mirror of
https://github.com/3b1b/manim.git
synced 2025-04-13 09:47:07 +00:00
48 lines
1.4 KiB
Python
48 lines
1.4 KiB
Python
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, end_points, alpha):
|
|
"""
|
|
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, axis=OUT):
|
|
"""
|
|
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) / np.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():
|
|
return path_along_arc(-np.pi)
|
|
|
|
|
|
def counterclockwise_path():
|
|
return path_along_arc(np.pi)
|