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Home modified by Philipp Allgeuer

Philipp Allgeuer — Mon, 22 Jan 2018 11:36:49 -0000

--- v7
+++ v8
@@ -1,18 +1,48 @@
-#Matlab/Octave Rotations Library#
+# Matlab/Octave Rotations Library
+
 **Author:** Philipp Allgeuer
-**Version:** 1.3.0
-**Date:** 31/10/16

-##General Overview##
-The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant. For more information on fused angles and tilt angles, please refer to http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf . The *fused angles* and *tilt angles* rotation representations are the invention of the author.
+**Version:** 1.4.0

-##Getting Started##
-Clone the rotations library into the required local target directory. Usually when working with Matlab/Octave the `RotationsLib` directory will not be your working directory. Refer to `help LoadRotations` to see how to best add the `RotationsLib` directory to your path for a working session. It may be a good idea to initially run the unit tests of the library when getting started. Refer to `help LoadRotationsTest` to see how to best add the `Test` directory to your path for a working session, and refer to `help RunAllTests` for running of the unit tests. For example:
+**Date:** 22/01/18
+
+## General Overview
+The Matlab/Octave rotations library is a collection of functions, bundled as 
+m-scripts, that address computations and numerical handling of rotations in 3D 
+Euclidean space. The rotation representations that are supported are rotation 
+matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), 
+fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, 
+inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality 
+detection, vector rotation and much more have been implemented for each rotation 
+representation. Tilt vector addition and the relative and absolute tilt phase 
+spaces are also supported. Unit tests for each function are provided to ensure 
+that the library is performant. For more information on fused angles and tilt 
+angles, please refer to 
+http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf . The *fused 
+angles* and *tilt angles* rotation representations are the invention of the 
+author, as with the tilt phase space. 
+
+## Getting Started
+Clone the rotations library into the required local target directory. Usually
+when working with Matlab/Octave the `RotationsLib` directory will not be your
+working directory. Refer to `help LoadRotations` to see how to best add the
+`RotationsLib` directory to your path for a working session. It may be a good
+idea to initially run the unit tests of the library when getting started. Refer
+to `help LoadRotationsTest` to see how to best add the `Test` directory to your
+path for a working session, and refer to `help RunAllTests` for running of the
+unit tests. For example:

     >> run ../Libraries/RotationsLib/LoadRotationsTest.m
     >> RunAllTests('Normal')

-There is an element of randomisation in the unit tests in order to make them more encompassing. As such, there is a very minor chance that one of the tests fails because a single test case (one of often several tens of thousands) has an error above the prescribed allowable threshold. Although as much as possible has been done to try to avoid the possibility of such scenarios, the extent to which this is possible is limited by the presence of singularities in the rotation representations, floating point errors, and the use of (unavoidable and required) functions of high numerical sensitivity. For example:
+There is an element of randomisation in the unit tests in order to make them
+more encompassing. As such, there is a very minor chance that one of the tests
+fails because a single test case (one of often several tens of thousands) has an
+error above the prescribed allowable threshold. Although as much as possible has
+been done to try to avoid the possibility of such scenarios, the extent to which
+this is possible is limited by the presence of singularities in the rotation
+representations, floating point errors, and the use of (unavoidable and required)
+functions of high numerical sensitivity. For example:

     >> acos(1 - eps) % Expect acos(1) = 0
     ans =
@@ -26,26 +56,39 @@
     >> alpha = acos(2*(Quat(1)*Quat(1) + Quat(4)*Quat(4)) - 1)
     >> calpha = sqrt(1 - sth*sth - sphi*sphi)

-can quickly turn into comparatively larger errors in the output variables, for certain *highly specific* input scenarios.
+can quickly turn into comparatively larger errors in the output variables, for
+certain *highly specific* input scenarios.

-##Quick Help##
-Every function of the library is documented and well-commented, so a good starting point on how to use a particular function is the `help` command. A good starting point in understanding the conventions and formats used for the five rotation representations is `help Ensure*` and `help *Equal`, where `*` is any of `Euler`, `Fused`, `Quat`, `Rotmat` and `Tilt`. A summary of the five rotation representations is shown in the following table.
+## Quick Help
+Every function of the library is documented and well-commented, so a good
+starting point on how to use a particular function is the `help` command. A good
+starting point in understanding the conventions and formats used for the five
+rotation representations is `help Ensure*` and `help *Equal`, where `*`
+is any of `Euler`, `Fused`, `Quat`, `Rotmat` and `Tilt`. A summary of the five
+rotation representations is shown in the following table.

