- published: 18 Jan 2016
- views: 341627
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Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful.
Extra footage: https://youtu.be/ISbJ9S0fzwY
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Support us on Patreon: http://www.patreon.com/numberphile
Special thanks to these supporters:
Jeff Straathof
Christian Cooper
Peggy Youell
Ken Baron
Today I Found Out
Roman Urbanovski
Mehdi Razavi
John Buchan
Bill Shillito
Andrzej 'Yester' Fiedukowicz
Susan Silver
Lê
OK Merli
Spiked Math
RexDex
Thomas Buckingham
Peter Kær
Henry Reich
George Greene
Arnas
Paul Bates
Michael Surrago
plusunim
Tracy Parry
Stan Ciprian
Mark Klamerus
Keith Vertrees
Tyler O'Connor
Kristian Joensen
Valentin
James P Buckley
Michael
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for quaternion multiplication. For the sake of brevity, I don't cover the famous application to 3D rotations in this video (perhaps in a subsequent one) but, of course, one must first know how to multiply two quaternions before talking about specific applications.
- published: 19 Jun 2016
- views: 7935
An overview of what quaternians are, how to do a basic rotation in 3d space, and how to use software to do it easier. Made because I thought I worked harder than I should've needed to to rotate things in 3D space myself!
If you're trying to do quaternion arithmetic yourself, my favorite guide is here:
http://www.youtube.com/watch?v=r9jWCbpLvHw
It involves lattice multiplication, so you'd better be prepared! Khanacademy has a great primer here:
https://www.khanacademy.org/math/arithmetic/multiplication-division/lattice_multiplication/v/lattice-multiplication
And for a more detailed introduction, this much more personable teacher has appeared on the youtube scene since I made this video, and I've heard great things about it:
http://www.youtube.com/watch?v=uRKZnFAR7yw
Good luck!
- published: 28 Feb 2013
- views: 100018
Quaternions are the mathematical tool behind rotation calculation. People new in motion tracking designs could think Euler angles are more intuitive and simple than quaternions. It is in fact the opposite. If quaternions can look complicated at the beginning, this video targets to demystify quaternions and show how easy it is to use them.
- published: 20 Apr 2016
- views: 538
Watch this video in context on Unity's learning pages here - http://unity3d.com/learn/tutorials/modules/intermediate/scripting/quaternions
Quaternions are a system of rotation that allowed for smooth incremental rotations in objects. In this video, you were learn about the quaternion system used in Unity and you will explore a few of the methods that allow you to work with it.
Help us caption & translate this video!
http://amara.org/v/V69K/
- published: 27 Sep 2013
- views: 64458
http://demonstrations.wolfram.com/FromQuaternionTo3DRotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Any nonzero quaternion ? has a corresponding unitary (length one) quaternion in the same direction as ?. Unitary quaternions are an elegant and efficient way to formalize 3D rotations.
Contributed by: Isabelle Cattiaux-Huillard and Gudrun Albrecht
Audio created with WolframTones:
http://tones.wolfram.com
- published: 12 Dec 2013
- views: 8754
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent rotations of 3 dimensional space using some kind of analog of complex numbers for rotations of the plane.
This is the first of three lectures on this development, and here we set the stage by introducing complex numbers and explaining some of their natural links with rotations of the plane. There is a lot of information in this lecture, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further. In particular the last slide (page 9) could easily be stared at for an hour or two.
Even old hands at complex analysis may find something novel here to stimulate their thinking, as I insist on a completely logical and rational approach to mathematics--no waffling with angles or ``transcendental notions/functions'' involving ``real numbers''. In fact such a pure algebraic approach is exactly what is needed to set the stage for a good understanding of quaternions.
In particular you will learn that the most fundamental fact about complex numbers is properly stated using the notion of quadrance, that turns are a viable substitute for angles, and that the rational parametrization of a circle is intimately linked to a quadratic map at the level of complex numbers. These ideas will prepare us for appreciating the rotation problem in three dimensions, which we tackle in the next lecture, and then the introduction of quaternions, which we explain in the following one.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
- published: 17 May 2013
- views: 39910
Quaternions are like vector3's, but instead of a position in 3D space, it saves a rotation in 3D space.
Unity Engine used in accordance to the Unity3D End User License Agreement, found here:
http://unity3d.com/unity/unity-end-user-license-3.x.html
- published: 28 Jul 2011
- views: 38415
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors.
Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics, computer vision and crystallographic texture analysis. In practical applications, they can be used alongside other methods, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application.
In modern mathematical language, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore also a domain. In fact, the quaternions were the first noncommutative division algebra to be discovered. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by 
(Unicode U+210D, ℍ). It can also be given by the Clifford algebra classifications Cℓ0,2(R) ≅ Cℓ03,0(R). The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only two finite-dimensional division rings containing the real numbers as a proper subring, the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which quaternions are the largest associative algebra.
