from __future__ import annotations from typing import Callable, Sequence from isosurfaces import plot_isoline from manimlib.constants import * from manimlib.mobject.types.vectorized_mobject import VMobject from manimlib.utils.config_ops import digest_config class ParametricCurve(VMobject): CONFIG = { "t_range": [0, 1, 0.1], "epsilon": 1e-8, # TODO, automatically figure out discontinuities "discontinuities": [], "use_smoothing": True, } def __init__( self, t_func: Callable[[float], np.ndarray], t_range: Sequence[float] | None = None, **kwargs ): digest_config(self, kwargs) if t_range is not None: self.t_range[:len(t_range)] = t_range # To be backward compatible with all the scenes specifying t_min, t_max, step_size self.t_range = [ kwargs.get("t_min", self.t_range[0]), kwargs.get("t_max", self.t_range[1]), kwargs.get("step_size", self.t_range[2]), ] self.t_func = t_func VMobject.__init__(self, **kwargs) def get_point_from_function(self, t: float) -> np.ndarray: return 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_approximately_smooth() if not self.has_points(): self.set_points([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): CONFIG = { "color": YELLOW, "x_range": [-8, 8, 0.25], } def __init__( self, function: Callable[[float], float], x_range: Sequence[float] | None = None, **kwargs ): digest_config(self, kwargs) self.function = function if x_range is not None: self.x_range[:len(x_range)] = x_range def parametric_function(t): return [t, function(t), 0] super().__init__(parametric_function, self.x_range, **kwargs) class ImplicitFunction(VMobject): CONFIG = { "x_range": [-FRAME_X_RADIUS, FRAME_X_RADIUS], "y_range": [-FRAME_Y_RADIUS, FRAME_Y_RADIUS], "min_depth": 5, "max_quads": 1500, "use_smoothing": True } def __init__( self, func: Callable[[float, float], float], **kwargs ): digest_config(self, kwargs) self.function = func super().__init__(**kwargs) def init_points(self): p_min, p_max = ( np.array([self.x_range[0], self.y_range[0]]), np.array([self.x_range[1], self.y_range[1]]), ) curves = plot_isoline( fn=lambda u: self.function(u[0], u[1]), pmin=p_min, pmax=p_max, min_depth=self.min_depth, max_quads=self.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 self.use_smoothing: self.make_smooth() return self