 **Representation** | **Code** | **Format** | **Universal set**
 --- |:---:| --- | ---
-ZYX Euler angles | `Euler` | `[psi theta phi] =`
`(yaw, pitch, roll)` | (-π,π] × \[-π/2,π/2\] × (-π,π]
-Fused angles | `Fused` | `[psi theta phi h] =`
`(fused yaw, fused pitch, fused roll)` | (-π,π] × \[-π/2,π/2\] × \[-π/2,π/2\] × {-1,1}
+ZYX Euler angles | `Euler` | `[psi theta phi] =`
`(yaw, pitch, roll)` | (-π,π] × [-π/2,π/2] × (-π,π]
+Fused angles | `Fused` | `[psi theta phi h] =`
`(fused yaw, fused pitch, fused roll)` | (-π,π] × [-π/2,π/2] × [-π/2,π/2] × {-1,1}
 Quaternion | `Quat` | `[w x y z]` | ℚ
 Rotation matrix | `Rotmat` | `3x3 matrix` | SO(3)
-Tilt angles | `Tilt` | `[psi gamma alpha] =`
`(fused yaw, tilt axis angle, tilt angle)` | (-π,π] × (-π,π] × \[0,π\]
+Tilt angles | `Tilt` | `[psi gamma alpha] =`
`(fused yaw, tilt axis angle, tilt angle)` | (-π,π] × (-π,π] × [0,π]

-Note that in the library, `ZVec` refers to the bottom row of the rotation matrix representation. This corresponds to the global z-axis, expressed in terms of the rotated coordinate frame. `Axis` refers to the representation of a rotation by its axis and angle of rotation.
+Note that in the library, `ZVec` refers to the bottom row of the rotation matrix 
+representation. This corresponds to the global z-axis, expressed in terms of the 
+rotated coordinate frame. `Axis` refers to the representation of a rotation by 
+its axis and angle of rotation.

-##Where To Get More Help?##
-If a look into the source code does not resolve an issue you have with the library, then you can contact the author at the email address given in the *Bugs and Improvements* section.
+## Where To Get More Help?
+If a look into the source code does not resolve an issue you have with the
+library, then you can contact the author at the email address given in the *Bugs
+and Improvements* section.

-##Bugs and Improvements##
-I welcome all feedback, suggestions and bug reports. If you improve or fix anything about the library then I encourage you to let me know so that the library can be improved for everyone!
+## Bugs and Improvements
+I welcome all feedback, suggestions and bug reports. If you improve or fix
+anything about the library then I encourage you to let me know so that the
+library can be improved for everyone!

 **Email:** `pallgeuer[at]ais.uni-bonn.de`

Home modified by Philipp Allgeuer

Philipp Allgeuer — Mon, 31 Oct 2016 14:25:31 -0000

--- v6
+++ v7
@@ -4,7 +4,7 @@
 **Date:** 31/10/16

 ##General Overview##
-The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant. For more information on fused angles and tilt angles, please refer to http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf. The *fused angles* and *tilt angles* rotation representations are the invention of the author.
+The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant. For more information on fused angles and tilt angles, please refer to http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf . The *fused angles* and *tilt angles* rotation representations are the invention of the author.

 ##Getting Started##
 Clone the rotations library into the required local target directory. Usually when working with Matlab/Octave the `RotationsLib` directory will not be your working directory. Refer to `help LoadRotations` to see how to best add the `RotationsLib` directory to your path for a working session. It may be a good idea to initially run the unit tests of the library when getting started. Refer to `help LoadRotationsTest` to see how to best add the `Test` directory to your path for a working session, and refer to `help RunAllTests` for running of the unit tests. For example:

Home modified by Philipp Allgeuer

Philipp Allgeuer — Mon, 31 Oct 2016 14:24:27 -0000

--- v5
+++ v6
@@ -1,10 +1,10 @@
 #Matlab/Octave Rotations Library#
 **Author:** Philipp Allgeuer
-**Version:** 1.2.1
-**Date:** 05/11/14
+**Version:** 1.3.0
+**Date:** 31/10/16

 ##General Overview##
-The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant. For more information on fused angles and tilt angles, please refer to http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf.
+The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant. For more information on fused angles and tilt angles, please refer to http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf. The *fused angles* and *tilt angles* rotation representations are the invention of the author.

