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# Quaternion animation

Quaternion animation with rotation and quat fixed point animation. Created with the program quat.exe uni stuttgart germany Quaternionen sind 4-Tupel reeller Zahlen, auf denen eine Multiplikation definiert ist. Sie besitzen dementsprechend imaginäre Einheiten für die gilt: Auf Quaternionen kann eine Norm definiert werden . Einheitsquaternionen haben als Norm . Das konjugierte Quaternion ist von der Form Für ein Einheitsquaternion gilt, dass das Inverse das konjugierte Quaternion ist Rotation mit Quaternionen. Quaternionen SS 2006 - Animation Quaternionen und Quaoaring Dr. Tobias Breiner tbreiner@gdv.informatik.uni-frankfurt.de 26/100 Kurze Auffrischung der Oberstufenmathematik Komplexe Zahlen (1) Im 16. Jahrhundert stellte Rafaello Bombelli die Frage, was die Lösung von sei. Lösung durch Leonard Euler 1777: Einführung der imaginären Einheit i mit => Komplexe Zahlen −1 i⋅i =−1 SS 2006. Quaternions, Interpolation and Animation @inproceedings{Dam2000QuaternionsIA, title={Quaternions, Interpolation and Animation}, author={E. Dam and M. Koch and M. Lillholm}, year={2000} } E. Dam, M. Koch, M. Lillholm; Published 2000; Computer Science; The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce.

computer animation, so do cameras. The rotations of these objects are best described using a four coordinate system, quaternions, as is shown in this paper. Of all quaternions, those on the unit sphere are most suitable for animation, but the question of how to construct curves on spheres has not been much explored. This paper gives one answer by presenting a new kind of spline curve, created. Explaining how quaternions, a four-dimensional number system, describe 3d rotation Visualising Quaternions, Converting to and from Euler Angles, Explanation of Quaternions Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular.

Erstellt eine Animation des Werts einer Quaternion-Eigenschaft zwischen zwei Zielwerten unter Verwendung der linearen Interpolation für eine angegebene Duration.Animates the value of a Quaternion property between two target values using linear interpolation over a specified Duration In some cases, you might actually want to use quaternions in GLSL, for instance if you do skeletal animation on the GPU. There is no quaternion type in GLSL, but you can pack one in a vec4, and do the math yourself in the shader. How do I convert a quaternion to a matrix ? mat4 RotationMatrix = quaternion:: toMat4 (quaternion); You can now use it to build your Model matrix as usual: mat4. It has IK legs. I animated its foot and didn't realize that they were Quaterinon. I made lot of actions with it. Now... as I will make more actions with this character, I would like to convert every Action with its rotation data to Euler. So, after changing its rotation mode, the bone would have the same visual rotation as it had with Quaternions

### Quaternion animation - YouTub

1. Another special case, common in animation, is evaluation with fixed ends and equal parametric steps. If p k−1 and p k are two consecutive values, and if c is twice their dot product (constant for all steps), then the next value, p k+1, is the reflection p k+1 = c p k − p k−1. Quaternion Slerp. When Slerp is applied to unit quaternions, the quaternion path maps to a path through 3D.
2. Quaternions, In terp olation and Animation Erik B. Dam Martin Ko c h Lillholm erikdam@diku.dk myth@diku.dk grumse@diku.dk T ec hnical Rep ort DIKU-TR-98/5 Departmen t of Computer Science Univ ersit y of Cop enhagen Univ ersitetspark en 1 DK-2100 Kbh Denmark July 17, 1998. Abstract The main topics of this tec hnical rep ort are quaternions, their mathematical prop-erties, and ho w they can b e.
3. If I wanted to compute the magnitude of the resulting quaternion then I would need to consider the quaternion's scalar part according to the formula described in the section titled Quaternion Norm. But since I'm only interested in rotating a vector by a quaternion I only want to consider the result of the vector part (and thus discard the scalar part when I compute the magnitude of the.
4. ation May 7 '09 at 14:04. That.
5. Rotation and Orientation in Unity. Rotations in 3D applications are usually represented in one of two ways: Quaternions or Euler angles. Each has its own uses and drawbacks. Unity uses Quaternions internally, but shows values of the equivalent Euler angles in the Inspector A Unity window that displays information about the currently selected.

