGIN
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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.iterables import cartesian_product
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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(VMobject):
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def __init__(
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self,
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func,
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stroke_color: ManimColor = BLUE,
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stroke_opacity: float = 1.0,
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center: Vect3 = ORIGIN,
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sample_points: Optional[Vect3Array] = None,
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x_density: float = 2.0,
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y_density: float = 2.0,
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z_density: float = 2.0,
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width: float = 14.0,
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height: float = 8.0,
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depth: float = 0.0,
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stroke_width: float = 2,
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tip_width_ratio: float = 4,
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tip_len_to_width: float = 0.01,
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max_vect_len: float | None = None,
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min_drawn_norm: float = 1e-2,
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flat_stroke: bool = False,
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norm_to_opacity_func=None,
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norm_to_rgb_func=None,
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**kwargs
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):
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self.func = func
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self.stroke_width = stroke_width
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self.tip_width_ratio = tip_width_ratio
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self.tip_len_to_width = tip_len_to_width
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self.min_drawn_norm = min_drawn_norm
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self.norm_to_opacity_func = norm_to_opacity_func
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self.norm_to_rgb_func = norm_to_rgb_func
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if max_vect_len is not None:
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self.max_vect_len = max_vect_len
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else:
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densities = np.array([x_density, y_density, z_density])
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dims = np.array([width, height, depth])
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self.max_vect_len = 1.0 / densities[dims > 0].mean()
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if sample_points is None:
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self.sample_points = self.get_sample_points(
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center, width, height, depth,
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x_density, y_density, z_density
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)
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else:
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self.sample_points = sample_points
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self.init_base_stroke_width_array(len(self.sample_points))
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super().__init__(
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stroke_color=stroke_color,
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stroke_opacity=stroke_opacity,
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flat_stroke=flat_stroke,
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**kwargs
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)
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n_samples = len(self.sample_points)
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self.set_points(np.zeros((8 * n_samples - 1, 3)))
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self.set_stroke(width=stroke_width)
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self.set_joint_type('no_joint')
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self.update_vectors()
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def get_sample_points(
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self,
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center: np.ndarray,
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width: float,
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height: float,
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depth: float,
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x_density: float,
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y_density: float,
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z_density: float
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) -> np.ndarray:
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to_corner = np.array([width / 2, height / 2, depth / 2])
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spacings = 1.0 / np.array([x_density, y_density, z_density])
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to_corner = spacings * (to_corner / spacings).astype(int)
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lower_corner = center - to_corner
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upper_corner = center + to_corner + spacings
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return cartesian_product(*(
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np.arange(low, high, space)
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for low, high, space in zip(lower_corner, upper_corner, spacings)
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))
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def init_base_stroke_width_array(self, n_sample_points):
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arr = np.ones(8 * n_sample_points - 1)
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arr[4::8] = self.tip_width_ratio
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arr[5::8] = self.tip_width_ratio * 0.5
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arr[6::8] = 0
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arr[7::8] = 0
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self.base_stroke_width_array = arr
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def set_sample_points(self, sample_points: Vect3Array):
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self.sample_points = sample_points
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return self
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def set_stroke(self, color=None, width=None, opacity=None, behind=None, flat=None, recurse=True):
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super().set_stroke(color, None, opacity, behind, flat, recurse)
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if width is not None:
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self.set_stroke_width(float(width))
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return self
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def set_stroke_width(self, width: float):
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if self.get_num_points() > 0:
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self.get_stroke_widths()[:] = width * self.base_stroke_width_array
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self.stroke_width = width
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return self
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def update_vectors(self):
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tip_width = self.tip_width_ratio * self.stroke_width
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tip_len = self.tip_len_to_width * tip_width
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samples = self.sample_points
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# Get raw outputs and lengths
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outputs = self.func(samples)
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norms = np.linalg.norm(outputs, axis=1)[:, np.newaxis]
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# How long should the arrows be drawn?
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max_len = self.max_vect_len
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if max_len < np.inf:
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drawn_norms = max_len * np.tanh(norms / max_len)
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else:
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drawn_norms = norms
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# What's the distance from the base of an arrow to
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# the base of its head?
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dist_to_head_base = np.clip(drawn_norms - tip_len, 0, np.inf)
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# Set all points
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unit_outputs = np.zeros_like(outputs)
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np.true_divide(outputs, norms, out=unit_outputs, where=(norms > self.min_drawn_norm))
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points = self.get_points()
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points[0::8] = samples
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points[2::8] = samples + dist_to_head_base * unit_outputs
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points[4::8] = points[2::8]
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points[6::8] = samples + drawn_norms * unit_outputs
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for i in (1, 3, 5):
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points[i::8] = 0.5 * (points[i - 1::8] + points[i + 1::8])
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points[7::8] = points[6:-1:8]
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# Adjust stroke widths
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width_arr = self.stroke_width * self.base_stroke_width_array
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width_scalars = np.clip(drawn_norms / tip_len, 0, 1)
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width_scalars = np.repeat(width_scalars, 8)[:-1]
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self.get_stroke_widths()[:] = width_scalars * width_arr
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# Potentially adjust opacity and color
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if self.norm_to_opacity_func is not None:
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self.get_stroke_opacities()[:] = self.norm_to_opacity_func(
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np.repeat(norms, 8)[:-1]
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)
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if self.norm_to_rgb_func is not None:
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self.get_stroke_colors()
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self.data['stroke_rgba'][:, :3] = self.norm_to_rgb_func(
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np.repeat(norms, 8)[:-1]
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)
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self.note_changed_data()
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return self
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class TimeVaryingVectorField(VectorField):
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def __init__(
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self,
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# Takes in an array of points and a float for time
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time_func,
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**kwargs
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):
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self.time = 0
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super().__init__(func=lambda p: time_func(p, self.time), **kwargs)
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self.add_updater(lambda m, dt: m.increment_time(dt))
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always(self.update_vectors)
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def increment_time(self, dt):
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self.time += dt
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class OldVectorField(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:
|
|
line.anim = VShowPassingFlash(
|
|
line,
|
|
run_time=line.virtual_time,
|
|
**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) -> 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)
|