This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Quaternion
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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12:25Fantastic Quaternions - Numberphile
Fantastic Quaternions - NumberphileFantastic Quaternions - Numberphile
Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful. Extra footage: https://youtu.be/ISbJ9S0fzwY NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Support us on Patreon: http://www.patreon.com/numberphile Special thanks to these supporters: Jeff Straathof Christian Cooper Peggy Youell Ken Baron Today I Found Out Roman Urbanovski Mehdi Razavi John Buchan Bill Shillito Andrzej 'Yester' Fiedukowicz Susan Silver Lê OK Merli Spiked Math RexDex Thomas Buckingham Peter Kær Henry Reich George Greene Arnas Paul Bates Michael Surrago plusunim Tracy Parry Stan Ciprian Mark Klamerus Keith Vertrees Tyler O'Connor Kristian Joensen Valentin James P Buckley Michael -
17:51Quaternions Explained Briefly
Quaternions Explained BrieflyQuaternions Explained Briefly
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for quaternion multiplication. For the sake of brevity, I don't cover the famous application to 3D rotations in this video (perhaps in a subsequent one) but, of course, one must first know how to multiply two quaternions before talking about specific applications. -
13:41Quaternions Explained by Dan
Quaternions Explained by DanQuaternions Explained by Dan
An overview of what quaternians are, how to do a basic rotation in 3d space, and how to use software to do it easier. Made because I thought I worked harder than I should've needed to to rotate things in 3D space myself! If you're trying to do quaternion arithmetic yourself, my favorite guide is here: http://www.youtube.com/watch?v=r9jWCbpLvHw It involves lattice multiplication, so you'd better be prepared! Khanacademy has a great primer here: https://www.khanacademy.org/math/arithmetic/multiplication-division/lattice_multiplication/v/lattice-multiplication And for a more detailed introduction, this much more personable teacher has appeared on the youtube scene since I made this video, and I've heard great things about it: http://www.youtube.com/watch?v=uRKZnFAR7yw Good luck! -
39:07Quaternions
QuaternionsQuaternions
Lecture 09: The application of Unit Quaternions to rotations -
10:37Math for Game Developers - Rotation Quaternions
Math for Game Developers - Rotation QuaternionsMath for Game Developers - Rotation Quaternions
We build on the idea of axis-angle rotations to start constructing quaternions. Find the source code here: https://github.com/BSVino/MathForGameDevelopers/tree/quaternions Question? Leave a comment below, or ask me on Twitter: https://twitter.com/VinoBS -
5:21Arrow Tech Trivia - 11 - Demystify the Quaternion
Arrow Tech Trivia - 11 - Demystify the QuaternionArrow Tech Trivia - 11 - Demystify the Quaternion
Quaternions are the mathematical tool behind rotation calculation. People new in motion tracking designs could think Euler angles are more intuitive and simple than quaternions. It is in fact the opposite. If quaternions can look complicated at the beginning, this video targets to demystify quaternions and show how easy it is to use them. -
5:11Quaternions - Unity Official Tutorials
Quaternions - Unity Official TutorialsQuaternions - Unity Official Tutorials
Watch this video in context on Unity's learning pages here - http://unity3d.com/learn/tutorials/modules/intermediate/scripting/quaternions Quaternions are a system of rotation that allowed for smooth incremental rotations in objects. In this video, you were learn about the quaternion system used in Unity and you will explore a few of the methods that allow you to work with it. Help us caption & translate this video! http://amara.org/v/V69K/ -
0:25From Quaternion to 3D Rotation
From Quaternion to 3D RotationFrom Quaternion to 3D Rotation
http://demonstrations.wolfram.com/FromQuaternionTo3DRotation The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Any nonzero quaternion ? has a corresponding unitary (length one) quaternion in the same direction as ?. Unitary quaternions are an elegant and efficient way to formalize 3D rotations. Contributed by: Isabelle Cattiaux-Huillard and Gudrun Albrecht Audio created with WolframTones: http://tones.wolfram.com -
58:24FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I
FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions IFamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent rotations of 3 dimensional space using some kind of analog of complex numbers for rotations of the plane. This is the first of three lectures on this development, and here we set the stage by introducing complex numbers and explaining some of their natural links with rotations of the plane. There is a lot of information in this lecture, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further. In particular the last slide (page 9) could easily be stared at for an hour or two. Even old hands at complex analysis may find something novel here to stimulate their thinking, as I insist on a completely logical and rational approach to mathematics--no waffling with angles or ``transcendental notions/functions'' involving ``real numbers''. In fact such a pure algebraic approach is exactly what is needed to set the stage for a good understanding of quaternions. In particular you will learn that the most fundamental fact about complex numbers is properly stated using the notion of quadrance, that turns are a viable substitute for angles, and that the rational parametrization of a circle is intimately linked to a quadratic map at the level of complex numbers. These ideas will prepare us for appreciating the rotation problem in three dimensions, which we tackle in the next lecture, and then the introduction of quaternions, which we explain in the following one. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... . -
10:40ep8 What is a Quaternion? Unity3D Game Design Tutorial
ep8 What is a Quaternion? Unity3D Game Design Tutorialep8 What is a Quaternion? Unity3D Game Design Tutorial
Quaternions are like vector3's, but instead of a position in 3D space, it saves a rotation in 3D space. Unity Engine used in accordance to the Unity3D End User License Agreement, found here: http://unity3d.com/unity/unity-end-user-license-3.x.html
-
Fantastic Quaternions - Numberphile
Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful. Extra footage: https://youtu.be/ISbJ9S0fzwY NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Support us on Patreon: http://www.patreon.com/numberphile Special thanks to these supporters: Jeff Straathof Christian Cooper Peggy Youell Ken Baron Today I Found Out Roman Urbanovski Mehdi Razavi John Buchan Bill Shillito Andrzej 'Yester' Fiedukowicz Susan Silver Lê OK Merli Spiked Math RexDex Thomas Buckingham Peter Kær Henry Reich George Greene Arnas Pa...