Quaternions are used extensively in animation to describe smooth transitions between known orientations. This is known as interpolation. This is an example of an area where quaternions are preferred to rotation matrices as smooth interpolation is not possible with the latter. Here's quaternion interpolation in action: >>> import numpy >>> numpy.set_printoptions(suppress=True) # Suppress. Quaternions provide smooth interpolation of animated rotations and always produce the most efficient path between keyframes in comparison to Euler angles. Quaternions store the overall orientation of an object rather than a series of individual rotations. This means that a single Quaternion stores the same amount of rotation data as three Euler angles. Since Quaternions store only orientation. Die Quaternionen (Singular: die Quaternion, von lateinisch quaternio, -ionis f. Vierheit) sind ein Zahlenbereich, der den Zahlenbereich der reellen Zahlen erweitert - ähnlich den komplexen Zahlen und über diese hinaus. Beschrieben (und systematisch fortentwickelt) wurden sie ab 1843 von Sir William Rowan Hamilton; sie werden deshalb auch hamiltonsche Quaternionen oder Hamilton-Zahlen.

### Quaternionen ::: Computeranimatio

1. Unity's default behaviour is to resample these animations and generate a new Quaternion keyframe for every frame in the animation, in an attempt to avoid any situations where the rotation between keyframes may exceed the Quaternion's valid range. For example, imagine two keyframes, 6 frames apart, with values for X as 0 on the first keyframe and 270 on the second keyframe. Without.
2. The animation progresses from the animated property's base value or a previous animation's output value to the value specified by the To property. By Die Animation verläuft vom Basiswert der zu animierenden Eigenschaft oder vom Ausgabewert einer vorherigen Animation bis zur Summe dieses Werts und des Werts, der von der-Eigenschaft angegeben wird By
3. Quaternions, Interpolation and Animation by Erik B. Dam, Martin Koch, Martin Lillholm. Publisher: University of Copenhagen 1998 Number of pages: 103. Description: The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce quaternion mathematics and discuss why quaternions are a better choice for implementing.
4. 3D-Animation ist ein technisch intensiver Prozess, bei dem häufig viele Spezialisten den Charakter modellieren, Quaternionen bilden einen vierdimensionalen Raum, für den Operationen wie Addition und Multiplikation definiert sind. Um einen Punkt zu rotieren, wird er zunächst als Quaternion dargestellt, die Rotation im Quaternion-Raum angewandt, und wieder in die üblichen kartesischen.

Quaternion Basics. A quaternion is a four-element vector that can be used to encode any rotation in a 3D coordinate system. Technically, a quaternion is composed of one real element and three complex elements, and it can be used for much more than rotations. In this application note we'll be ignoring the theoretical details about quaternions and providing only the information that is needed to. If this animation is the first in a composition chain /// this value will be the snapshot value if one is available or the /// base property value if it is not; otherise this value will be the /// value returned by the previous animation in the chain with an /// animationClock that is not Stopped. /// </ param > /// < param name. Dieses Rollout enthält Optionen, mit denen Sie zwischen dem Euler- und dem Quaternion-Controller für Biped-Animationen umschalten können. Mit diesen Optionen können Sie Animationen im Kurveneditor auf unterschiedliche Art und Weise kontrollieren. Weitere Informationen hierzu finden Sie unter Arbeiten mit Euler-Kurven bei Biped-Animationen GitHub Issues - A place where you can report bugs, suggest features, ask for help, and have general discussions about Animation Nodes. Stack Exchange - A place where you can browse, read, and ask questions related to Animation Nodes using the animation-nodes tag Quaternions have become a popular tool in 3d game development - and for a good reason. Once you understand them, quaternions are really pretty amazing. Also, unlike the other tutorials, I'm going to more or less be assuming that you know nothing about quaternion math in this tutorial. Here are the basics of a quaternion: A quaternion represents two things. It has an x, y, and z component.

