| Type: | Package |
| Title: | Conversion Between Attitude Representations of DCM, Euler Angles, Quaternions, and Euler Vectors |
| Version: | 1.0.2 |
| Encoding: | UTF-8 |
| Description: | Conversion between attitude representations: DCM, Euler angles, Quaternions, and Euler vectors. Plus conversion between 2 Euler angle set types (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx). Fully vectorized code, with warnings/errors for Euler angles (singularity, out of range, invalid angle order), DCM (orthogonality, not proper, exceeded tolerance to unity determinant) and Euler vectors(not unity). Also quaternion and other useful functions. Based on SpinCalc by John Fuller and SpinConv by Paolo de Leva. |
| License: | GPL (≥ 3) |
| Author: | Jose Gama [aut, cre], John Fuller [aut, cph], Paolo Leva [aut, cph] |
| Maintainer: | Jose Gama <rxprtgama@gmail.com> |
| Repository: | CRAN |
| Repository/R-Forge/Project: | rspincalc |
| Repository/R-Forge/Revision: | 16 |
| Repository/R-Forge/DateTimeStamp: | 2015-07-16 22:34:34 |
| Date/Publication: | 2015-07-17 12:51:32 |
| NeedsCompilation: | no |
| Packaged: | 2015-07-16 22:45:13 UTC; rforge |
Convert from Direction Cosine Matrix to Euler Angles
Description
DCM2EA converts from Direction Cosine Matrix (DCM) to Euler Angles (EA).
Usage
DCM2EA(DCM, EulerOrder='zyx', tol = 10 * .Machine$double.eps, ichk = FALSE,
ignoreAllChk = FALSE)
Arguments
DCM |
Direction Cosine Matrix (DCM) is a rotation matrix 3x3 (N=1) or an array 3x3xN |
EulerOrder |
Euler Angles (EA) is a vector [psi, theta, phi] |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Details
Euler Angles (EA) xyz <=> x(roll) y(pitch) z(yaw) Type 1 Rotations (Tait-Bryan angles): xyz - xzy - yxz - yzx - zyx - zxy Singular if second rotation angle is -90 or 90 degrees. Type 2 Rotations (proper Euler angles): xyx - xzx - yxy - yzy - zxz - zyz Singular if second rotation angle is 0 or 180 degrees.
Euler angles [psi, theta, phi] range from -90 to 90 degrees. Tait-Bryan angles [psi, theta, phi] range from 0 to 180 degrees. Angles about Euler vectors range from 0 to 180 degrees.
Value
Euler Angles (EA) vector [psi, theta, phi]
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
DCM <- matrix(c(-0.3573404, -0.1515663, 0.9215940, 0.6460385, 0.6724915,
0.3610947, -0.6744939, 0.7244189, -0.1423907),3,3,byrow=TRUE)
DCM2EA(DCM,'xyz')
Convert from Direction Cosine Matrix to Euler Vectors
Description
DCM2EV converts from Direction Cosine Matrix (DCM) to Euler Vectors (EV).
Usage
DCM2EV(DCM, tol = 10 * .Machine$double.eps, ichk = FALSE, ignoreAllChk = FALSE)
Arguments
DCM |
Direction Cosine Matrix (DCM) is a rotation matrix 3x3 (N=1) or an array 3x3xN. |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
Euler Vectors (EV) vector [m1, m2, m3, MU]
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
DCM <- matrix(c(-0.3573404, -0.1515663, 0.9215940, 0.6460385, 0.6724915,
0.3610947, -0.6744939, 0.7244189, -0.1423907),3,3,byrow=TRUE)
DCM2EV(DCM)
Convert from Direction Cosine Matrix to rotation Quaternions
Description
DCM2Q converts from Direction Cosine Matrix (DCM) to Quaternions (Q).
Usage
DCM2Q(DCM, tol = 10 * .Machine$double.eps, ichk = FALSE, ignoreAllChk = FALSE)
Arguments
DCM |
Direction Cosine Matrix (DCM) is a rotation matrix 3x3 (N=1) or an array 3x3xN |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
Quaternion (Q) vector [q1, q2, q3, q4].
