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Function: mtoq
Purpose: transforms a rotation matrix into a quaternion. If the
matrix does not perform a rotation, then its behavior may be ill-
defined
Inputs: m: a 3x3 element array or an Nx3x3 element array
Returns: q
Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/mtoq.pro $
(See general/misc/quaternion/mtoq.pro)
Function: qang,q
Purpose: calculate the angle of a unit quaternion or an array of unit
quaternions
Inputs: q: a 4 element array, or an Nx4 element array, representing quaternion(s)
Returns: phi where q = [cos(phi/2),V*sin(phi/2)]
throws error of failure, because negative one could be
an acceptable return value
Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qang.pro $
(See general/misc/quaternion/qang.pro)
Function: qcompose,v,theta
Purpose: compose quaternions from vectors and angles
Inputs: vec: 3 element array or an Nx3 element array
theta: an angle or an N element array of angles(in radians)
Keywords: free: Flag to allow thetas outside [0,pi)
Returns: a 4 element quaternion or an Nx4 element array of quaternions
;Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: egrimes $
$LastChangedDate: 2017-06-02 10:32:30 -0700 (Fri, 02 Jun 2017) $
$LastChangedRevision: 23388 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qcompose.pro $
(See general/misc/quaternion/qcompose.pro)
Function: qconj,q
Purpose: calculate the conjugate a quaternion or an array of quaternions
Inputs: q: a 4 element array, or an Nx4 element array, representing quaternion(s)
Returns: q*
Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qconj.pro $
(See general/misc/quaternion/qconj.pro)
Function: qdecompose,q
Purpose: decompose quaternions into axes and angeles
Inputs: q: a 4 element quaternion or an Nx4 element array of quaternions
Returns: a 4 element array with a[0] = angle, and a[1:3] = axis, or
an Nx4 element array or -1L on failure
;Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
As per the euve implementation, if q[0] is outside of the range of
acos...[-1,1] the value of the quaternion will be turned into an
identity quaternion...in other words clipped, this seems suspect,
a better solution may be to wrap the value back into range using
modular arithmatic, future modifiers of this routine should consider
adding this.
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qdecompose.pro $
(See general/misc/quaternion/qdecompose.pro)
Function: qdiv,q1,q2
Purpose: divide q1 by q2, in other words returns a quaternion q3
s.t. q3*q2 = q1
Inputs: q1: a 4 element array, or an Nx4 element array, representing quaternion(s)
q2: a 4 element array, or an Nx4 element array, representing quaternion(s)
Returns: q1/q2, or -1 on failure
;Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qdiv.pro $
(See general/misc/quaternion/qdiv.pro)
Function: qdotp,q1,q2
Purpose: calculate the dot product of two quaternions or two arrays of quaternions
Inputs: q1: a 4 element array, or an Nx4 element array, representing quaternion(s)
q2: a 4 element array, or an Nx4 element array, representing quaternion(s)
Returns: q1.q2, or -1 on failure
;Notes:
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
The scalar component can be thought of as the amount of rotation that
the quaternion performs
like any vector the if t = the angle between q1 and q2 in 4-space
the q1.q2 = ||q1||*||q2||*cos(t) where || denotes the norm(length) of
the quaternion in 4-space
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: aaflores $
$LastChangedDate: 2012-01-23 16:50:12 -0800 (Mon, 23 Jan 2012) $
$LastChangedRevision: 9593 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qdotp.pro $
(See general/misc/quaternion/qdotp.pro)
Procedure:
qham
Purpose:
Calculate the Hamilton product of two quaternions
Calling Sequence:
p = qham(q1,q2)
Input:
q1: a 4 element array, or an Nx4 element array, representing quaternion(s)
q2: a 4 element array, or an Nx4 element array, representing quaternion(s)
Output:
Returns Hamilton product (q1)(q2) or -1 on failure
Notes:
General routine format copied from qdotp
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
$LastChangedBy: aaflores $
$LastChangedDate: 2016-02-11 18:04:52 -0800 (Thu, 11 Feb 2016) $
$LastChangedRevision: 19966 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qham.pro $
(See general/misc/quaternion/qham.pro)
Function: qinv,q
Purpose: calculate the inverse of a quaternion or an array of quaternions
Inputs: q: a 4 element array, or an Nx4 element array, representing quaternion(s)
Returns: q^-1
Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qinv.pro $
(See general/misc/quaternion/qinv.pro)
Function: qmult,q1,q2
Purpose: multiply two quaternions or two arrays of quaternions
Inputs: q1: a 4 element array, or an Nx4 element array, representing quaternion(s)