Is babylon animation doing slerp with quaternions on their own, and which property I should pas to babylon animation to make movements with quaternions. or this stuff is not supported and I should code method, which will produce array of points, and pass this though keys to babylon animation with position property. This question is a little bit confusing me, because I don't find any clear. Quaternion animation doesn't animate. Ask Question Asked 3 years, 1 month ago. Active 3 years, 1 month ago. Viewed 57 times 0. I'm trying to do a quaternion animation in the visual layer. But then I run the code it doesn't animate, it just jumps between the two states. I'm doing something wrong? var compositor = ElementCompositionPreview.GetElementVisual(this).Compositor; var visual. In computer animation, so do cameras. The rotations of these objects are best described using a four coordinate system, quaternions, as is shown in this paper. Of all quaternions, those on the unit sphere are most suitable for animation, but the question of how to construct curves on spheres has not been much explored

Quaternion cube rotation animation. Ask Question Asked 9 years, 6 months ago. Active 9 years ago. Viewed 2k times 6. 4. I created this Rubiks Cube with Papervison3D. With some resources I created a Cube with 27 minicubes inside (3*3*3 = 27). Rotating the Rubiks Cube on mouse move is already done. (I do not rotate the camera.) All the behavior of a Rubiks Cube is in there already. But I'm a bit. Quaternions, although not well known, provide a fundamental and solid base to describe the orientation of an object or a vector. They are efficient and well suited to solve rotation and orientation problems in computer graphics and animation. This paper describes two new methods for splining quaternions so that they can be used within a keyframe animation system Subject: Re: [glTF] Animation: quaternion vs. axis-angle @RemiArnaud's point is that glTF is not an inter-exchange format. So adopters may convert assets to fit their needs. But it doesn't mean we can afford or want to specify here more variations of the same concept than what we absolutely need for a V1.0. Always better to be a bit frustrating, get more feedback and open up later. (nothing. Understanding Quaternions. Posted on June 25, 2012 by Jeremiah. Understanding Quaternions. In this article I will attempt to explain the concept of Quaternions in an easy to understand way. I will explain how you might visualize a Quaternion as well as explain the different operations that can be applied to quaternions

That's odd, I'm sure I tried that (wherein the inverse/conjugate of the quaternion is simply q(-x,-y,-z,w)).It's quite possible that I was just multiplying them in the incorrect order.As a happy side-note coincidence, I don't actually need to use this anymore, the main flaw in my animation code wa Quaternionen, Interpolation und Animation (PDF) . Leandra, Vicci (2001). Quaternionen und Rotationen im 3-Raum: Die Algebra und ihre geometrische Interpretation (PDF) . Howell, Thomas; Lafon, Jean-Claude (1975). Die Komplexität des Quaternion-Produkts, TR75-245 (PDF) . Cornell Universität. Horn, Berthold KP (2001). Einige Hinweise zu Quaternionen und Rotation von Einheiten (PDF.

QuaterNet: A Quaternion-based Recurrent Model for Human Motion. In British Machine Vision Conference (BMVC), 2018. We provide the code for reproducing our results (short-term prediction) and generating/rendering locomotion animations (long-term generation), as well as pre-trained models. Abstrac 3D Animation Quaternion Visualization. Follow 54 views (last 30 days) Sven Dietrich on 9 Sep 2020. Vote. 0 ⋮ Vote. 0. Commented: Sven Dietrich on 14 Sep 2020 I have to to visualize/animate some IMU data to see how the rotation looks like and to know which axes I must analyse in the following steps. Until now I analysed the movement with rotations on the axes, but it looks wron, because of. Quaternions, Interpolation and Animation Erik B. Dam. Martin Koch. Martin Lillholm. erikdam@diku.dk. myth@diku.dk. grumse@diku.dk. Technical Report DIKU-TR-98/5 Department of Computer Science. Unity: 'Quaternion.RotateTowards' animation is too fast (instantaneous) Ask Question Asked 1 year, 7 months ago. Active 1 year, 7 months ago. Viewed 470 times 0 \$\begingroup\$ I have a 'block-on-a-hinge' scenario where I just want it to smoothly rotate into the position of a stair step. I messed with this for a day and finally verified that my start and end angles are correct. The problem now. Unity considers [quaternions] a wart. Their animation system defaults to Eulers and as pointed out in the other thread they needed to support Eulers to actually handle animations users were created in external packages. I don't yet see solid evidence for this — if Unity wanted to change their internal representation, they could. Again from the docs, In Unity all Game Object rotations are.  ### [PDF] Quaternions, Interpolation and Animation Semantic