published: 18 Jan 2016 -
Quaternions Explained Briefly
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for quaternion multiplication. For the sake of brevity, I don't cover the famous application to 3D rotations in this video (perhaps in a subsequent one) but, of course, one must first know how to multiply two quaternions before talking about specific applications.
published: 19 Jun 2016 -
Quaternions Explained by Dan
An overview of what quaternians are, how to do a basic rotation in 3d space, and how to use software to do it easier. Made because I thought I worked harder than I should've needed to to rotate things in 3D space myself! If you're trying to do quaternion arithmetic yourself, my favorite guide is here: http://www.youtube.com/watch?v=r9jWCbpLvHw It involves lattice multiplication, so you'd better be prepared! Khanacademy has a great primer here: https://www.khanacademy.org/math/arithmetic/multiplication-division/lattice_multiplication/v/lattice-multiplication And for a more detailed introduction, this much more personable teacher has appeared on the youtube scene since I made this video, and I've heard great things about it: http://www.youtube.com/watch?v=uRKZnFAR7yw Good luck!
published: 28 Feb 2013 -
-
Math for Game Developers - Rotation Quaternions
We build on the idea of axis-angle rotations to start constructing quaternions. Find the source code here: https://github.com/BSVino/MathForGameDevelopers/tree/quaternions Question? Leave a comment below, or ask me on Twitter: https://twitter.com/VinoBS
published: 11 Jul 2013 -
Arrow Tech Trivia - 11 - Demystify the Quaternion
Quaternions are the mathematical tool behind rotation calculation. People new in motion tracking designs could think Euler angles are more intuitive and simple than quaternions. It is in fact the opposite. If quaternions can look complicated at the beginning, this video targets to demystify quaternions and show how easy it is to use them.
published: 20 Apr 2016 -
Quaternions - Unity Official Tutorials
Watch this video in context on Unity's learning pages here - http://unity3d.com/learn/tutorials/modules/intermediate/scripting/quaternions Quaternions are a system of rotation that allowed for smooth incremental rotations in objects. In this video, you were learn about the quaternion system used in Unity and you will explore a few of the methods that allow you to work with it. Help us caption & translate this video! http://amara.org/v/V69K/
published: 27 Sep 2013 -
From Quaternion to 3D Rotation
http://demonstrations.wolfram.com/FromQuaternionTo3DRotation The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Any nonzero quaternion ? has a corresponding unitary (length one) quaternion in the same direction as ?. Unitary quaternions are an elegant and efficient way to formalize 3D rotations. Contributed by: Isabelle Cattiaux-Huillard and Gudrun Albrecht Audio created with WolframTones: http://tones.wolfram.com
published: 12 Dec 2013 -
FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent rotations of 3 dimensional space using some kind of analog of complex numbers for rotations of the plane. This is the first of three lectures on this development, and here we set the stage by introducing complex numbers and explaining some of their natural links with rotations of the plane. There is a lot of information in this lecture, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further. In particular the last slide (page 9) could easily be stared at ...
published: 17 May 2013 -
ep8 What is a Quaternion? Unity3D Game Design Tutorial
Quaternions are like vector3's, but instead of a position in 3D space, it saves a rotation in 3D space. Unity Engine used in accordance to the Unity3D End User License Agreement, found here: http://unity3d.com/unity/unity-end-user-license-3.x.html
published: 28 Jul 2011
Fantastic Quaternions - Numberphile
- Order: Reorder
- Duration: 12:25
- Updated: 18 Jan 2016
- views: 341627
Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful.
