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