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Home modified by Philipp Allgeuer

Philipp Allgeuer — Mon, 22 Jan 2018 12:25:14 -0000

--- v7
+++ v8
@@ -1,14 +1,14 @@
-#Rotations Conversion Library#
+# Rotations Conversion Library
 **Author:** Philipp Allgeuer
-**Version:** 1.1.0
-**Date:** 12/08/16
+**Version:** 1.2.0
+**Date:** 22/01/18

-##General Overview##
-The Rotations Conversion Library (RCL) is a collection of functions that address common 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`). In addition to the core competency of being able to convert between each of the representations, operations such as inversion, ZYX yaw extraction, fused yaw extraction, renormalisation, equality detection, vector rotation and much more have been implemented. Unit tests for each function are provided to ensure that the library performs exactly as it should. The implementation of the Rotations Conversion Library is based on the very related Matlab/Octave Rotations Library (MORL), which is a highly tested reference implementation for the required conversion algorithms (see https://sourceforge.net/projects/rotationslib/).
+## General Overview
+The Rotations Conversion Library (RCL) is a collection of functions that address common 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`). In addition to the core competency of being able to convert between each of the representations, operations such as inversion, ZYX yaw extraction, fused yaw extraction, renormalisation, equality detection, vector rotation and much more have been implemented. 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 performs exactly as it should. The implementation of the Rotations Conversion Library is based on the very related Matlab/Octave Rotations Library (MORL), which is a highly tested reference implementation for the required conversion algorithms (see https://sourceforge.net/projects/rotationslib/).

-Please note that the ***fused angles*** and ***tilt angles*** rotation representations are the invention of the author, and have been specifically designed to overcome the many limitations and peculiarities of the Euler angles representation. More information can be found in the IROS paper *"Fused Angles: A Representation of Body Orientation for Balance"* (at time of writing available online at http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf).
+Please note that the ***fused angles*** and ***tilt angles*** rotation representations are the invention of the author, and have been specifically designed to overcome the many limitations and peculiarities of the Euler angles representation. More information can be found in the IROS paper *"Fused Angles: A Representation of Body Orientation for Balance"* (at time of writing available online at http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf). The tilt phase space is also an invention of the author.

-##Getting Started##
+## Getting Started
 This library is implemented as a collection of platform-independent C++ source files. To get started (if you haven't done so already) download the latest ZIP of the library from the SourceForge page, and extract it to the desired location on your computer.

 There are three ways of using the library:
@@ -18,9 +18,7 @@

 Due to the small and efficient nature of the library, one of the first two options is recommended. Very minimal benefit is expected from building a dynamic library.

-Note that as at release v1.1.0, the required source files are simply `rot_conv.h` and `rot_conv.cpp`.
-
-##Notes on Numerical Stability##
+## Notes on Numerical Stability
 Although as much as possible has been done to try to avoid the problems associated with numerical stability and accuracy, 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:
 ~~~
 Code:
@@ -41,7 +39,7 @@
 ~~~
 can quickly turn into comparatively larger errors in the output variables, for certain *highly specific* input scenarios.

-##Quick Help##
+## Quick Help
 Every function of the library is well-commented. A summary of the five rotation representations is shown in the following table.

 **Representation** | **Code** | **Format** | **Universal set**
@@ -54,10 +52,10 @@

 The ***fused angles*** and ***tilt angles*** rotation representations are the invention of the author (see *General Overview*).

-##Where To Get More Help?##
+## 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##
+## 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 — Fri, 28 Oct 2016 15:15:25 -0000

--- v6
+++ v7
@@ -6,7 +6,7 @@
 ##General Overview##
 The Rotations Conversion Library (RCL) is a collection of functions that address common 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`). In addition to the core competency of being able to convert between each of the representations, operations such as inversion, ZYX yaw extraction, fused yaw extraction, renormalisation, equality detection, vector rotation and much more have been implemented. Unit tests for each function are provided to ensure that the library performs exactly as it should. The implementation of the Rotations Conversion Library is based on the very related Matlab/Octave Rotations Library (MORL), which is a highly tested reference implementation for the required conversion algorithms (see https://sourceforge.net/projects/rotationslib/).

-Please note that the ***fused angles*** and ***tilt angles*** rotation representations are the invention of the author, and have been specifically designed to overcome the many limitations and peculiarities of the Euler angles representation. More information can be found in the IROS paper *"Fused Angles: A Representation of Body Orientation for Balance"* (at time of writing available online at http://www.ais.uni-bonn.de/papers/IROS_2015_Allgeuer.pdf).
+Please note that the ***fused angles*** and ***tilt angles*** rotation representations are the invention of the author, and have been specifically designed to overcome the many limitations and peculiarities of the Euler angles representation. More information can be found in the IROS paper *"Fused Angles: A Representation of Body Orientation for Balance"* (at time of writing available online at http://www.ais.uni-bonn.de/~pallgeuer/papers/IROS_2015_fused.pdf).

