3b1b-manim/manimlib/utils/paths.py
2022-02-12 23:47:23 +08:00

58 lines
1.7 KiB
Python

import math
from typing import Callable
import numpy as np
from manimlib.constants import OUT
from manimlib.utils.bezier import interpolate
from manimlib.utils.space_ops import get_norm
from manimlib.utils.space_ops import rotation_matrix_transpose
STRAIGHT_PATH_THRESHOLD = 0.01
def straight_path(
start_points: np.ndarray,
end_points: np.ndarray,
alpha: float
) -> np.ndarray:
"""
Same function as interpolate, but renamed to reflect
intent of being used to determine how a set of points move
to another set. For instance, it should be a specific case
of path_along_arc
"""
return interpolate(start_points, end_points, alpha)
def path_along_arc(
arc_angle: float,
axis: np.ndarray = OUT
) -> Callable[[np.ndarray, np.ndarray, float], np.ndarray]:
"""
If vect is vector from start to end, [vect[:,1], -vect[:,0]] is
perpendicular to vect in the left direction.
"""
if abs(arc_angle) < STRAIGHT_PATH_THRESHOLD:
return straight_path
if get_norm(axis) == 0:
axis = OUT
unit_axis = axis / get_norm(axis)
def path(start_points, end_points, alpha):
vects = end_points - start_points
centers = start_points + 0.5 * vects
if arc_angle != np.pi:
centers += np.cross(unit_axis, vects / 2.0) / math.tan(arc_angle / 2)
rot_matrix_T = rotation_matrix_transpose(alpha * arc_angle, unit_axis)
return centers + np.dot(start_points - centers, rot_matrix_T)
return path
def clockwise_path() -> Callable[[np.ndarray, np.ndarray, float], np.ndarray]:
return path_along_arc(-np.pi)
def counterclockwise_path() -> Callable[[np.ndarray, np.ndarray, float], np.ndarray]:
return path_along_arc(np.pi)