"""Module for line creation, representation and manipulation."""
import numpy as np
from .biquaternion import BiQuaternion
[docs]def quat_to_pluecker(quat):
"""Generate pluecker coordinates from a given BiQuaternion."""
if np.allclose(np.array([quat.scal], dtype=float), 0) and np.allclose(
np.array([quat.eps], dtype=float), 0
):
return [*quat.coeffs[1:4], *[-quat.coeffs[5 + i] for i in range(3)]]
else:
raise ValueError("Object not a valid description of a line")
[docs]def pluecker_to_quat(coord):
"""Generate BiQuaternion reperesentation of a line with specified
Pluecker coordinates."""
return BiQuaternion([0, *coord[0:3], 0, *[-coord[i + 3] for i in range(3)]])
[docs]def line_to_pluecker(direction, point):
"""Generate Pluecker coordinates for a line with given direction through a point."""
return [*direction, *(-np.cross(direction, point))]
[docs]def act_on_line(quaternion, lin):
"""Let a BiQuaternion act on a line."""
return quaternion * lin * quaternion.conjugate()