 ##Getting Started##
 This library is implemented as a collection of platform-independent C++ source files. To get started (if you haven't done so already) download the latest ZIP of the library from the SourceForge page, and extract it to the desired location on your computer.

Home modified by Philipp Allgeuer

Philipp Allgeuer — Fri, 12 Aug 2016 16:59:43 -0000

--- v5
+++ v6
@@ -1,7 +1,7 @@
 #Rotations Conversion Library#
 **Author:** Philipp Allgeuer
-**Version:** 1.0.1
-**Date:** 11/08/16
+**Version:** 1.1.0
+**Date:** 12/08/16

 ##General Overview##
 The Rotations Conversion Library (RCL) is a collection of functions that address common 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`). In addition to the core competency of being able to convert between each of the representations, operations such as inversion, ZYX yaw extraction, fused yaw extraction, renormalisation, equality detection, vector rotation and much more have been implemented. Unit tests for each function are provided to ensure that the library performs exactly as it should. The implementation of the Rotations Conversion Library is based on the very related Matlab/Octave Rotations Library (MORL), which is a highly tested reference implementation for the required conversion algorithms (see https://sourceforge.net/projects/rotationslib/).
@@ -18,7 +18,7 @@

 Due to the small and efficient nature of the library, one of the first two options is recommended. Very minimal benefit is expected from building a dynamic library.

-Note that as at release v1.0.1, the required source files are simply `rot_conv.h` and `rot_conv.cpp`.
+Note that as at release v1.1.0, the required source files are simply `rot_conv.h` and `rot_conv.cpp`.

 ##Notes on Numerical Stability##
 Although as much as possible has been done to try to avoid the problems associated with numerical stability and accuracy, 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:

Home modified by Philipp Allgeuer

Philipp Allgeuer — Thu, 11 Aug 2016 14:57:40 -0000

--- v4
+++ v5
@@ -46,11 +46,11 @@

 **Representation** | **Code** | **Format** | **Universal set**
 --- |:---:| --- | ---
-ZYX Euler angles | `Euler` |  (ψ, θ, φ) = 
`(yaw, pitch, roll)` | (-π,π] × \[-π/2,π/2\] × (-π,π]
-Fused angles | `Fused` | `(ψ, θ, φ, h) =`
`(fused yaw, fused pitch, fused roll, hemi)` | (-π,π] × \[-π/2,π/2\] × \[-π/2,π/2\] × {-1,1}
-Quaternion | `Quat` | `(w, x, y, z)]` | ℚ
+ZYX Euler angles | `Euler` |  (ψ, θ, φ) =
`(yaw, pitch, roll)` | (-π,π] × \[-π/2,π/2\] × (-π,π]
+Fused angles | `Fused` | (ψ, θ, φ, h) =
`(fused yaw, fused pitch, fused roll, hemi)` | (-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` | `(ψ, γ, α) =`
`(fused yaw, tilt axis angle, tilt angle)` | (-π,π] × (-π,π] × \[0,π\]
+Tilt angles | `Tilt` | (ψ, γ, α) =
`(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 (see *General Overview*).

Home modified by Philipp Allgeuer

Philipp Allgeuer — Thu, 11 Aug 2016 14:55:13 -0000

--- v3
+++ v4
@@ -47,10 +47,10 @@
 **Representation** | **Code** | **Format** | **Universal set**
 --- |:---:| --- | ---
 ZYX Euler angles | `Euler` |  (ψ, θ, φ) = 
`(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
+Fused angles | `Fused` | `(ψ, θ, φ, h) =`
`(fused yaw, fused pitch, fused roll, hemi)` | (-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` | `(ψ, γ, α) =`
`(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 (see *General Overview*).

