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/rotation [ Modules ]

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NAME

module rotation

PURPOSE

This module defines rotation matrices and evaluates the spherical

rotation/rotateTo [ Functions ]

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NAME

function rotateTo(targ, v_in)

PURPOSE

Rotate some vector with the same matrix as one would use to rotate the z-axis onto a vector 'targ'.

INPUTS

• real, dimension(1:3) :: targ -- Target vector
• real, dimension(1:3) :: v_in -- Vector before rotation

OUTPUT

• real, dimension(1:3) :: v_out -- Vector after rotation

USAGE

• calling b = rotateTo( a, (/0.,0.,1./) ) b is the unit-vector in direction of a

rotation/rotateFrom [ Functions ]

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NAME

function rotateFrom(targ, v_in)

PURPOSE

Rotates some vector with the same matrix as one would use to rotate the vector 'targ' onto the z-axis

INPUTS

• real, dimension(1:3) :: targ -- Target vector
• real, dimension(1:3) :: v_in -- Vector before rotation

OUTPUT

• real, dimension(1:3) :: v_out -- Vector after rotation

USAGE

• calling b = rotateFrom( a, a ) b is (/ 0., 0., |a| /)
• calling b = rotateTo( a, (/ 0., 0., 1. /) ) c = rotateFrom( a, b ) c is (/ 0., 0., 1. /) again.

rotation/rotateYZ [ Functions ]

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NAME

function rotateYZ(theta, phi, v_in, cosTheta)

PURPOSE

Does first a rotation around the y-axis with angle theta, then around z with angle phi.

Rotates the z-axis on a vector which has the spherical coordinates theta and phi.

INPUTS

• real :: phi -- Angle around z-axis
• real :: theta -- Angle around y-Axis
• real, dimension(1:3) :: v_in -- Vector before rotation
• real, OPTIONAL :: cosTheta -- cos(theta)

OUTPUT

• real, dimension(1:3) :: v_out -- Vector after rotation

NOTES

if optional parameter cosTheta is given, cosT and sinT are calculated using this parameter instead of theta

rotation/rotateYZback [ Functions ]

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NAME

function rotateYZback(theta, phi, v_in, cosTheta)

PURPOSE

Does first a rotation around the z-axis with angle -theta, then around y with angle -phi.

Is the back rotation performed by rotateYZ

INPUTS

• real :: phi -- Angle around z-axis
• real :: theta -- Angle around y-Axis
• real, dimension(1:3) :: v_in -- Vector before rotation
• real, OPTIONAL :: cosTheta -- cos(theta)

OUTPUT

• real, dimension(1:3) :: v_out -- Vector after rotation

NOTES

if optional parameter cosTheta is given, cosT and sinT are calculated using this parameter instead of theta

rotation/rotateZY [ Functions ]

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NAME

function rotateZY(theta, phi, v_in, cosTheta)

PURPOSE

Does first rotation around z and thereafter around y.

As a result, e.g. the vector which had originally the spherical coordinates theta and phi is now rotated on the z-Axis. It's basically the inverse of rotateYZ.

INPUTS

• real :: phi -- Angle around z-axis [radian]
• real :: theta -- Angle around y-Axis [radian]
• real, dimension(1:3) :: v_in -- Vector before rotation
• real, OPTIONAL :: cosTheta -- cos(theta)

OUTPUT

• real, dimension(1:3) :: v_out -- Vector after rotation

NOTES

if optional parameter cosTheta is given, cosT and sinT are calculated using this parameter instead of theta

rotation/get_phi_theta [ Subroutines ]

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NAME

subroutine get_phi_theta(vector, theta, phi)

PURPOSE

Translate the input "vector" into spherical coordinates. Returns phi and theta of vector:

• x-axis defines phi=0
• z-axis defines theta=0

INPUTS

• real, dimension(1:3) :: vector --

OUTPUT

• real :: phi -- phi [radian], range: 0 <= phi <= 2*pi
• real :: theta -- theta [radian], range: 0 <= theta <= pi