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
DCM <- matrix(c(-0.3573404, -0.1515663, 0.9215940, 0.6460385, 0.6724915,
0.3610947, -0.6744939, 0.7244189, -0.1423907),3,3,byrow=TRUE)
DCM2Q(DCM)
Generate uniform random direction cosine matrices
Description
DCMrandom generates uniform random direction cosine matrices.
Usage
DCMrandom(n=NA, tol = 10 * .Machine$double.eps, ignoreAllChk=FALSE)
Arguments
n |
Optional integer for the number of generated direction cosine matrices, default = 1. |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
DCM |
Direction cosine matrix or array (DCM). |
Author(s)
Jose Gama
Examples
DCMrandom()
DCMrandom(5)
Convert from Euler Angles to Direction Cosine Matrix
Description
EA2DCM converts from Euler Angles (EA) to Direction Cosine Matrix (DCM).
Usage
EA2DCM(EA, EulerOrder='zyx', tol = 10 * .Machine$double.eps, ichk = FALSE,
ignoreAllChk = FALSE)
Arguments
EA |
Euler Angles (EA) vector [psi, theta, phi]. |
EulerOrder |
Euler Order (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx) |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Details
Euler Angles (EA) xyz <=> x(roll) y(pitch) z(yaw) Type 1 Rotations (Tait-Bryan angles): xyz - xzy - yxz - yzx - zyx - zxy Singular if second rotation angle is -90 or 90 degrees. Type 2 Rotations (proper Euler angles): xyx - xzx - yxy - yzy - zxz - zyz Singular if second rotation angle is 0 or 180 degrees.
Euler angles [psi, theta, phi] range from -90 to 90 degrees. Tait-Bryan angles [psi, theta, phi] range from 0 to 180 degrees. Angles about Euler vectors range from 0 to 180 degrees.
Value
Direction Cosine Matrix (DCM) 3x3xN.
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
EAxyx <- c(-170.6607, 110.937, 136.2344) * (pi/180)
EA2DCM(EAxyx,'xyx')
Convert from Euler Angles to Euler Angles
Description
EA2EA converts from Euler Angles (EA) to Euler Angles (EA).
Usage
EA2EA(EA, EulerOrder1='zyx', EulerOrder2='zyx', tol = 10 * .Machine$double.eps,
ichk = FALSE, ignoreAllChk = FALSE)
Arguments
EA |
Euler Angles (EA) vector [psi, theta, phi]. |
EulerOrder1 |
Euler Order 1 (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx) |
EulerOrder2 |
Euler Order 2 (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx) |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Details
Euler Angles (EA) xyz <=> x(roll) y(pitch) z(yaw) Type 1 Rotations (Tait-Bryan angles): xyz - xzy - yxz - yzx - zyx - zxy Singular if second rotation angle is -90 or 90 degrees. Type 2 Rotations (proper Euler angles): xyx - xzx - yxy - yzy - zxz - zyz Singular if second rotation angle is 0 or 180 degrees.
Euler angles [psi, theta, phi] range from -90 to 90 degrees. Tait-Bryan angles [psi, theta, phi] range from 0 to 180 degrees. Angles about Euler vectors range from 0 to 180 degrees.
Value
Euler Angles (EA) vector [psi, theta, phi].
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
## Not run:
EAxyx <- c(-170.6607, 110.937, 136.2344)
EA2EA(EAxyx,'xyx','xyz')
EA2EA(EAxyx,'xyx','xzy')
EA2EA(EAxyx,'xyx','yzx')
EA2EA(EAxyx,'xyx','yxz')
EA2EA(EAxyx,'xyx','zxy')
EA2EA(EAxyx,'xyx','zyx')
EA2EA(EAxyx,'xyx','xzx')
EA2EA(EAxyx,'xyx','yxy')
EA2EA(EAxyx,'xyx','yzy')
EA2EA(EAxyx,'xyx','zxz')
EA2EA(EAxyx,'xyx','zyz')
## End(Not run)
Convert from Euler Angles to Euler Vectors
Description
EA2EV converts from Euler Angles (EA) to Euler Vectors (EV).
