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- from __future__ import annotations
- from isosurfaces import plot_isoline
- import numpy as np
- from manimlib.constants import FRAME_X_RADIUS, FRAME_Y_RADIUS
- from manimlib.constants import YELLOW
- from manimlib.mobject.types.vectorized_mobject import VMobject
- from typing import TYPE_CHECKING
- if TYPE_CHECKING:
- from typing import Callable, Sequence, Tuple
- from manimlib.typing import ManimColor, Vect3
- class ParametricCurve(VMobject):
- def __init__(
- self,
- t_func: Callable[[float], Sequence[float] | Vect3],
- t_range: Tuple[float, float, float] = (0, 1, 0.1),
- epsilon: float = 1e-8,
- # TODO, automatically figure out discontinuities
- discontinuities: Sequence[float] = [],
- use_smoothing: bool = True,
- **kwargs
- ):
- self.t_func = t_func
- self.t_range = t_range
- self.epsilon = epsilon
- self.discontinuities = discontinuities
- self.use_smoothing = use_smoothing
- super().__init__(**kwargs)
- def get_point_from_function(self, t: float) -> Vect3:
- return np.array(self.t_func(t))
- def init_points(self):
- t_min, t_max, step = self.t_range
- jumps = np.array(self.discontinuities)
- jumps = jumps[(jumps > t_min) & (jumps < t_max)]
- boundary_times = [t_min, t_max, *(jumps - self.epsilon), *(jumps + self.epsilon)]
- boundary_times.sort()
- for t1, t2 in zip(boundary_times[0::2], boundary_times[1::2]):
- t_range = [*np.arange(t1, t2, step), t2]
- points = np.array([self.t_func(t) for t in t_range])
- self.start_new_path(points[0])
- self.add_points_as_corners(points[1:])
- if self.use_smoothing:
- self.make_smooth(approx=True)
- if not self.has_points():
- self.set_points(np.array([self.t_func(t_min)]))
- return self
- def get_t_func(self):
- return self.t_func
- def get_function(self):
- if hasattr(self, "underlying_function"):
- return self.underlying_function
- if hasattr(self, "function"):
- return self.function
- def get_x_range(self):
- if hasattr(self, "x_range"):
- return self.x_range
- class FunctionGraph(ParametricCurve):
- def __init__(
- self,
- function: Callable[[float], float],
- x_range: Tuple[float, float, float] = (-8, 8, 0.25),
- color: ManimColor = YELLOW,
- **kwargs
- ):
- self.function = function
- self.x_range = x_range
- def parametric_function(t):
- return [t, function(t), 0]
- super().__init__(parametric_function, self.x_range, **kwargs)
- class ImplicitFunction(VMobject):
- def __init__(
- self,
- func: Callable[[float, float], float],
- x_range: Tuple[float, float] = (-FRAME_X_RADIUS, FRAME_X_RADIUS),
- y_range: Tuple[float, float] = (-FRAME_Y_RADIUS, FRAME_Y_RADIUS),
- min_depth: int = 5,
- max_quads: int = 1500,
- use_smoothing: bool = False,
- joint_type: str = 'no_joint',
- **kwargs
- ):
- super().__init__(joint_type=joint_type, **kwargs)
- p_min, p_max = (
- np.array([x_range[0], y_range[0]]),
- np.array([x_range[1], y_range[1]]),
- )
- curves = plot_isoline(
- fn=lambda u: func(u[0], u[1]),
- pmin=p_min,
- pmax=p_max,
- min_depth=min_depth,
- max_quads=max_quads,
- ) # returns a list of lists of 2D points
- curves = [
- np.pad(curve, [(0, 0), (0, 1)])
- for curve in curves
- if curve != []
- ] # add z coord as 0
- for curve in curves:
- self.start_new_path(curve[0])
- self.add_points_as_corners(curve[1:])
- if use_smoothing:
- self.make_smooth()
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