quaternion algebra to be introduced will also allow us to easily compose rotations. This is because quaternion composition takes merely sixteen multiplications and twelve additions. The development of quaternions is attributed to W. R. Hamilton  in 1843. Legend has it that Hamilton was walking with his wife Helen at the Royal Irish Academy when he was suddenly struck by the idea of adding a. A specialized PropertyAnimation that defines an animation between two quaternions. By default spherical linear interpolation is used. This can be changed to the faster but less accurate normalized linear interpolation by setting the type property. Instead of specifying quaternions directly in the from and to properties, it is also possible to provide euler angles in degrees in the. 8. As I (seem to) know from some comments the use of Quaternion or Euler depends on what we want to animate and that Quaternion can handle very complex animation and avoid problems which sometimes occur in Euler. But in which occasions (simple walk/run animation, jump/bounce animation, etc.) is Quaternion commendable and are there any. frog = (GameObject)Instantiate(gameCharacterPrefab, objectPoolPosition, Quaternion.identity); Get the Animation component. anim = frog.GetComponent<Animation>(); Play animation name. anim.Play(AnimName); Stop animation . anim.Stop(); Share. Improve this answer. Follow answered Jun 9 '18 at 3:13. Programmer Programmer. 102k 15 15 gold badges 171 171 silver badges 261 261 bronze badges. Add a.

### Visualizing quaternions, an explorable video serie

• Quaternion Rotation. Maya provides smooth quaternion interpolation of animated rotations. Quaternions calculate rotation interpolation using four vectors: the X, Y, and Z axes and an angle of rotation (W). This prevents the gimbal lock and flipping problems that are sometimes encountered with Euler angle interpolation. Maya also supports Euler.
• Contribute to ubisoft/ubisoft-laforge-animation-dataset development by creating an account on GitHub. Skip to content. Sign up Why GitHub? The global quaternion loss (L2Q) is the L2 distance computed between estimated and ground-truth global quaternion vectors g, averaged over each time step t and over all sequences s in the test set. Global position loss. The global position loss (L2P) is.
• This is Quaternion Animation by denis coleman on Vimeo, the home for high quality videos and the people who love them
• Using quaternions, you can generate a rotation matrix, apply that matrix to the acceleration output, and see your acceleration relative to an absolute orientation. With the absolute orientation, you can isolate the vibrations and accelerations your car goes through when it turns. You even can trace out the twists and turns of an object as it moves through space. I think this sensor opens up.
• Surely every major 3D package that allows skeletal animation together with quaternion interpolation (i.e. Maya, Max, Blender, etc) must have solved exactly this problem? language-agnostic math animation quaternions euler-angles. Share. Improve this question. Follow edited Apr 5 '10 at 23:10. Will Baker . asked Jun 23 '09 at 6:55. Will Baker Will Baker. 2,509 4 4 gold badges 18 18 silver badges.
• One of the least understood features of Cinema 4D is the ability to work with Quaternion rotations. There will be times when using Quaternions will save the day, especially when it comes to animation. 3D Artist Matthew O'Neill shares some insights into working with Quaternions Quaternion equations have been used to do physics, ranging from classical physics, to the Maxwell equations, and into Quantum Mechanics. It should be possible to use the equations for a hydrogen atom to generate a technically accurate picture of the atom in various states. Someday it may be possible to generate an animation of two hydrogen atoms fusing to form a helium atom 1. