Source code for espressomd.math

#
# Copyright (C) 2010-2022 The ESPResSo project
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# This file is part of ESPResSo.
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# ESPResSo is free software: you can redistribute it and/or modify
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import math
from .script_interface import ScriptInterfaceHelper, script_interface_register


[docs] @script_interface_register class CylindricalTransformationParameters(ScriptInterfaceHelper): """ Class to hold and validate the parameters needed for a cylindrical transformation. The three parameters are available as attributes but are read-only. Parameters ---------- center : (3,) array_like of :obj:`float`, default = [0, 0, 0] Position of the origin of the cylindrical coordinate system. axis : (3,) array_like of :obj:`float`, default = [0, 0, 1] Orientation vector of the ``z``-axis of the cylindrical coordinate system. orientation: (3,) array_like of :obj:`float`, default = [1, 0, 0] The axis on which ``phi = 0``. Notes ----- If you provide no arguments, the defaults above are set. If you provide only a ``center`` and an ``axis``, an ``orientation`` will be automatically generated that is orthogonal to ``axis``. """ _so_name = "Math::CylindricalTransformationParameters"
[docs] def calc_quaternions_from_angles(polar_angle, azimuthal_angle): """ Convert the spherical coordinate representation of a vector to a quaternion that corresponds to that direction. Note that this quaternion is not unique, as the third degree of freedom (rotation around the given vector) is not specified. Parameters ---------- polar_angle : :obj:`float` The polar angle (angle with the z-axis) in the range [0, pi]. azimuthal_angle : :obj:`float` The azimuthal angle (angle with the x-axis) in the range [0, 2 pi). Returns ------- quaternion : (4,) list of :obj:`float` """ q1w = math.cos(polar_angle / 2.) q1x = 0. q1y = math.sin(polar_angle / 2.) q1z = 0. q2w = math.cos(azimuthal_angle / 2.) q2x = 0. q2y = 0. q2z = math.sin(azimuthal_angle / 2.) q3w = q1w * q2w - q1x * q2x - q1y * q2y - q1z * q2z q3x = q1w * q2x + q1x * q2w - q1y * q2z + q1z * q2y q3y = q1w * q2y + q1x * q2z + q1y * q2w - q1z * q2x q3z = q1w * q2z - q1x * q2y + q1y * q2x + q1z * q2w return [q3w, q3x, q3y, q3z]