# Bezier¶

manimlib/utils/bezier.py 这个文件中主要实现了和贝塞尔曲线、插值有关的函数

manimlib.utils.bezier.bezier(points: Iterable[float | np.ndarray]) → Callable[[float], float | np.ndarray]

manimlib.utils.bezier.partial_bezier_points(points: Sequence[np.ndarray], a: float, b: float) → list[float]

Given an list of points which define a bezier curve, and two numbers 0<=a<b<=1, return an list of the same size, which describes the portion of the original bezier curve on the interval [a, b].

This algorithm is pretty nifty, and pretty dense.

manimlib.utils.bezier.partial_quadratic_bezier_points(points: Sequence[np.ndarray], a: float, b: float) → list[float]

manimlib.utils.bezier.interpolate(start: T, end: T, alpha: np.ndarray | float) → T

manimlib.utils.bezier.set_array_by_interpolation(arr: np.ndarray, arr1: np.ndarray, arr2: np.ndarray, alpha: float, interp_func: Callable[[np.ndarray, np.ndarray, float], np.ndarray] = <function interpolate>) → np.ndarray

manimlib.utils.bezier.integer_interpolate(start: T, end: T, alpha: float) → tuple[int, float]

alpha is a float between 0 and 1. This returns an integer between start and end (inclusive) representing appropriate interpolation between them, along with a “residue” representing a new proportion between the returned integer and the next one of the list.

For example, if start=0, end=10, alpha=0.46, This would return (4, 0.6).

manimlib.utils.bezier.mid(start: T, end: T) → T

manimlib.utils.bezier.inverse_interpolate(start: T, end: T, value: T) → float

manimlib.utils.bezier.match_interpolate(new_start: T, new_end: T, old_start: T, old_end: T, old_value: T) → T

manimlib.utils.bezier.get_smooth_quadratic_bezier_handle_points(points: Sequence[np.ndarray]) → np.ndarray | list[np.ndarray]

Figuring out which bezier curves most smoothly connect a sequence of points.

Given three successive points, P0, P1 and P2, you can compute that by defining h = (1/4) P0 + P1 - (1/4)P2, the bezier curve defined by (P0, h, P1) will pass through the point P2.

So for a given set of four successive points, P0, P1, P2, P3, if we want to add a handle point h between P1 and P2 so that the quadratic bezier (P1, h, P2) is part of a smooth curve passing through all four points, we calculate one solution for h that would produce a parbola passing through P3, call it smooth_to_right, and another that would produce a parabola passing through P0, call it smooth_to_left, and use the midpoint between the two.

manimlib.utils.bezier.diag_to_matrix(l_and_u: tuple, diag: numpy.ndarray) → numpy.ndarray

Converts array whose rows represent diagonal entries of a matrix into the matrix itself. See scipy.linalg.solve_banded

l, u 为非零下上对角线数，diag 为将以对角线形式填充的矩阵

manimlib.utils.bezier.is_closed(points: Sequence[np.ndarray]) → bool