# OctaDist  Copyright (C) 2019  Rangsiman Ketkaew et al.
#
# This program is free software: you can redistribute it and/or modify
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

import numpy as np

[docs]def project_atom_onto_line(p, a, b):
"""
Find the point projection on the line, which defined by two distinct end points.

::

a <----> b

P(x) = x1 + (p - x1).(x2 - x1)/(x2-x1).(x2-x1) * (x2-x1)

Parameters
----------
p : array_like
Coordinate of point to project.
a : array_like
Coordinate of head atom of the line.
b : array_like
Coordinate of tail atom of the line.

Returns
-------
projected_point : array_like
The projected point on the orthogonal line.

Examples
--------
>>> # point to project
>>> p = [10.1873, 5.7463, 5.615]
>>> # head and end points of line
>>> a = [8.494, 5.9735, 4.8091]
>>> b = [9.6526, 6.4229, 7.3079]
>>> project_atom_onto_line(p, a, b)
[9.07023235 6.19701012 6.05188388]

"""
p = np.asarray(p, dtype=np.float64)
a = np.asarray(a, dtype=np.float64)
b = np.asarray(b, dtype=np.float64)

ap = p - a
ab = b - a

projected_point = a + (np.dot(ap, ab) / np.dot(ab, ab)) * ab

return projected_point

[docs]def project_atom_onto_plane(p, a, b, c, d):
"""
Find the orthogonal vector of point onto the given plane.
The equation of plane is Ax + By + Cz = D and point is (L, M, N),
then the location on the plane that is closest to the point (P, Q, R) is

::

(P, Q, R) = (L, M, N) + λ * (A, B, C)

where λ = (D - ( A*L + B*M + C*N)) / (A^2 + B^2 + C^2).

Parameters
----------
p : array_like
Point to project.
a : int or float
Coefficient of the equation of the plane.
b : int or float
Coefficient of the equation of the plane.
c : int or float
Coefficient of the equation of the plane.
d : int or float
Coefficient of the equation of the plane.

Returns
-------
projected_point: array_like
The projected point on the orthogonal plane.

Examples
--------
>>> # point to project
>>> p = [10.1873, 5.7463, 5.615]
>>> # coefficient of the equation of the plane
>>> a = -3.231203733528
>>> b = -0.9688526458499996
>>> c = 0.9391692927779998
>>> d = -4.940497273569501
>>> project_atom_onto_plane(p, a, b, c, d)
[2.73723598 3.51245316 7.78040705]

"""
p = np.asarray(p, dtype=np.float64)
plane = np.array([a, b, c], dtype=np.float64)

lambda_plane = (d - (a * p[0] + b * p[1] + c * p[2])) / np.dot(plane, plane)

projected_point = p + lambda_plane * plane

return projected_point