 ##Getting Started##
 Clone the rotations library into the required local target directory. Usually when working with Matlab/Octave the `RotationsLib` directory will not be your working directory. Refer to `help LoadRotations` to see how to best add the `RotationsLib` directory to your path for a working session. It may be a good idea to initially run the unit tests of the library when getting started. Refer to `help LoadRotationsTest` to see how to best add the `Test` directory to your path for a working session, and refer to `help RunAllTests` for running of the unit tests. For example:
@@ -39,7 +39,7 @@
 Rotation matrix | `Rotmat` | `3x3 matrix` | SO(3)
 Tilt angles | `Tilt` | `[psi gamma alpha] =`
`(fused yaw, tilt axis angle, tilt angle)` | (-π,π] × (-π,π] × \[0,π\]

-The *fused angles* and *tilt angles* rotation representations are the invention of the author.
+Note that in the library, `ZVec` refers to the bottom row of the rotation matrix representation. This corresponds to the global z-axis, expressed in terms of the rotated coordinate frame. `Axis` refers to the representation of a rotation by its axis and angle of rotation.

 ##Where To Get More Help?##
 If a look into the source code does not resolve an issue you have with the library, then you can contact the author at the email address given in the *Bugs and Improvements* section.

Home modified by Philipp Allgeuer

Philipp Allgeuer — Fri, 28 Oct 2016 15:27:41 -0000

--- v4
+++ v5
@@ -4,7 +4,7 @@
 **Date:** 05/11/14

 ##General Overview##
-The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant.
+The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant. For more information on fused angles and tilt angles, please refer to http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf.

 ##Getting Started##
 Clone the rotations library into the required local target directory. Usually when working with Matlab/Octave the `RotationsLib` directory will not be your working directory. Refer to `help LoadRotations` to see how to best add the `RotationsLib` directory to your path for a working session. It may be a good idea to initially run the unit tests of the library when getting started. Refer to `help LoadRotationsTest` to see how to best add the `Test` directory to your path for a working session, and refer to `help RunAllTests` for running of the unit tests. For example:

Home modified by Philipp Allgeuer

Philipp Allgeuer — Sat, 14 Mar 2015 09:23:56 -0000

--- v3
+++ v4
@@ -39,9 +39,7 @@
 Rotation matrix | `Rotmat` | `3x3 matrix` | SO(3)
 Tilt angles | `Tilt` | `[psi gamma alpha] =`
`(fused yaw, tilt axis angle, tilt angle)` | (-π,π] × (-π,π] × \[0,π\]

-The *fused angles* and *tilt angles* rotation representations are the invention of the author, and are discussed academically in:
-
-> P. Allgeuer and S. Behnke, "Fused Angles for Body Orientation Representation", in *Proceedings of the 9th Workshop on Humanoid Soccer Robots, IEEE-RAS Int. Conference on Humanoid Robots*, Madrid, Spain, 2014.
+The *fused angles* and *tilt angles* rotation representations are the invention of the author.

 ##Where To Get More Help?##
 If a look into the source code does not resolve an issue you have with the library, then you can contact the author at the email address given in the *Bugs and Improvements* section.

Home modified by Philipp Allgeuer

Philipp Allgeuer — Wed, 05 Nov 2014 12:07:39 -0000

--- v2
+++ v3
@@ -1,7 +1,7 @@
 #Matlab/Octave Rotations Library#
 **Author:** Philipp Allgeuer
-**Version:** 1.2.0
-**Date:** 22/10/14
+**Version:** 1.2.1
+**Date:** 05/11/14

 ##General Overview##
 The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant.

Home modified by Philipp Allgeuer

Philipp Allgeuer — Tue, 04 Nov 2014 17:52:02 -0000

--- v1
+++ v2
@@ -1,8 +1,58 @@
-Welcome to your wiki!
+#Matlab/Octave Rotations Library#
+**Author:** Philipp Allgeuer
+**Version:** 1.2.0
+**Date:** 22/10/14

-This is the default page, edit it as you see fit. To add a new page simply reference it within brackets, e.g.: [SamplePage].
+##General Overview##
+The Matlab/Octave rotations library is a collection of functions, bundled as m-scripts, that address computations and numerical handling of rotations in 3D Euclidean space. The rotation representations that are supported are rotation matrices (`Rotmat`), Quaternions (`Quat`), intrinsic ZYX Euler angles (`Euler`), fused angles (`Fused`) and tilt angles (`Tilt`). Operations such as composition, inversion, ZYX yaw extraction, fused yaw extraction, random generation, equality detection, vector rotation and much more have been implemented for each rotation representation. Unit tests for each function are provided to ensure that the library is performant.

