quaternion
shareExamples
quaternion's examples
- Simple module providing a quaternion class for manipulating rotations easily. Return the angle in radians between this quaternion and another. — “Python: module OpenGLContext.quaternion”,
- Quaternions are the things that scare all manner of mice and men. Quaternions have become a popular tool in 3d game development - and for a good reason. — “Part Five: Quaternions”,
- When Gibbs first deprecated the quaternion product and split it into a cross product and Generally, the quaternion advocates seem to feel the opponents are lazy or thick-headed, and that deeper understanding of quaternions would lead to deeper appreciation. — “Quaternion - CGAFaq”,
- In mathematics, the quaternions are a non-commutative extension of the complex numbers. Every quaternion is a real linear combination of the basis quaternions 1, i, j, and k, i.e. every quaternion is uniquely. — “Quaternion - Definition”,
- Quaternion definition, a group or set of four persons or things. See more. — “Quaternion | Define Quaternion at ”,
- Quaternions are commonly used to represent orientations and rotations in 3d games. They are more efficient than using 3d matrices in number of operations, storage and quaternions also avoid gimbal lock. Quaternion class * By Will Perone * Original: 12-09-2003 * Revised: 27-09-2003 * 22-11-2003 * 10-12. — “Quaternion Math Class”,
- In mathematics, the quaternions are a non-commutative extension of the complex numbers. Every quaternion is a real linear combination of the basis quaternions 1, i, j, and k, i.e. every quaternion is uniquely. — “Online Encyclopedia and Dictionary - Quaternion”, fact-
- This quaternion of revilers has traduced Origen, but not on the same grounds, one having found one cause of accusation against him, and another another; and thus each has demonstrated that what he has taken no objection to, he has fully accepted. — “quaternion - Wiktionary”,
- Quaternions are a mathematical construct that represents a rotation in three dimensions. There are two ways to explain a quaternion: the technical way and the practical way. — “Legacy:Quaternion - Unreal Wiki”,
- For other uses, see Quaternion (disambiguation). This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Graphical representation of quaternion units product as 90°-rotation. — “Quaternion - Wikipedia, the free encyclopedia”,
- Flash MX 2004 ActionScript2.0 Library: Quaternion - Wright Internet Solutions Implements the behaviours of the Quaternion Class -- provides methods for quaternion transformation. — “WIS AS2 Library : com.wis.math.alg.Quaternion Documentation”, members.shaw.ca
- Quaternion(float x, float y, float z, float w) Creates a quaternion from four components. Sets this quaternion to the rotation described by the given angle and normalized axis. — “Quaternion”,
- Maths - Quaternions. This page is an introduction to Quaternions, the pages below this have more detail about their algebra and how to use them to represent 3D rotations. Quaternions were discovered on 16 October 1843 by William Rowan Hamilton. — “Maths - Quaternions - Martin Baker”,
- Quaternion Julia fractals are created by the same principle as the more traditional Julia set except that it uses 4 dimensional complex numbers instead of 2 dimensional complex numbers. For more details on quaternion maths (how to add and multiple) see the reference given in the header above. — “Quaternion Julia Fractals”, local.wasp.uwa.edu.au
- A quaternion can be represented as. where w is the real component and x,y and z are the The same quaternion can also be expressed as. where w is the "scalar" and v = (x,y,z) is the "vector". Note, that even though v is called a vector, it is not a typical three dimensional vector but rather a. — “Quaternion - Math Images”,
- note that a quaternion algebra can be formed over a ﬁnite ﬁeld K, where every quaternion A principal interest in the study of quaternion algebras is the orders and ideals over an. — “QUATERNION ALGEBRAS”, echidna.maths.usyd.edu.au
- Explanation of quaternion and 3D rotation with quaternion Quaternion is a geometrical operator to represent the relationship (relative length and relative orientation) between two vectors in 3D space. — “Quaternion”, songho.ca
- quaternion n. A set of four persons or items. Mathematics . Any number of the form a + bi + cj + dk where a, b, c, and d are real numbers, ij = k, i. — “quaternion: Definition from ”,
Videos
related videos for quaternion
- Using Quaternion for Lagrangians in EM and GEM, Cartesian This talk shows how to derive the Maxwell equations starting from quaternions, a type of 4D number. A variation of the EM Lagrangian leads to the GEM field equations. A time dependent form of Newton's field equations can be seen in the GEM field equations, a good thing. The equations are written in Cartesian coordinates, the ones which I am most comfortable. Due to a question I was asked, I redid the derivation using manifestly covariant symbols.