Usage
EA2EV(EA, EulerOrder='zyx', tol = 10 * .Machine$double.eps, ichk = FALSE,
ignoreAllChk = FALSE)
Arguments
EA |
Euler Angles (EA) vector [psi, theta, phi]. |
EulerOrder |
Euler Order (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx) |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Details
Euler Angles (EA) xyz <=> x(roll) y(pitch) z(yaw) Type 1 Rotations (Tait-Bryan angles): xyz - xzy - yxz - yzx - zyx - zxy Singular if second rotation angle is -90 or 90 degrees. Type 2 Rotations (proper Euler angles): xyx - xzx - yxy - yzy - zxz - zyz Singular if second rotation angle is 0 or 180 degrees.
Euler angles [psi, theta, phi] range from -90 to 90 degrees. Tait-Bryan angles [psi, theta, phi] range from 0 to 180 degrees. Angles about Euler vectors range from 0 to 180 degrees.
Value
Euler Vectors (EV) vector [m1, m2, m3, MU].
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
EAxyx <- c(-170.6607, 110.937, 136.2344) * (pi/180)
EA2EV(EAxyx,'xyx')
Convert from Euler Angles to rotation Quaternions
Description
EA2Q converts from Euler Angles (EA) to Quaternions (Q).
Usage
EA2Q(EA, EulerOrder='zyx', ichk = FALSE, ignoreAllChk = FALSE)
Arguments
EA |
Euler Angles (EA) vector [psi, theta, phi]. |
EulerOrder |
Euler Order (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx) |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Details
Euler Angles (EA) xyz <=> x(roll) y(pitch) z(yaw) Type 1 Rotations (Tait-Bryan angles): xyz - xzy - yxz - yzx - zyx - zxy Singular if second rotation angle is -90 or 90 degrees. Type 2 Rotations (proper Euler angles): xyx - xzx - yxy - yzy - zxz - zyz Singular if second rotation angle is 0 or 180 degrees.
Euler angles [psi, theta, phi] range from -90 to 90 degrees. Tait-Bryan angles [psi, theta, phi] range from 0 to 180 degrees. Angles about Euler vectors range from 0 to 180 degrees.
Value
Quaternions (Q) vector [q1, q2, q3, q4].
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
EAxyx <- c(-170.6607, 110.937, 136.2344) * (pi/180)
EA2Q(EAxyx,'xyx')
Generate uniform random Euler Angles
Description
EArandom generates uniform random Euler Angles.
Usage
EArandom(n=NA, EulerOrder='zyx', tol = 10 * .Machine$double.eps, ignoreAllChk=FALSE)
Arguments
n |
Optional integer for the number of generated Euler Angles, default = 1. |
EulerOrder |
Euler Order (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx). |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
EA |
Euler Angles (EA). |
Author(s)
Jose Gama
Examples
EArandom()
EArandom(5)
Convert from Euler Vectors to Direction Cosine Matrix
Description
EV2DCM converts from Euler Vectors (EV) to Direction Cosine Matrix (DCM).
Usage
EV2DCM(EV, tol = 10 * .Machine$double.eps, ichk = FALSE, ignoreAllChk = FALSE)
Arguments
EV |
Euler Vectors (EV) vector [m1, m2, m3, MU]. |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
Direction Cosine Matrix (DCM) 3x3xN.
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
EV <- c(-0.1995301, -0.8765382, -0.4380279, 114.4324 * (pi/180))
EV2DCM(EV,1e-7)
#EV2DCM(EV)
Convert from Euler Vectors to Euler Angles
Description
EV2EA converts from Euler Vectors (EV) to Euler Angles (EA).