q2: a 4 element array, or an Nx4 element array, representing quaternion(s)
Returns: q1*q2, or -1 on failure
;Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qmult.pro $
(See general/misc/quaternion/qmult.pro)
Function: qnorm,q
Purpose: calculate the norm a quaternion or an array of quaternions
Inputs: q: a 4 element array, or an Nx4 element array, representing quaternion(s)
Returns: norm(q): sqrt(a^2+b^2+c^2+d^2) or -1L on fail
will be a single element or an N length array
Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
This implementation of norm does not apply the squareroot sometimes
applied to a norm. If required the sqrt can easily be applied by the user
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qnorm.pro $
(See general/misc/quaternion/qnorm.pro)
Function: qnormalize
Purpose: normalize a quaternion or an array of quaternions
Inputs: q: a 4 element array, or an Nx4 element array, representing quaternion(s)
Returns: q/(sqrt(norm(q))) or -1L on fail
Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qnormalize.pro $
(See general/misc/quaternion/qnormalize.pro)
Function: qslerp,q,x1,x2
Purpose: uses spherical linear interpolation to interpolate
quaternions between elements of q
Inputs: q: an Nx4 element array, representing a list of quaternions
with N > 1, all quaternions must be unit quaternions(ie length/norm = 1)
x1: The input abscissa values of the quaternions,an array of
length N, abscissa values must also be monotonic
x2: The output abscissa values for the quaternions, can have
as many elements as wanted but must fall on the interval
[x[0],x[N-1]], an M element array, abscissa values must also
be monotonic
geometric(optional): this keyword allows you to specify that
it use the geometric formula for the slerp. The default
formula is probably faster and more numerically stable, the
geometric option is just available for testing
Testing of the geometric method indicates that the norm of
the interpolated quaternions strays easily from unit length,
when it renormalizes results may be destabilized
eq_tolerance: Set to specify the tolerance used when determining
whether two numbers are equal (default: 1e-12). This tolerance
will be used in checking equivalence of:
-quaternion lengths
-input vs. output abscissae
-quaternion direction (inner product)
Returns: an Mx4 element array of interpolated quaternions or -1L on
failure
;Notes:
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
The scalar component can be thought of as the amount of rotation that
the quaternion performs
While the code may seem a little esoteric, it is vectorized and
provides the most accurate results it can get
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: aaflores $
$LastChangedDate: 2016-04-05 12:33:56 -0700 (Tue, 05 Apr 2016) $
$LastChangedRevision: 20724 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qslerp.pro $
(See general/misc/quaternion/qslerp.pro)
Function: qtom
Purpose: transforms quaternions into rotation matrices
Inputs: a 4 element array representing a quaternion or an Nx4 element
array representing an array of quaternions
Returns: a 3x3 matrix or an Nx3x3 array
Notes: Implementation largely copied from the euve c library for
quaternions
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qtom.pro $
(See general/misc/quaternion/qtom.pro)
Function quaternion_rotation,v,q
Usage: v_prime = quaternion_rotation(v,q)
Purpose: Rotate a vector v using the quaternion q
Inputs: v: a 3 element array, or an Nx3 element array, representing the vectors
q: a 4 element array, or an Nx4 element array, representing UNIT quaternion(s)
Alternatively- If last_index=1 then:
arrays can be v: 3xN element array
Q: 4xN element array
Written by: Davin Larson
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/quaternion_rotation.pro $
(See general/misc/quaternion/quaternion_rotation.pro)
Function: qvalidate,q,argname,fxname
Purpose: validate inputs for the idl quaternion library
Inputs: q: a 4 element array, or an Nx4 element array, representing quaternion(s)
argname: the name of the argument to be used in error messages
Returns: an Nx4 array or -1, it will turn 4 element quaternion arrays
into 1x4 element quaternion arrays
Notes: This function is here because I noticed a lot of the error
checking code was being repeated, and it was making the functions
long and hard to read
Represention has q[0] = scalar component
q[1] = vector x
q[2] = vector y
q[3] = vector z
The vector component of the quaternion can also be thought of as
an eigenvalue of the rotation the quaterion performs
Written by: Patrick Cruce(pcruce@igpp.ucla.edu)
$LastChangedBy: pcruce $
$LastChangedDate: 2016-10-14 11:01:12 -0700 (Fri, 14 Oct 2016) $
$LastChangedRevision: 22098 $
$URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/tags/spedas_4_0/general/misc/quaternion/qvalidate.pro $
(See general/misc/quaternion/qvalidate.pro)