quaternions's examples

  • There seems to be a great deal of confusion and apprehension regarding quaternions in the game industry. In this author's experience, everything from commercial engine source to forum and newsgroup posts to books directed towards game developers. — “Quaternions - Games and Simulations”,
  • Quaternions in Classical Mechanics. The invention of the calculus of quaternions is a step Quaternions were invented by Sir William Rowan Hamilton as an extension to the complex. — “Quaternions in Classical Mechanics”,
  • Using quaternions, as opposed to storing the three Euler angles of in three GLfloats or a Quaternions are not subject to gimbal lock. Euler angles are, so quaternions will allow. — “iPhone Development: OpenGL ES from the Ground Up 9”,
  • Computer graphics uses quaternions as coordinates for rotations and orientations. environmental niche, quaternions work so well they are able to. — “Quaternions”, cs.caltech.edu
  • Hamilton also created the quaternion, an interesting mathematical notion, but it finds no Curiously, quaternions can be applied to relativity, and some examples will be given. — “Quaternions”, mysite.du.edu
  • Quaternions are numbers of the form , where , , and are real numbers and each of denotes The need for quaternions became apparent after the successful introduction of complex. — “Quaternions - encyclopedia article - Citizendium”,
  • 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 ”,
  • In mathematics, the quaternions are a non-commutative extension of the complex numbers. form the quaternion group of order 8, Q8.The scalar part of the quaternion is a while. — “Quaternion - Definition”,
  • In this tutorial I hope to shed some light on the mystery shrouding these so-called quaternions which are all the buzz these days. of thorough, yet elementary, explanations of the quaternions, and have yet to find anything satisfactory. — “Quaternions - GPWiki”,
  • For other uses, see Quaternion (disambiguation). This article includes a list of In mathematics, the quaternions are a number system that extends the. — “Quaternion - Wikipedia, the free encyclopedia”,
  • Description The skew body of quaternions is an usefull tool to handle The product of the quaternions (a, b, c, d)(w, x, y, z) = (aw+by+cz+dx, ax+bw+cz−dy, ay. — “Package quaternions'”, cran.r-
  • The non-zero quaternions form a group under multiplication with (1,0, The unit quaternions, which lie on a 3-sphere embedded in 4-space, form a subgroup. — “HAKMEM QUATERNIONS -- DRAFT, NOT YET PROOFED”,
  • If you are interested in better understanding quaternions, look at the proof that quaternions can be used to compute rotations Quaternions are an extension of complex numbers. Instead of just i, we have three different numbers that are. — “Using Quaternions to Represent Rotation”, genesis3
  • The quaternion number system was discovered by Hamilton, a physicist who was looking for Quaternions have developed a wide-spread. use in computer graphics and robotics research. — “QUATERNIONS”, graphics.idav.ucdavis.edu
  • Definition of Quaternions in the Online Dictionary. Meaning of Quaternions. Pronunciation of Quaternions. Translations of Quaternions. Quaternions synonyms, Quaternions antonyms. Information about Quaternions in the free online English. — “Quaternions - definition of Quaternions by the Free Online”,
  • The set of Quaternions is an algebraic structure first studied by the and physicists alike, for it was hoped that quaternions would provide. — “Abstract Algebra/Quaternions - Wikibooks, collection of open”,
  • Quaternions are not an invention but parts of the procedure had to be invented in order The use of quaternions has a profound effect on science because: 1) It recognizes a. — “Iverson and Pond On Quaternions”,
  • Maths - Quaternions. This page is an introduction to Quaternions, the pages below this Quaternions form an interesting algebra where each object contains 4 scalar variables. — “Maths - Quaternions - Martin Baker”,