Usage
EV2EA(EV, EulerOrder='zyx', tol = 10 * .Machine$double.eps, ichk = FALSE,
ignoreAllChk = FALSE)
Arguments
EV |
Euler Vectors (EV) vector [m1, m2, m3, MU]. |
EulerOrder |
Euler Order (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx) |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Details
Euler Angles (EA) xyz <=> x(roll) y(pitch) z(yaw) Type 1 Rotations (Tait-Bryan angles): xyz - xzy - yxz - yzx - zyx - zxy Singular if second rotation angle is -90 or 90 degrees. Type 2 Rotations (proper Euler angles): xyx - xzx - yxy - yzy - zxz - zyz Singular if second rotation angle is 0 or 180 degrees.
Euler angles [psi, theta, phi] range from -90 to 90 degrees. Tait-Bryan angles [psi, theta, phi] range from 0 to 180 degrees. Angles about Euler vectors range from 0 to 180 degrees.
Value
Euler Angles (EA) vector [psi, theta, phi].
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
## Not run:
EV <- c(-0.1995301, -0.8765382, -0.4380279, 114.4324 * (pi/180))
EV2EA(EV,'xyx')
## End(Not run)
Convert from Euler Vectors to rotation Quaternions
Description
EV2Q converts from Euler Vectors (EV) to Quaternions (Q).
Usage
EV2Q(EV, tol = 10 * .Machine$double.eps, ichk = FALSE, ignoreAllChk = FALSE)
Arguments
EV |
Euler Vectors (EV) vector [m1, m2, m3, MU]. |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
Quaternions (Q) vector [q1, q2, q3, q4].
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
EV <- c(-0.1995301, -0.8765382, -0.4380279, 114.4324 * (pi/180))
EV2Q(EV,1e-7)
#EV2Q(EV)
Generate uniform random Euler Vectors
Description
EVrandom generates uniform random Euler Vectors.
Usage
EVrandom(n=NA, tol = 10 * .Machine$double.eps, ignoreAllChk=FALSE)
Arguments
n |
Optional integer for the number of generated Euler Vectors, default = 1. |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
EV |
Euler Vectors (EV). |
Author(s)
Jose Gama
Examples
EVrandom()
EVrandom(5)
Convert from rotation Quaternions to Direction Cosine Matrix
Description
Q2DCM converts from Quaternions to Direction Cosine Matrix (DCM).
Usage
Q2DCM(Q, tol = 10 * .Machine$double.eps, ichk = FALSE, ignoreAllChk = FALSE)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
Direction Cosine Matrix (DCM) 3x3xN.
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q2DCM(Q)
Convert from rotation Quaternions to Euler Angles
Description
Q2EA converts from Quaternions (Q) to Euler Angles (EA) based on D. M.
Henderson (1977).
Q2EA.Xiao is the algorithm by J. Xiao (2013) for the Princeton Vision
Toolkit - included here to allow reproducible research.
Usage
Q2EA(Q, EulerOrder='zyx', tol = 10 * .Machine$double.eps, ichk = FALSE,
ignoreAllChk = FALSE)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
EulerOrder |
Euler Order (xyx, yzy, zxz, xzx, yxy, zyz, xyz, yzx, zxy, xzy, yxz, zyx). |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Details
Euler Angles (EA) xyz <=> x(roll) y(pitch) z(yaw) Type 1 Rotations (Tait-Bryan angles): xyz - xzy - yxz - yzx - zyx - zxy Singular if second rotation angle is -90 or 90 degrees. Type 2 Rotations (proper Euler angles): xyx - xzx - yxy - yzy - zxz - zyz Singular if second rotation angle is 0 or 180 degrees.
Euler angles [psi, theta, phi] range from -90 to 90 degrees. Tait-Bryan angles [psi, theta, phi] range from 0 to 180 degrees. Angles about Euler vectors range from 0 to 180 degrees.
Value
Euler Angles (EA) vector [psi, theta, phi].