Extra footage: https://youtu.be/ISbJ9S0fzwY
NUMBERPHILE
Website:...
Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful.
Extra footage: https://youtu.be/ISbJ9S0fzwY
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Support us on Patreon: http://www.patreon.com/numberphile
Special thanks to these supporters:
Jeff Straathof
Christian Cooper
Peggy Youell
Ken Baron
Today I Found Out
Roman Urbanovski
Mehdi Razavi
John Buchan
Bill Shillito
Andrzej 'Yester' Fiedukowicz
Susan Silver
Lê
OK Merli
Spiked Math
RexDex
Thomas Buckingham
Peter Kær
Henry Reich
George Greene
Arnas
Paul Bates
Michael Surrago
plusunim
Tracy Parry
Stan Ciprian
Mark Klamerus
Keith Vertrees
Tyler O'Connor
Kristian Joensen
Valentin
James P Buckley
Michael
wn.com/Fantastic Quaternions Numberphile
Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful.
Extra footage: https://youtu.be/ISbJ9S0fzwY
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Support us on Patreon: http://www.patreon.com/numberphile
Special thanks to these supporters:
Jeff Straathof
Christian Cooper
Peggy Youell
Ken Baron
Today I Found Out
Roman Urbanovski
Mehdi Razavi
John Buchan
Bill Shillito
Andrzej 'Yester' Fiedukowicz
Susan Silver
Lê
OK Merli
Spiked Math
RexDex
Thomas Buckingham
Peter Kær
Henry Reich
George Greene
Arnas
Paul Bates
Michael Surrago
plusunim
Tracy Parry
Stan Ciprian
Mark Klamerus
Keith Vertrees
Tyler O'Connor
Kristian Joensen
Valentin
James P Buckley
Michael
- published: 18 Jan 2016
- views: 341627
Quaternions Explained Briefly
- Order: Reorder
- Duration: 17:51
- Updated: 19 Jun 2016
- views: 7935
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with...
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for quaternion multiplication. For the sake of brevity, I don't cover the famous application to 3D rotations in this video (perhaps in a subsequent one) but, of course, one must first know how to multiply two quaternions before talking about specific applications.
wn.com/Quaternions Explained Briefly
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for quaternion multiplication. For the sake of brevity, I don't cover the famous application to 3D rotations in this video (perhaps in a subsequent one) but, of course, one must first know how to multiply two quaternions before talking about specific applications.
- published: 19 Jun 2016
- views: 7935
Quaternions Explained by Dan
- Order: Reorder
- Duration: 13:41
- Updated: 28 Feb 2013
- views: 100018
An overview of what quaternians are, how to do a basic rotation in 3d space, and how to use software to do it easier. Made because I thought I worked harder tha...
An overview of what quaternians are, how to do a basic rotation in 3d space, and how to use software to do it easier. Made because I thought I worked harder than I should've needed to to rotate things in 3D space myself!
If you're trying to do quaternion arithmetic yourself, my favorite guide is here:
http://www.youtube.com/watch?v=r9jWCbpLvHw
It involves lattice multiplication, so you'd better be prepared! Khanacademy has a great primer here:
https://www.khanacademy.org/math/arithmetic/multiplication-division/lattice_multiplication/v/lattice-multiplication
And for a more detailed introduction, this much more personable teacher has appeared on the youtube scene since I made this video, and I've heard great things about it:
http://www.youtube.com/watch?v=uRKZnFAR7yw
Good luck!
wn.com/Quaternions Explained By Dan
An overview of what quaternians are, how to do a basic rotation in 3d space, and how to use software to do it easier. Made because I thought I worked harder than I should've needed to to rotate things in 3D space myself!
If you're trying to do quaternion arithmetic yourself, my favorite guide is here:
http://www.youtube.com/watch?v=r9jWCbpLvHw
It involves lattice multiplication, so you'd better be prepared! Khanacademy has a great primer here:
https://www.khanacademy.org/math/arithmetic/multiplication-division/lattice_multiplication/v/lattice-multiplication
And for a more detailed introduction, this much more personable teacher has appeared on the youtube scene since I made this video, and I've heard great things about it:
http://www.youtube.com/watch?v=uRKZnFAR7yw
Good luck!
- published: 28 Feb 2013
- views: 100018
Quaternions
- Order: Reorder
- Duration: 39:07
- Updated: 19 Dec 2014
- views: 45430
Lecture 09: The application of Unit Quaternions to rotations
Lecture 09: The application of Unit Quaternions to rotations
wn.com/Quaternions
Math for Game Developers - Rotation Quaternions
- Order: Reorder
- Duration: 10:37
- Updated: 11 Jul 2013
- views: 37539
We build on the idea of axis-angle rotations to start constructing quaternions.
Find the source code here: https://github.com/BSVino/MathForGameDevelopers/tree...
We build on the idea of axis-angle rotations to start constructing quaternions.
Find the source code here: https://github.com/BSVino/MathForGameDevelopers/tree/quaternions
Question? Leave a comment below, or ask me on Twitter: https://twitter.com/VinoBS
wn.com/Math For Game Developers Rotation Quaternions
Arrow Tech Trivia - 11 - Demystify the Quaternion
- Order: Reorder
- Duration: 5:21
- Updated: 20 Apr 2016
- views: 538
Quaternions are the mathematical tool behind rotation calculation. People new in motion tracking designs could think Euler angles are more intuitive and simple ...
Quaternions are the mathematical tool behind rotation calculation. People new in motion tracking designs could think Euler angles are more intuitive and simple than quaternions. It is in fact the opposite. If quaternions can look complicated at the beginning, this video targets to demystify quaternions and show how easy it is to use them.
wn.com/Arrow Tech Trivia 11 Demystify The Quaternion
Quaternions are the mathematical tool behind rotation calculation. People new in motion tracking designs could think Euler angles are more intuitive and simple than quaternions. It is in fact the opposite. If quaternions can look complicated at the beginning, this video targets to demystify quaternions and show how easy it is to use them.
- published: 20 Apr 2016
- views: 538
Quaternions - Unity Official Tutorials
- Order: Reorder
- Duration: 5:11
- Updated: 27 Sep 2013
- views: 64458
Watch this video in context on Unity's learning pages here - http://unity3d.com/learn/tutorials/modules/intermediate/scripting/quaternions
Quaternions are a sy...
Watch this video in context on Unity's learning pages here - http://unity3d.com/learn/tutorials/modules/intermediate/scripting/quaternions
Quaternions are a system of rotation that allowed for smooth incremental rotations in objects. In this video, you were learn about the quaternion system used in Unity and you will explore a few of the methods that allow you to work with it.
Help us caption & translate this video!
http://amara.org/v/V69K/
wn.com/Quaternions Unity Official Tutorials
Watch this video in context on Unity's learning pages here - http://unity3d.com/learn/tutorials/modules/intermediate/scripting/quaternions
Quaternions are a system of rotation that allowed for smooth incremental rotations in objects. In this video, you were learn about the quaternion system used in Unity and you will explore a few of the methods that allow you to work with it.
Help us caption & translate this video!
http://amara.org/v/V69K/
- published: 27 Sep 2013
- views: 64458
From Quaternion to 3D Rotation
- Order: Reorder
- Duration: 0:25
- Updated: 12 Dec 2013
- views: 8754
http://demonstrations.wolfram.com/FromQuaternionTo3DRotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new...
http://demonstrations.wolfram.com/FromQuaternionTo3DRotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Any nonzero quaternion ? has a corresponding unitary (length one) quaternion in the same direction as ?. Unitary quaternions are an elegant and efficient way to formalize 3D rotations.
Contributed by: Isabelle Cattiaux-Huillard and Gudrun Albrecht
Audio created with WolframTones:
http://tones.wolfram.com
wn.com/From Quaternion To 3D Rotation
http://demonstrations.wolfram.com/FromQuaternionTo3DRotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Any nonzero quaternion ? has a corresponding unitary (length one) quaternion in the same direction as ?. Unitary quaternions are an elegant and efficient way to formalize 3D rotations.
Contributed by: Isabelle Cattiaux-Huillard and Gudrun Albrecht
Audio created with WolframTones:
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- published: 12 Dec 2013
- views: 8754
FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I
- Order: Reorder
- Duration: 58:24
- Updated: 17 May 2013
- views: 39910
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with h...
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent rotations of 3 dimensional space using some kind of analog of complex numbers for rotations of the plane.
This is the first of three lectures on this development, and here we set the stage by introducing complex numbers and explaining some of their natural links with rotations of the plane. There is a lot of information in this lecture, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further. In particular the last slide (page 9) could easily be stared at for an hour or two.
Even old hands at complex analysis may find something novel here to stimulate their thinking, as I insist on a completely logical and rational approach to mathematics--no waffling with angles or ``transcendental notions/functions'' involving ``real numbers''. In fact such a pure algebraic approach is exactly what is needed to set the stage for a good understanding of quaternions.
In particular you will learn that the most fundamental fact about complex numbers is properly stated using the notion of quadrance, that turns are a viable substitute for angles, and that the rational parametrization of a circle is intimately linked to a quadratic map at the level of complex numbers. These ideas will prepare us for appreciating the rotation problem in three dimensions, which we tackle in the next lecture, and then the introduction of quaternions, which we explain in the following one.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
wn.com/Famousmathprobs 13A The Rotation Problem And Hamilton's Discovery Of Quaternions I
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent rotations of 3 dimensional space using some kind of analog of complex numbers for rotations of the plane.
This is the first of three lectures on this development, and here we set the stage by introducing complex numbers and explaining some of their natural links with rotations of the plane. There is a lot of information in this lecture, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further. In particular the last slide (page 9) could easily be stared at for an hour or two.
Even old hands at complex analysis may find something novel here to stimulate their thinking, as I insist on a completely logical and rational approach to mathematics--no waffling with angles or ``transcendental notions/functions'' involving ``real numbers''. In fact such a pure algebraic approach is exactly what is needed to set the stage for a good understanding of quaternions.
In particular you will learn that the most fundamental fact about complex numbers is properly stated using the notion of quadrance, that turns are a viable substitute for angles, and that the rational parametrization of a circle is intimately linked to a quadratic map at the level of complex numbers. These ideas will prepare us for appreciating the rotation problem in three dimensions, which we tackle in the next lecture, and then the introduction of quaternions, which we explain in the following one.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
- published: 17 May 2013
- views: 39910
ep8 What is a Quaternion? Unity3D Game Design Tutorial
- Order: Reorder
- Duration: 10:40
- Updated: 28 Jul 2011
- views: 38415
Quaternions are like vector3's, but instead of a position in 3D space, it saves a rotation in 3D space.
Unity Engine used in accordance to the Unity3D End User...
Quaternions are like vector3's, but instead of a position in 3D space, it saves a rotation in 3D space.
Unity Engine used in accordance to the Unity3D End User License Agreement, found here:
http://unity3d.com/unity/unity-end-user-license-3.x.html
wn.com/Ep8 What Is A Quaternion Unity3D Game Design Tutorial
Quaternions are like vector3's, but instead of a position in 3D space, it saves a rotation in 3D space.
Unity Engine used in accordance to the Unity3D End User License Agreement, found here:
http://unity3d.com/unity/unity-end-user-license-3.x.html
- published: 28 Jul 2011
- views: 38415
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12:25
Fantastic Quaternions - Numberphile
Dr James Grime discusses a type of number beyond the complex numbers, and why they are use...
published: 18 Jan 2016
Fantastic Quaternions - Numberphile
Fantastic Quaternions - Numberphile
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- published: 18 Jan 2016
- views: 341627
17:51
Quaternions Explained Briefly
This is a video I have been wanting to make for some time, in which I discuss what the qua...
published: 19 Jun 2016
Quaternions Explained Briefly
Quaternions Explained Briefly
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- published: 19 Jun 2016
- views: 7935
13:41
Quaternions Explained by Dan
An overview of what quaternians are, how to do a basic rotation in 3d space, and how to us...
published: 28 Feb 2013
Quaternions Explained by Dan
Quaternions Explained by Dan
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- published: 28 Feb 2013
- views: 100018
39:07
Quaternions
Lecture 09: The application of Unit Quaternions to rotations
published: 19 Dec 2014
Quaternions
Quaternions
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- published: 19 Dec 2014
- views: 45430
10:37
Math for Game Developers - Rotation Quaternions
We build on the idea of axis-angle rotations to start constructing quaternions.
Find the ...
published: 11 Jul 2013
Math for Game Developers - Rotation Quaternions
Math for Game Developers - Rotation Quaternions
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- published: 11 Jul 2013
- views: 37539
5:21
Arrow Tech Trivia - 11 - Demystify the Quaternion
Quaternions are the mathematical tool behind rotation calculation. People new in motion tr...
published: 20 Apr 2016
Arrow Tech Trivia - 11 - Demystify the Quaternion
Arrow Tech Trivia - 11 - Demystify the Quaternion
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- published: 20 Apr 2016
- views: 538
5:11
Quaternions - Unity Official Tutorials
Watch this video in context on Unity's learning pages here - http://unity3d.com/learn/tut...
published: 27 Sep 2013
Quaternions - Unity Official Tutorials
Quaternions - Unity Official Tutorials
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- published: 27 Sep 2013
- views: 64458
0:25
From Quaternion to 3D Rotation
http://demonstrations.wolfram.com/FromQuaternionTo3DRotation
The Wolfram Demonstrations P...
published: 12 Dec 2013
From Quaternion to 3D Rotation
From Quaternion to 3D Rotation
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- published: 12 Dec 2013
- views: 8754
58:24
FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimension...
published: 17 May 2013
FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I
FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I
- Report rights infringement
- published: 17 May 2013
- views: 39910
10:40
ep8 What is a Quaternion? Unity3D Game Design Tutorial
Quaternions are like vector3's, but instead of a position in 3D space, it saves a rotation...
published: 28 Jul 2011
ep8 What is a Quaternion? Unity3D Game Design Tutorial
ep8 What is a Quaternion? Unity3D Game Design Tutorial
- Report rights infringement
- published: 28 Jul 2011
- views: 38415
Fantastic Quaternions - Numberphile...