- (unpronounceable) - Beyond the Back Door - Quaternion (unpronounceable) Beyond the Back Door Live at the Starry Plough Pub January 5, 2006 Kelly Back - Guitar Dave Grossman - Bass Jan Jackson - Drums The Quaternion Julia Fractal animation was created specifically for this video based on the cover art image from the CD of this show.
- Quaternion Julia Fractal Quaternion Julia set, rendered using POVRay. Spiral rotation out from 0,0 to the unit circle and back, ten rotations total. See www.gmilburn.ca
- Randomized Δ-Edge-Coloring via Quaternion of Complex Colors You can find our paper at
- Dynamics in the Quaternions This video documents a very early version (1989) of the visualization research that led to the project Quaternion Julia Sets in Virtual Reality that premiered at Supercomputing '95. In 1989 John Hart, a master of science graduate student in the computer science department at UIC, hit upon the idea of using a distance estimation technique witch made computation more efficient and provided a basis for determining surface orientation of three and higher dimensional fractal objects. In the video, MS Student John Hart presents a visualization of the quaternion extension of a single Julia Set. The Julia set is rotated in the complex plane, and action which causes dynamic alterations to its quaternion extension. In 2002, and informational CD-ROM was created that showcases the history of this visualization research. The website can be found at -- www.evl.uic.edu Additionally, More information can be found on the EVL website -- www.evl.uic.edu
- MIT IAP Animating New Physics Day 2: Quaternion Quantum Field Theory Demystified Day 2 of the Animating New Physics project, an Independent Activities Period at MIT event done independently by The Stand-Up Physicist Doug Sweetser, class of '84. Why is quantum mechanics weird? A new explanation is provided that is based on doing Newtonian calculus correctly in Einstein's spacetime via quaternions. Div, grad, curl and all that live in the house of quaternions. Four simple rules will be used to rewrite well-know physics equations with quaternions: 1) keep 4-vectors together 2) drop all factors of i 3) write all constants 4) make equations dimensionless. This approach will be applied to Newton's second law, the uncertainty principle, the Schrodinger wave equation, the Klein-Gordon equation and the Dirac equation. The links between these vital equations are clearer when the same algebra tools are used consistently. Using quaternion animations, a visual understanding of the differences between classical physics, quantum mechanics, and quantum field theory will be supplied.
- Quaternion Julia Set Morphing Quaternion Julia Set. Created with Visions Of Chaos. .au
- Geometric Skinning with Approximate Dual Quaternion Blending Accompanying video for paper "Geometric Skinning with Approximate Dual Quaternion Blending", TOG 2008.
- Quaternion Julia Set 02 A Video Rendered with vvvv. all fractal calculation is done by the graphics card using pixel shader 3.0
- Julia 4D - Comparing Quaternion and Hypercomplex Comparing the two most common types of math used for 3D rendering of the Julia fractal. The 3D rendering is obtained by using a subset of the 4D numbers. On the left is quaternion and on the right hypercomplex. Note that hypercomplex is often used to mean one particular type from the family of hypercomplex numbers, in this case the one given by i*j=j*i=k j*k=k*j=-i k*i=i*k=-j i*i=j*j=-k*k=-1 Quaternion is given by i*j=-j*i=k j*k=-k*j=i k*i=-i*k=j i*i=j*j=k*k=-1 The Julia fractal is rendered in the c space and z is fixed (z=z*z+c).
- Quaternion fractal Quaternion fractal
- APS Talk: Quaternion Quantum Field Theory This talk was prepared for the Fall 2010 New England Sections of the American Physical Society and the American Association of Physics Teachers (NES APS/AAPT) Meeting at Brown University. Here is the abstract: Quaternion quantum field theory is introduced. The goal is for every equation that plays a role in quantum field theory gets rewritten using real-valued quaternions. Like the correspondence principle before it, the method is simple and systematic: keep 4-vectors together, drop factors of i, keep the constants, but make the expression dimensionless if possible. The differences between classical, relativistic and quantum mechanics equations are based on their constants and form. There should be enough time to derive the Schrodinger and Klein-Gordon equations. More current information is available at
- Interactive Visualization of Quaternion Julia Sets (1989) This video documents a very early version of the visualization research which led to the project Quaternion Julia Sets in Virtual Reality that premiered at Supercomputing '95. In 1989 John Hart, a master of science graduate student in the computer science department at UIC, hit upon the idea of using a distance estimation technique witch made computation more efficient and provided a basis for determining surface orientation of three and higher dimensional fractal objects. In the video, MS Student John Hart and Lou Kauffman are interviewed and they explain Quaternion Julia Sets and the complexities of the project. They also demonstrate the very esoteric handshake of The Fraternity of the Quaternion. More information can be found on the EVL website -- www.evl.uic.edu
- Quaternion Julia Fractal A spin around a raytraced 3D slice of a Julia fractal in 4D quaternion space. The renderer consisted of a couple of hundred lines of C/C++ code and used no significant optimization, but was still able to render each frame in about 3 seconds on an AMD Athlon 1200.