Home modified by Philipp Allgeuer

Philipp Allgeuer — Thu, 11 Aug 2016 14:31:15 -0000

--- v2
+++ v3
@@ -22,24 +22,23 @@

 ##Notes on Numerical Stability##
 Although as much as possible has been done to try to avoid the problems associated with numerical stability and accuracy, 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:
-
 ~~~
 Code:
-std::cout << "Expect acos(1) = 0, but with an epsilon of error it is " << acos(1.0 - std::numeric_limits<double>::epsilon()) << std::endl;
-std::cout << "Expect sqrt(0) = 0, but with an epsilon of error it is " << sqrt(0.0 + std::numeric_limits<double>::epsilon()) << std::endl;
+double eps = std::numeric_limits<double>::epsilon();
+std::cout << "Epsilon is " << eps << std::endl;
+std::cout << "Expect acos(1) = 0, but with an epsilon of error it is " << acos(1.0 - eps) << std::endl;
+std::cout << "Expect sqrt(0) = 0, but with an epsilon of error it is " << sqrt(0.0 + eps) << std::endl;

 Output:
+Epsilon is 2.22045e-16
 Expect acos(1) = 0, but with an epsilon of error it is 2.10734e-08
 Expect sqrt(0) = 0, but with an epsilon of error it is 1.49012e-08
 ~~~
-
 This means that very tiny floating point errors in required expressions such as
-
 ~~~
 double alpha = acos(2.0*(q.w()*q.w() + q.z()*q.z()) - 1.0)
 double calpha = sqrt(1.0 - (sth*sth + sphi*sphi))
 ~~~
-
 can quickly turn into comparatively larger errors in the output variables, for certain *highly specific* input scenarios.

 ##Quick Help##
@@ -47,7 +46,7 @@

 **Representation** | **Code** | **Format** | **Universal set**
 --- |:---:| --- | ---
-ZYX Euler angles | `Euler` | `[psi theta phi] =`
`(yaw, pitch, roll)` | (-π,π] × \[-π/2,π/2\] × (-π,π]
+ZYX Euler angles | `Euler` |  (ψ, θ, φ) = 
`(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)

Home modified by Philipp Allgeuer

Philipp Allgeuer — Thu, 11 Aug 2016 13:45:55 -0000

--- v1
+++ v2
@@ -1,8 +1,70 @@
-Welcome to your wiki!
+#Rotations Conversion Library#
+**Author:** Philipp Allgeuer
+**Version:** 1.0.1
+**Date:** 11/08/16

-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 Rotations Conversion Library (RCL) is a collection of functions that address common 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`). In addition to the core competency of being able to convert between each of the representations, operations such as inversion, ZYX yaw extraction, fused yaw extraction, renormalisation, equality detection, vector rotation and much more have been implemented. Unit tests for each function are provided to ensure that the library performs exactly as it should. The implementation of the Rotations Conversion Library is based on the very related Matlab/Octave Rotations Library (MORL), which is a highly tested reference implementation for the required conversion algorithms (see https://sourceforge.net/projects/rotationslib/).

-The wiki uses [Markdown](/p/rotconvlib/wiki/markdown_syntax/) syntax.
+Please note that the ***fused angles*** and ***tilt angles*** rotation representations are the invention of the author, and have been specifically designed to overcome the many limitations and peculiarities of the Euler angles representation. More information can be found in the IROS paper *"Fused Angles: A Representation of Body Orientation for Balance"* (at time of writing available online at http://www.ais.uni-bonn.de/papers/IROS_2015_Allgeuer.pdf).

-[[members limit=20]]
+##Getting Started##
+This library is implemented as a collection of platform-independent C++ source files. To get started (if you haven't done so already) download the latest ZIP of the library from the SourceForge page, and extract it to the desired location on your computer.
+
+There are three ways of using the library:
+1. Directly include the source files in your project, and build them with the rest of your project.
+2. Build a static library (e.g. `*.a` or `*.lib`) of the source code and link your project to it.
+3. Build a dynamic library (e.g. `*.so` or `*.dll`) of the source code and link your project to it.
+
+Due to the small and efficient nature of the library, one of the first two options is recommended. Very minimal benefit is expected from building a dynamic library.
+
+Note that as at release v1.0.1, the required source files are simply `rot_conv.h` and `rot_conv.cpp`.
+
+##Notes on Numerical Stability##
+Although as much as possible has been done to try to avoid the problems associated with numerical stability and accuracy, 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:
+
+~~~
+Code:
+std::cout << "Expect acos(1) = 0, but with an epsilon of error it is " << acos(1.0 - std::numeric_limits<double>::epsilon()) << std::endl;
+std::cout << "Expect sqrt(0) = 0, but with an epsilon of error it is " << sqrt(0.0 + std::numeric_limits<double>::epsilon()) << std::endl;
+
+Output:
+Expect acos(1) = 0, but with an epsilon of error it is 2.10734e-08
+Expect sqrt(0) = 0, but with an epsilon of error it is 1.49012e-08
+~~~
+
+This means that very tiny floating point errors in required expressions such as
+
+~~~
+double alpha = acos(2.0*(q.w()*q.w() + q.z()*q.z()) - 1.0)
+double calpha = sqrt(1.0 - (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 well-commented. 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 (see *General Overview*).
+
+##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 Conversion Library.
+[[project_screenshots]]
+[[project_admins]]
 [[download_button]]

Home modified by Philipp Allgeuer

Philipp Allgeuer — Thu, 11 Aug 2016 12:11:08 -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)