related videos for quaternions

  • Polar Representations of Quaternions The polar representation of quaternions is identical to what happens for complex numbers except the imaginary i gets replaced by an imaginary 3-vector, i, j, and k. To get to an event from the origin requires heading off in a certain direction at a certain speed. This is what the polar representation of quaternions accomplishes. The preprint is available at
  • Quaternion fractal Quaternion fractal
  • Derive Maxwell and More: Why, Plus quaternions and Hypercomplex numbers 1 of 4 Day 1 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. This 28 minute video covers why I do this research. There is a pop quiz to see if you have the math skills to follow the rest of the work. An explanation of quaternions and hypercomplex numbers is provided. Tell God what to say using high school math (can you factor B2 - E2?) packaged in an old and unfamiliar way known as quaternions. Applying the Euler-Lagrange equations to this Lagrangian (about as tough as a Sudoku puzzle), the Maxwell equations will be derived. The derivation will be repeated with an even less popular rule for spacetime multiplication, one with no minus signs at all, leading to field equations for gravity. Combine these two, and the result unifies gravity with the other three forces of Nature but without the Higgs. The Lagrangian and field equations all fit on a t-shirt.
  • 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
  • Skinning with Dual Quaternions Accompanying video for paper "Skinning with Dual Quaternions", I3D 2007.
  • 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.
  • 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
  • Physics FAQ: Maxwell and quaternions The Stand-Up Physicist short answer to short question: What about the hidden work by Maxwell using quaternions? No worries, it is an Internet rumor which when investigated, turned up nothing interesting. Web references Maxwell treatise, edition 1, the section: bit.ly Andre Waser's paper:
  • 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 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
  • Quaternions and Floretions in Blender Since my last video I've written a Python script to generate these shapes and forms (in effect short algorithms based on quaternion/floretion multiplication) directly in Blender. This is great as it saves me a lot of time in testing algorithm parameters and researching possibilities. Thanks to Manolo Camp for the first song (Butterfly)!
  • Quaternion Fractal 2 Quaternions play an important role in quantum mechanics.
  • GEM Blog: Quaternions for Third Graders A dramatic reading of the blog "Quaternions for Third Graders" by The Stand-Up Physicist available at Science20.com (bit.ly In this episode, the properties of numbers are demonstrated using clay balls and pipe cleaners.
  • 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.
  • 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.
  • Interaction And Quaternions Simple program to demonstrate my shiney new quaternion class, my new input manager and my new OBJ file importer :) All written in C++ in a couple of weeks. The framerate is solid on my PC, but the video capture looks a bit jumpy :( Designed to be used with a Gamepad, was actually a bit of a pain using SDL to get the joystick inputs. Quaternion and camera classes work really well, and the mesh loader is comming along nicely! Update soon ;)
  • Quaternion Fractal 1 Quaternions play an important role in quantum mechanics.
  • IET Dissertation: PSD on top of dual-quaternion skinning This video shows an example of our method (Pose space deformation on top of dual-quaternion skinning) compared to the current standard (PSD on top of Skeletal subspace deformation). The results were obtained using 4 example poses and show that our method provides better interpolation between the poses.
  • Lorentz boosts using Quaternions A description of a 2 page paper showing how to represent a Lorentz boost using real-valued quaternions. The simple expression uses hyperbolic sines and cosines. The paper is available on the visual physics preprint server,
  • Quaternion Julia Set The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. The classical filled-in Julia set contains points in the complex plane that remain bounded on repeated application of quadratic function qn + 1 = qn^2 + c. Quaternions are 4-tuples of real numbers with a noncommutative multiplication; this Demonstration... Contributed by: Fred Klingener
  • 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.
  • 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.
  • The Stand-Up Physicist: A Personal Issue with Tensors or Peace Through Maxwell In this show by the Stand-Up Physicist, Doug Sweetser delves into an issue he does not quite understand regarding tensors. First tensors are defined, and the odd Greek letter operations explained. A type of 4D number, the quaternions, is shown to do the same work without Greek. The subject of his confusion are the tensor rules for derivatives. It is shown that quaternions to the same thing less confusion. A road to the Maxwell equations is sketched, showing the power of using quaternions
  • Quaternions and rotation storing rotation axis values in float variables versus quaternions
  • Kork can use quaternions
  • 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.
  • Command Line Quaternions: 4D Square A 4 dimensional square.
  • IET: Dissertation PSD on top of Dual Quaternions-D. Murtagh This video shos an example of our method (Pose space deformation on top of dual-quaternion skinning) compared to the current standard (PSD on top of Skeletal subspace deformation). The results were obtained using 3 example poses and show that our method provides better interpolation between the poses. More information at www.cs.tcd.ie
  • Quaternions visualizations in matlab quaternion.110 Quaternions visualizations in matlab
  • Quaternions and rotation (I know it's been covered a lot) storing overall rotation value in variables versus quaternions
  • Quaternion Julia Set HD First part is tracing around the circle part of the Mandelbrot Set for real and imaginary 1 components. Second part is tracing around the cardioid part of the Mandelbrot Set for real and imaginary 1 components. Both movies used maximum iterations of 15 for the higher detail and each pixel was rendered at 3x3 over sampling to reduce aliasing. Created with Visions Of Chaos .au
  • Quaternion Fractal 3 Quaternions play an important role in quantum mechanics.
  • Julia sets in 4D (using quaternions) Animation of 4D Julia sets using simple raycaster running on CUDA. Uses Gouraud shading only, at least for now. Seeds for the fractals are chosen from the randomly generated spline, so that visual changes are smooth (well, they are smooth in almost all points ;)). Mor info on 4D Julia sets: local.wasp.uwa.edu.au
  • Quaternion Julia Set Morphing Quaternion Julia Set. Created with Visions Of Chaos. .au
  • 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
  • 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.
  • the quaternion handshake You had the quaternion in you hands all this time and didn't know about it! the quaternions are mathematical abstract group/ ring / algebra that can be used to represent axial rotations.
  • Quaternion Julia Set A quaternion julia set animation I created with a basic raytracer I wrote for the purpose.
  • 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
  • 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.
  • 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.
  • nvining: @nuclearfossil I think after Diana G. wrote the big rant about how we "don't need quaternions", she was shunned by the industry as an idiot.
  • izfrey: And the cat is out of the bag - I'll be giving a talk at SIGGRAPH 2011 http://t.co/JPXkbrK
  • andrew_b_berg: It's time to break out the quaternions
  • GaryMucklow: orbital rotation quaternions? Head go boom #game-dev-in-training
  • mattieuMattieu: Woah. Hello there, quaternions. Didn't expect to see you here...
  • bcrunos: RT @MiegakureGame: 4D Rotations and the 4D equivalent of Quaternions http:///news/?p=115