- RotationProblem
- Using Quaternions for EM and GEM, Manifestly Covariant Form This talk shows how to derive the Maxwell equations starting from quaternions, a type of 4D number. A variation of the EM Lagrangian leads to the GEM field equations. A time dependent form of Newton's field equations can be seen in the GEM field equations, a good thing. NOTE: this is _exactly_ the same talk as one with a similar title, except I changed the notation from the Cartesian t, x, y, z to far more general 0-3 subscripts.
- Quaternion Fractal 1 Quaternions play an important role in quantum mechanics.
- embedded quaternion-based attitude estimation using kalman filtering This board Mariano Lizarraga and I built is tracking the attitude quaternion and the MEMS gyro biases using a Kalman filter. The filter is running embedded at 100Hz, all in floating point.
- Quaternion Julia Set 01 A Video Rendered with vvvv. all fractal calculation is done by the graphics card using pixel shader 3.0.
- Quaternion Interpolation For this project, I implemented three interpolation methods using quaternions. The three methods are Slerp( Spherical Linear Interpolation), Squad (Cubic Interpolation), and Lerp (Linear Interpolation). I am using OpenGL to render the scene.
- Quaternions and rotation (I know it's been covered a lot) storing overall rotation value in variables versus quaternions
- Quaternion Band playes "Superstition" (Stevie Wonder Cover) live in Studio 1 Arad www.quaternion.ro quaternion.hi5.com Trupa Quaternion din Arad cu piesa "Superstition" (Stevie Wonder Cover) live in Studio 1 in Arad, martie 2009; The Quaternion Band playes "Superstition" (Stevie Wonder Cover) live in Studio 1 Arad, March 2009
- Quaternion Preview Preview for the 4th in Q. I already broke a record, it's in the preview, you'll see. And if you see something that looks like a "2" in there, it's a cursive Q, okay? xD
- dual quaternions quaternion.110 Rotation and displacement of tetrahedron (rigid body) with dual quaternion q=qd*qr, where qd=1+ep+ep*i*2+ep*j*2+ep*j*2, qr=0.86603+i*0.35355+j*0+k*0.35355 Matlab animation.
- Graphs for Real, Complex, Quaternions, and Hypercomplex Numbers Graph theory is an area of study that details the ways vertices can be connected along edges. Edges can be either undirectional or directional. In this video, graph theory is applied to number theory with some interesting results. All directional edges are imaginary numbers. All undirectional edges are either the real numbers or hypercomplex numbers. It is speculated that the real numbers can most accurately be mapped to time, and the imaginary numbers to space.
- Command Line Quaternions: Gamma Matrices Gamma matrices are used in relativistic quantum field theory calculations. De Leo Nad researchers in Mexico (J. Lopex-Bonilla, L. Rosales-Roldan, and A. Xuniga-Segundo) have noticed that quaternion triple products can do the same work algebraically. Starting with one quaternion world line, 16 new ones can be generated by mixing up where t, x, y, and z go within the quaternion.
- Quaternion based Extended Kalman Filter for a 9DOF IMU A video showing our implementation of an Extended Kalman filter for the estimation of the position of the Inertial Motion Unit of STMicroelectronics iNEMO, a unit with a tri-axis accelerometer, tri-axis magnetometer and a tri-axis gyro. For information contact us: [email protected] [email protected] Source code and documentation available here:
- Command Line Quaternions: Addition Adding one quaternion over and over to another quaternion generates what physicists call an inertial observer. Amazing that the simplest step in math creates something at the foundation of special relativity
- Quaternion Julia Fractal A quaternion julia fractal, rendered with some early work-in-progress of a self-made renderer. The color is calculated from the interpolated surface normal at each intersection: color = (normal+(1,1,1))/2 The c parameter is linearly interpolated between a and b: a = -0.125 - 0.256i + 0.847j + 0.0895k b = 0.3145 + 0.8126i + 0.2125j - 0.6664k roughly ;) For more information on this refer to: 0) 1) local.wasp.uwa.edu.au 2) graphics.cs.uiuc.edu
- Line RIder - Quaternion 4th in Q. The .sol can be downloaded from but it probably only works on Macs. Anyways, enjoy, I probably forgot a few people in the credits, but MEH xD
- Quaternion Fractal 3 Quaternions play an important role in quantum mechanics.