Quaternions Explained Briefly...
Quaternions Explained by Dan...
Quaternions...
Math for Game Developers - Rotation Quaternions...
Arrow Tech Trivia - 11 - Demystify the Quaternion...
Quaternions - Unity Official Tutorials...
From Quaternion to 3D Rotation...
FamousMathProbs 13a: The rotation problem and Hami...
ep8 What is a Quaternion? Unity3D Game Design Tuto...
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[VIDEO] FBI's New Probe Of Clinton Emails Linked To Weiner Sexting Case
Edit WorldNews.com 28 Oct 2016
The FBI's letter, sent 11 days before Election Day, reopens a controversy that has roiled the Clinton campaign for months.In Manchester, N.H., earlier today Donald Trump told a cheering crowd the election "might not be as rigged as I thought." ... The case was then closed.Today, Comey said ... "We cannot let her take her criminal scheme into the Oval Office." . ....
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FBI: New Clinton emails prompt further investigation
Edit The Associated Press 28 Oct 2016
WASHINGTON (AP) -- The FBI is telling Congress it is investigating whether new emails that may contain classified information have emerged in its probe of Hillary Clinton's private server ... ....
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Second Large Court Judgment This Year Against Johnson & Johnson Use Of Talc
Edit WorldNews.com 28 Oct 2016
For the second time this year, Johnson and Johnson was ordered to pay multi-million dollar judgments to a defendant who claimed the company’s talcum powder products cause ovarian cancer, a report from the Inquistr Friday said. In February, the company was ordered to pay the family of Jackie Fox, who is deceased, $72 million in damages. This week, a St ... Talc is a mineral substance composed of magnesium, oxygen and silicon....
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We Now Have All The New Horizons Data From Pluto
Edit IFL Science 28 Oct 2016
After over 15 months since the historic flyby of Pluto, NASA has finally finished the downlink of New Horizons' full set of data. The last item was a segment of an observation sequence about Pluto and its largest moon Charon. It finally arrived at the mission operations center at the Johns Hopkins Applied Physics Laboratory (APL) at 5.48 am EDT on October 25 ... ....
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Hillary Clinton calls on FBI to immediately release all information it has on newly discovered emails
Edit NZ Herald 29 Oct 2016
DES MOINES, Iowa (AP) " Hillary Clinton calls on FBI to immediately release all information it has on newly discovered emails ... ....
Celebrate Hamilton Day, a Better Mathematical Holiday
Edit Slate 14 Oct 2016
Quaternions—that’s what Hamilton called his number quadruples—have proven extremely useful, for one thing. Eclipsed for much of the 20th century by such tools as vector analysis and matrix algebra, quaternions have more recently enjoyed a renaissance ... We have quaternions to thank for Tomb Raider’s Lara Croft, for the eye-popping special effects in The Matrix Reloaded, and for Curiosity’s 2012 landing on Mars....
Government of Canada invests up to $54 million in next-generation aircraft technologies (Department of Industry of Canada)
Edit Public Technologies 11 Oct 2016
'The Horizon Technology Demonstration Program presents a singular opportunity for Quaternion Aerospace, a company on the West Coast, to participate in a novel aircraft development program of national interest ... In addition to Bombardier, the companies that make up the consortium are Rolls-Royce, Thales, OPAL-RT, Quaternion Aerospace, FusiA, Liebherr, Axis, and Microturbo (Safran)....
Government of Canada invests up to $54 million in next-generation aircraft technologies (ITO - Industrial Technologies Office)
Edit Public Technologies 11 Oct 2016
'The Horizon Technology Demonstration Program presents a singular opportunity for Quaternion Aerospace, a company on the West Coast, to participate in a novel aircraft development program of national interest ... In addition to Bombardier, the companies that make up the consortium are Rolls-Royce, Thales, OPAL-RT, Quaternion Aerospace, FusiA, Liebherr, Axis, and Microturbo (Safran)....
Government of Canada invests up to $54 million in next-generation aircraft technologies (Government of Canada)
Edit Public Technologies 11 Oct 2016
'The Horizon Technology Demonstration Program presents a singular opportunity for Quaternion Aerospace, a company on the West Coast, to participate in a novel aircraft development program of national interest ... In addition to Bombardier, the companies that make up the consortium are Rolls-Royce, Thales, OPAL-RT, Quaternion Aerospace, FusiA, Liebherr, Axis, and Microturbo (Safran)....
Innovation Minister Navdeep Bains announces aerospace funding of up to $54 million (AIAC - Aerospace Industries Association of Canada)
Edit Public Technologies 11 Oct 2016
(Source. AIAC - Aerospace Industries Association of Canada) October 11, 2016 ... The consortium will be led by Bombardier; its partners are Rolls-Royce, Thales, Microturbo (Safran), Liebherr, OPAL-RT, Quaternion Aerospace, FusiA, Axis, the University of Victoria, Ryerson University, the University of Toronto, McGill University, National Research Council Canada, and Polytechnique Montréal ... Associated Links. ... About AIAC. ... For information.....