Author(s)
Jose Gama
References
D. M. Henderson, 1977 Shuttle Program. Euler Angles, Quaternions, and Transformation Matrices Working Relationships. National Aeronautics and Space Administration (NASA), N77-31234/6
J. Xiao, 2013 Princeton Vision Toolkit. Available from: http://vision.princeton.edu/code.html http://vision.princeton.edu/pvt/GCBreader/quaternion.m
John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
## Not run:
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q2EA(Q,'xyx')
## End(Not run)
Convert from rotation Quaternions to Euler Vectors
Description
Q2EV converts from Quaternions (Q) to Euler Vectors (EV).
Usage
Q2EV(Q, tol = 10 * .Machine$double.eps, ichk = FALSE, ignoreAllChk = FALSE)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
tol |
Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. |
ichk |
Logical, FALSE=disables near-singularity warnings. |
ignoreAllChk |
Logical, TRUE=disables all warnings and error checks (use with caution!). |
Value
Euler Vectors (EV) vector [m1, m2, m3, MU].
Author(s)
Jose Gama
References
by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors
Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv
See Also
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q2EV(Q)
Convert from rotation Quaternions to OpenGL rotation matrix
Description
DCM2EA converts from Quaternions (Q) to OpenGL rotation matrix.
Usage
Q2GL(Q)
Arguments
Q |
rotation Quaternions (Q) vector [q1, q2, q3, q4]. |
Value
OpenGL rotation matrix 4x4xN.
Author(s)
Jose Gama
References
Python - IMU Brick 2012 http://www.tinkerforge.com/doc/Software/Bricks/IMU_Brick_Python.html
See Also
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q2GL(Q)
Angular difference between 2 quaternions
Description
QangularDifference returns the angular difference between 2 quaternions.
Usage
QangularDifference(Q1, Q2)
Arguments
Q1 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Q2 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Real value = angular difference between 2 quaternions.
Author(s)
Jose Gama
Examples
Q1 <- Qrandom()
Q2 <- Qrandom()
QangularDifference(Q1, Q2)
Quaternion conjugate
Description
Qconj performs a quaternion conjugate operation.
Usage
Qconj(Q)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Conjugate quaternion (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Qconj(Q)
Quaternion inverse
Description
Qinv calculated the quaternion inverse.
Usage
Qinv(Q)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Quaternion inverse (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Qinv(Q)
Linear quaternion interpolation
Description
Qlerp linear quaternion interpolation.
Qslerp spherical linear interpolation.
QslerpNoInvert version of slerp, used by squad, that does not check for theta > 90.
Qspline spherical cubic interpolation.
Qsquad spherical and Quadrangle linear interpolation.
Qbezier Shoemake-Bezier interpolation using De Castlejau algorithm.
Qspline for 3 quaternions, qn-1,qn and qn+1, calculate a control point to be used in spline interpolation.
Usage
Qlerp(Q1, Q2, fracT)
Arguments
Q1 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Q2 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
fracT |
Fraction of . |
Value
Q |
Zero or one-valued quaternion (Q) vector [q1, q2, q3, q4] or matrix n x 4. |
Author(s)
Jose Gama
Examples
Q1 <- Qrandom()
Q2 <- Qrandom()
Qlerp(Q1, Q2, 0.1)
Quaternion logarithm
Description
Qlog performs a quaternion logarithm operation.
Qexp performs a quaternion exponential operation.
Usage
Qlog(Q)
Qexp(Q)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Result quaternion (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Qlog(Q)
Qexp(Q)
Norm of a quaternion
Description
Qnorm calculates the norm of a quaternion.
Usage
Qnorm(Q)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Norm of the quaternion.
Author(s)
Jose Gama
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Qnorm(Q)
Quaternion normalization
Description
Qnormalize performs a quaternion normalization.
Usage
Qnormalize(Q)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Normalized quaternion (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Qnormalize(Q)
Generate uniform random unit quaternions
Description
Qrandom generates uniform random unit quaternions.
Usage
Qrandom(n=NA)
Arguments
n |
Optional integer for the number of generated quaternions, default = 1. |
Value
Q |
Uniform random unit quaternion (Q) vector [q1, q2, q3, q4] or matrix n x 4. |
Author(s)
Jose Gama
Examples
Qrandom()
Qrandom(5)
Updates current attitude quaternion
Description
Qrot updates the current attitude quaternion.