- quaternion julia set transformation created with chaoscope
- Quaternion Camera This is the result of playing around with Quaternions and basic scene graphs for 2 days. The weapons fire shown towards the end of the video uses a pixel shader written in HLSL, but is extremely slow (with a few of them the FPS slows dramatically) and needs more time to improve.
- BARGOOMA! - HyperFunk - Quaternion Julia Fractal Animation BARGOOMA! - HyperFunk (Improv) Gene Jun (Idiot Flesh) - Guitar Dave Grossman (unpronounceable) - Bass (Bass Looping) Jan Jackson (unpronounceable) - Drums Quaternion raytraced animation done with POV-Ray.
- Mechanical Poet - Natural Quaternion pt1 Natural Quaternion (Sylphs - Gnomes - Undines - Salamanders) (Music by Lex and Tom / Lyrics by Lex) I. SYLPHS I see the border of the wild wood An endless raving tide Electric view from altitude The forest spreading far and wide I'm staring on these discomposed seas Imbibing gummy smells The blankets rise above the trees Decolourising scenic dells THE LABYRINTH OF LANES AMONG THE GALLERIES OF MEADOWS A CHARMING OUTDOOR MUSEUM THE PATHLESS ROCKY CHAINS AND SOMBRE HOLTS IN SHADOWS MAGNETIC VISIONS FROM A PREDAWN DREAM II. GNOMES Amid the stalks enamelled by a silver web Bestead by oaks drowsing in the nature's lap I sop the motley chips of dreams they saw the night before I hear the pulsing flumps of the enormous wooden core THE LABYRINTH OF LANES AMONG THE GALLERIES OF MEADOWS A CHARMING OUTDOOR MUSEUM UNSETTLED GLOOMY FENS ARE GUGGLING IN THE SHADOWS UNCANNY VISIONS FROM A CREEPY DREAM Backwoods! Wicked and impious brats Always ambush here under the snags Deadwoods! Dire and ill silhouettes Prowling shadows of ogres or hags Babbling the curses Invoking the fear Tapping the hearses So grim and severe They are blustering near! III. UNDINES Somnolent fall is performing its chime Boat-flies crawl in a slight pantomime Grasshopper's viol is joining the glee Tracing a sweet melody Music sweeps over the quiescent pool Sated with odorous cool Lanterns of glow-worms are wheeling so freely Choirs of crickets parade on a lily Night's brimming over with wonderful theme Dying away in ...
- New Quaternion Math Leads to New Reasons Why Physics Work This is the talk I will present to the 8th International Conference on Clifford Algebras in Campinas, Brazil. The new two limit quaternion derivative definition has a real directional derivative for classical physics, and the norm of a derivative for quantum mechanics.
- Quaternion Band - Smooth (Carlos Santana & Rob Thomas cover) LIVE ! quaternion.hi5.com http Trupa Quaternion din Arad Romania..........LIVE LIVE LIVE
- Quaternion Fractal 2 Quaternions play an important role in quantum mechanics.
On Twitter
twitter about quaternion
- thecoshman: @goss2326 its basically 10% for doing each of them, 10 easy % this is handy btw http://j.mp/j3hV5J
- thecoshman: @goss2326 wait a minute... just went to look on blackboard to see if quaternion LERP was as straightforwar… (cont) http://deck.ly/~P74sr
- goss2326: @thecoshman the quaternion does not represent the heading, the heading is a normal vector, to roll, you creat… (cont) http://deck.ly/~HmANw
- thecoshman: @goss2326 I've got the quaternion to matrix sorted... its how I rotate the orientation Q around the heading vector for roll etc.
- knight666: I somehow managed to make a quaternion camera gimbal lock. I suck.
- goss2326: @thecoshman http://j.mp/lPai6Z this shows how the quaternion is converted to a rotation matrix to perform th… (cont) http://deck.ly/~7J7oZ
- thecoshman: @goss2326 if I want to rotate a vector... can I just use it as a quaternion with an angle of 0 and rotate it about an axis?
- AssafRaman: @davidjrogers We may be also missing performance on intel pc, I see bullet has sse accelerated math for vector, quaternion, matrix and more.