Sparton Navigation and Exploration Launches Next Generation AHRS with the AHRS-M2
Edit Stockhouse 26 Sep 2016
Sparton Navigation and Exploration Launches Next Generation AHRS with the AHRS-M2. Sparton Navigation and Exploration, a business unit of Sparton Corporation (NYSE.SPA), announced the release of the revolutionary AHRS-M2. The AHRS-M2 is a next generation Attitude Heading Reference System (AHRS) that delivers industry leading heading accuracy ... Features of AHRS-M2. ... • Full 360° rollover capability using quaternions or rotation matrix ... or....
Sparton Navigation and Exploration Launches Next Generation AHRS with the AHRS-M2 (Sparton Corporation)
Edit Public Technologies 26 Sep 2016
(Source. Sparton Corporation). DE LEON SPRINGS, Fla.--(BUSINESS WIRE)--Sep. 26, 2016-- Sparton Navigation and Exploration, a business unit of Sparton Corporation (NYSE.SPA), announced the release of the revolutionary AHRS-M2. The AHRS-M2 is a next generation Attitude Heading Reference System (AHRS) that delivers industry leading heading accuracy ... Features of AHRS-M2. ... • Full 360° rollover capability using quaternions or rotation matrix ... or....
Bruker Introduces New Generation of EBSD Detectors and Software for Advanced Post-Processing and Visualization of 3D EBSD/EDS Data Cubes (Bruker Corporation)
Edit Public Technologies 25 Jul 2016
(Source. Bruker Corporation) ... Due to an increase in sensitivity by a factor of three compared to its predecessor eFlash, the new eFlash will significantly expand the range of application fields where high-speed EBSD can be used ... He continued. 'With its state-of-the-art quaternion based approach, ESPRIT QUBE is the most advanced analytical software for processing and visualizing 3D EBSD and EDS data sets ... About Bruker Corporation (NASDAQ....
UNB scientists receive $4.3 million in NSERC discovery research grants (UNB - University of New Brunswick)
Edit Public Technologies 23 Jun 2016
Quantum groups and Quaternions; $16,000/year for 5 years Lavery, Jacqueline - Researcher, Biology; $35,000/year for 3 years MacQuarrie, Kerry - Professor, Civil Engineering; Science Director, Canadian Rivers Institute; Improving our understanding and predictions of the impacts of groundwater extraction on small streams; $22,000/year for 5 years ......
It’s not rocket science, but networking brings us all together
Edit The Irish Times 16 Oct 2015
What do social media, the street outside your door, your blood vessels and the number of people who catch the flu have in common?. All involve connecting networks of one kind or another ... Real-world advantages ... It is held each year on October 16th to commemorate the day when, in a flash of inspiration, Irish mathematician William Rowan Hamilton invented a new form of algebra, Quaternions, that is still in widespread use today....
William Rowan Hamilton: walker, graffiti artist, genius | Access Science
Edit The Irish Times 08 Oct 2015
When William Rowan Hamilton etched the formula for quaternions into Broombridge at Cabra one October morning in 1843, his act of graffiti made a major mark on mathematics. The four-dimensional quaternions he described have since enabled developments in telecommunications, computer and movie animation and even space travel, but it doesn’t stop there ... the piece is called One Small Scratch for a Man, One Giant Leap for Mathematics....
DAZ 3D Announces Launch of Victoria 7
Edit Seattle Post 24 Jun 2015
DAZ 3D announced today their release of Victoria 7, the latest edition in a line of the most successful and widely used female 3D figures in the world to the DAZ Marketplace. Salt Lake City, Utah (PRWEB) June 23, 2015 ... With Victoria 7 being based on Genesis 3, customers also get the advantages of dual quaternion skin-binding, non-triangle meshes, an optional lower resolution figure and UDIM standard UV's ... About DAZ 3D....
Fairchild Launches MEMS Product Line with Introduction of Intelligent IMU with High Performance 9-Axis Sensor Fusion (Fairchild Semiconductor International Inc)
Edit noodls 16 Jun 2015
(Source ... SAN JOSE, Calif. - June 16, 2015 - Fairchild (NASDAQ ... When combined with the XKF3 sensor fusion algorithms, the FIS1100 is the world's first complete consumer inertial measurement unit with orientation (quaternion) specifications, featuring pitch and roll accuracy of ±3° and yaw accuracy of ±5°. The FIS1100 uses Fairchild's proprietary MEMS process, designed specifically for inertial sensors ... Availability ... About Fairchild ... (noodl....
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