Blogs & Forum
blogs and forums about quaternions

  • “I have a feeling that my favorite feature of Papervision3D is actually the most overlooked feature of Papervision3D. Not because it is insignificant or”
    Quaternions in Papervision3D | ,

  • “Sie können Ihre Beiträge in diesem Forum nicht bearbeiten. in diesem Forum nicht löschen. Sie können an Umfragen in diesem Forum nicht mitmachen”
    — C/C++ Forum :: Quaternions?, c-

  • “So I figured I'd give quaternions a try for my latest graphical project. This is the first time I touched quaternions, and I'm beginning to think that learning all this nonint”
    Quaternions are fun; or, cross-browser 3D graphics, 110

  • “PLEASE SOS help - quaternions and 3d geometry My questio would be better placed on a forum for mathematics, but your electronic forum has already a board for maths and thus, here i go”
    — PLEASE SOS help - quaternions and 3d geometry,

  • “Archived messages from old discussion forum: By Sirstephen (Sirstephen) on Thursday, May 11, 2000 - 10:02 pm: Hi, I am trying to understand better the relationship between octonions and quaternions with respect to their possible use in relativity theories”
    — The relationship between Quaternions and Octonions - Mendel,

  • “Softimage XSI Discussion Forum, Resources, Industry News and Features. xsi 6.02 DELTA and Quaternions. Reply with quote. If you will try ro convert your rotation fcurves from Euler to Quaternion on Referenced Model you will see you curves converted in Animation Editor but next time you reload”
    — XSI Base Forum - xsi 6.02 DELTA and Quaternions,

  • “Well, if you are using the Flash API, you could use quaternions to calculate the angle you want, and convert them into euler Well, if you are using the Flash API, you could use quaternions to calculate the angle you want, and convert them into euler coordinates”
    — CopperCube Forum: Pitch,Roll,Yaw & Euler vs Quaternions,

  • “Maths - Rotations using quaternions - Forum Discussion. By: nobody ( Nobody/Anonymous ) Rotations using quaternions. 2003-07-24 18: flag to get more details of the book or to buy it from them. Quaternions and Rotation”
    — Maths -Quaternion transforms - Martin Baker,

related keywords for quaternions