- MelRox12: @S0phieH Quaternion.FromToRotation(AlignAxis,Vect) is the only extra, basically it takes one axis and align it to a given vector, simple?
- mendelsachs: Twistor Theory versus Quaternion GR http://bit.ly/fGCwbC
- NeoshamanTamago: @S0phieH sorry to bother you, did you have upside down gimbal lock when making sara's run? I use quaternion to align to contact and got it
- upperwell: Quaternion.CreateFromYawPitchRoll()とか簡単すぎてやばい
- engadget_rss: spatial location for iphone: quaternion & rotation matrix help: I need help with part of an iphone project... Ke... http://bit.ly/kMyXCa
- worldbiztweets: spatial location for iphone: quaternion & rotation matrix help: I need help with part of an iphone project. i wo... http://bit.ly/jzl7SX
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- Get_freelance: spatial location for iphone: quaternion & rotation matrix help: I need help with part of an iphone project... http:///3f9coo3
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- doodlehum: spatial location for iphone: quaternion & rotation matrix help: I need help with part of an iphone project. i wo... http://bit.ly/m4HvbZ
- sanjeev_insan: spatial location for iphone: quaternion & rotation matrix help: I need help with part of an iphone project. ... http://bit.ly/lfoHcM #fb
- sanjeev_insa: spatial location for iphone: quaternion & rotation matrix help: I need help with part of an iphone project. ... http://bit.ly/lfoHcM #fb
- w3digg: quaternion & rotation matrix help: I need help with part of an iphone project. i would like… http://goo.gl/fb/YcHfl
- fun_programming: #iphone #project spatial location for iphone by peelsasleep: quaternion & rotation matrix hel... http:///43putdz #dev #hiring
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- fleecebeast: AHA! Finally tracked down that quaternion bug that's been bothering me on and off for months. Oh quaternions, you're so crazy.
- wto_org: Digit UN staff and two pilots killed in shape accident in Bolivia: All quaternion Tied Nations staff in Bolivia ... http://bit.ly/jMfDWs
- NeoshamanTamago: Strange behaviour in unity, i'm using quaternion so what the ceiling run gimbal lock is for? only Transform Direction candidate for broken.
Blogs & Forum
blogs and forums about quaternion
“2) work out the rotation quaternion for each axis, by getting the dot 4) convert the rotation quaternion into a matrix and apply that rotation matrix”
— julapy " Blog Archive " quaternion rotation,“Positioning things in 3D can be difficult if you don't have a good understanding of, well, 3D. I often focus on cool new experiments, or some new feature”
— Geolocation in Papervision3D – Plus some Quaternion Stuff,“Quaternion Julia sets still explore the convergence of the system z z2 + c, but this time z and c are allowed to be quaternion-valued numbers. objects, only a slice (the intersection of the set with a plane) of the quaternion Julia sets is shown”
— Syntopia " Blog Archive " Quaternion Julia sets and GPU,“Mendel Sachs Discussion Forum " Mendel Sachs Physics Discussion Forums " Quaternion Calculus in General Relativity Users Browsing Forum. Yahoo! Bot and 0 Guests. Anisotropy of space-time. Quaternion Calculus in General Relativity. 1 Pages 1”
— Quaternion Calculus in General Relativity - Mendel Sachs,“ science forums and latest news discussions”
— Quaternion Waltz,“Softimage XSI Discussion Forum, Resources, Industry News and Features. Is there Quaternion Rotation(sp?) availble for XSI, to prevent Gimble Locks? right now I'm messing around with my animation, and I notice my Axis' are merging in to 1 axis, and causing a gimple lock. It's an ugly sight Atyss”
— XSI Base Forum - Quaternion Rotation?,“More than 20 Japanese flash coders share the blog/ You will be junkie for this crazy Japanese Flash news Quaternion notation employs an angle as the fourth element in its calculation of three-dimensional rotation”
— JActionScripters " Blog Archive " Quaternion notation of Vector3D,“Quaternion EM Where?”
— Quaternion EM... Where?, theidea.bz“Forum. Wiki. Pseudo-Inverse and Quaternion. Submitted by phamelin on Fri, http:///forum/orocos/orocos-users/kdl-patch-get-quaternion”
— Pseudo-Inverse and Quaternion | The Orocos Project,
Keywords
related keywords for quaternion
- quaternion rotation
- quaternion multiplication
- quaternion inverse
- quaternion interpolation
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- quaternion rotation between two points