Usage
Qrot(Q, w, dT)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
w |
Angular rate values [wx, wy, wz]. |
dT |
Inverse of update rate. |
Value
Q |
Updated quaternion (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
w <- c(0.1, 0.2, 0.3)
dT <- -.12
Qrot(Q,w,dT)
Generate zero-valued quaternions
Description
Qzero generates zero-valued quaternions.
Qone generates one-valued quaternions.
Usage
Qzero(n=NA)
Arguments
n |
Optional integer for the number of generated quaternions, default = 1. |
Value
Q |
Zero or one-valued quaternion (Q) vector [q1, q2, q3, q4] or matrix n x 4. |
Author(s)
Jose Gama
Examples
Qzero()
Qzero(5)
Qone()
Qone(5)
Determine if the variable is a pure rotation matrix
Description
isPureRotationMatrix determines if a matrix is pure rotation matrix (proper orthogonal matrix) with det(m)==1.
isPureQuaternion determines if a quaternion is a pure quaternion.
isRealQuaternion determines if a quaternion is a real quaternion.
isUnitQuaternion determines if a quaternion is a unit quaternion.
Usage
isPureRotationMatrix(DCM, tol = 0.01)
Arguments
DCM |
Direction Cosine Matrix (DCM) is a rotation matrix 3x3 (N=1) or an array 3x3xN. |
tol |
Tolerance value. |
Value
Logical, TRUE = matrix is pure rotation matrix.
Author(s)
Jose Gama
See Also
Examples
isPureRotationMatrix(matrix(rep(0,9),3,3,byrow=TRUE),.1)
isPureRotationMatrix(matrix(rep(1,9),3,3,byrow=TRUE),.1)
isPureRotationMatrix(matrix(c(0,0,-1,0,1,0,1,0,1),3,3,byrow=TRUE),.1)
DCMx10 <- DCMrandom(10)
isPureRotationMatrix(DCMx10)
Rotate a vector by a quaternion
Description
vectQrot performs a vector rotation by a quaternion.
Usage
vectQrot(Q, rr)
Arguments
Q |
Quaternion (Q) vector [q1, q2, q3, q4]. |
rr |
Vector [x, y, z]. |
Value
Rotated vector [x, y, z].
Author(s)
Jose Gama
Examples
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
v <- c(1, 2, 3)
vectQrot(Q, v)
Quaternion multiplication
Description
%Q*% performs a quaternion multiplication.
Usage
Q1 %Q*% Q2
Arguments
Q1 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Q2 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Quaternion result of multiplication (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
## Not run:
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q %Q*% Q
## End(Not run)
Quaternion division
Description
%Q/% performs a quaternion division.
Usage
Q1 %Q/% Q2
Arguments
Q1 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Q2 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Quaternion result of division (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
## Not run:
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q %Q/% Q
## End(Not run)
Quaternion subtraction
Description
%Q-% performs a quaternion subtraction.
Usage
Q1 %Q-% Q2
Arguments
Q1 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Q2 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Quaternion result of subtraction (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
## Not run:
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q %Q-% Q
## End(Not run)
Quaternion addition
Description
%Q+% performs a quaternion addition.
Usage
Q1 %Q+% Q2
Arguments
Q1 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Q2 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Quaternion sum (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
## Not run:
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q %Q+% Q
## End(Not run)
Quaternion dot product
Description
%Q.% performs a quaternion dot product.
Usage
Q1 %Q.% Q2
Arguments
Q1 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Q2 |
Quaternion (Q) vector [q1, q2, q3, q4]. |
Value
Q |
Quaternion result of dot product (Q) vector [q1, q2, q3, q4]. |
Author(s)
Jose Gama
Examples
## Not run:
Q <- c(-0.1677489, -0.7369231, -0.3682588, 0.5414703)
Q %Q.% Q
## End(Not run)