Source code for octadist.src.projection

# OctaDist  Copyright (C) 2019  Rangsiman Ketkaew et al.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
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#
# 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.
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# 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