-The wiki uses [Markdown](/p/rotationslib/wiki/markdown_syntax/) syntax.
+##Getting Started##
+Clone the rotations library into the required local target directory. Usually when working with Matlab/Octave the `RotationsLib` directory will not be your working directory. Refer to `help LoadRotations` to see how to best add the `RotationsLib` directory to your path for a working session. It may be a good idea to initially run the unit tests of the library when getting started. Refer to `help LoadRotationsTest` to see how to best add the `Test` directory to your path for a working session, and refer to `help RunAllTests` for running of the unit tests. For example:

-[[members limit=20]]
+    >> run ../Libraries/RotationsLib/LoadRotationsTest.m
+    >> RunAllTests('Normal')
+
+There is an element of randomisation in the unit tests in order to make them more encompassing. As such, there is a very minor chance that one of the tests fails because a single test case (one of often several tens of thousands) has an error above the prescribed allowable threshold. Although as much as possible has been done to try to avoid the possibility of such scenarios, the extent to which this is possible is limited by the presence of singularities in the rotation representations, floating point errors, and the use of (unavoidable and required) functions of high numerical sensitivity. For example:
+
+    >> acos(1 - eps) % Expect acos(1) = 0
+    ans =
+      2.1073e-08
+    >> sqrt(0 + eps) % Expect sqrt(0) = 0
+    ans =
+      1.4901e-08
+
+This means that very tiny floating point errors in required expressions such as
+
+    >> alpha = acos(2*(Quat(1)*Quat(1) + Quat(4)*Quat(4)) - 1)
+    >> calpha = sqrt(1 - sth*sth - sphi*sphi)
+
+can quickly turn into comparatively larger errors in the output variables, for certain *highly specific* input scenarios.
+
+##Quick Help##
+Every function of the library is documented and well-commented, so a good starting point on how to use a particular function is the `help` command. A good starting point in understanding the conventions and formats used for the five rotation representations is `help Ensure*` and `help *Equal`, where `*` is any of `Euler`, `Fused`, `Quat`, `Rotmat` and `Tilt`. A summary of the five rotation representations is shown in the following table.
+
+**Representation** | **Code** | **Format** | **Universal set**
+--- |:---:| --- | ---
+ZYX Euler angles | `Euler` | `[psi theta phi] =`
`(yaw, pitch, roll)` | (-π,π] × \[-π/2,π/2\] × (-π,π]
+Fused angles | `Fused` | `[psi theta phi h] =`
`(fused yaw, fused pitch, fused roll)` | (-π,π] × \[-π/2,π/2\] × \[-π/2,π/2\] × {-1,1}
+Quaternion | `Quat` | `[w x y z]` | ℚ
+Rotation matrix | `Rotmat` | `3x3 matrix` | SO(3)
+Tilt angles | `Tilt` | `[psi gamma alpha] =`
`(fused yaw, tilt axis angle, tilt angle)` | (-π,π] × (-π,π] × \[0,π\]
+
+The *fused angles* and *tilt angles* rotation representations are the invention of the author, and are discussed academically in:
+
+> P. Allgeuer and S. Behnke, "Fused Angles for Body Orientation Representation", in *Proceedings of the 9th Workshop on Humanoid Soccer Robots, IEEE-RAS Int. Conference on Humanoid Robots*, Madrid, Spain, 2014.
+
+##Where To Get More Help?##
+If a look into the source code does not resolve an issue you have with the library, then you can contact the author at the email address given in the *Bugs and Improvements* section.
+
+##Bugs and Improvements##
+I welcome all feedback, suggestions and bug reports. If you improve or fix anything about the library then I encourage you to let me know so that the library can be improved for everyone!
+
+**Email:** `pallgeuer[at]ais.uni-bonn.de`
+
+##Screenshots##
+The screenshots below show an example of some graphical output of the Rotations Library.
+[[project_screenshots]]
+[[project_admins]]
 [[download_button]]

Home modified by Philipp Allgeuer

Philipp Allgeuer — Tue, 04 Nov 2014 17:40:28 -0000

Welcome to your wiki!

This is the default page, edit it as you see fit. To add a new page simply reference it within brackets, e.g.: [SamplePage].

The wiki uses Markdown syntax.

Project Members:

Philipp Allgeuer (admin)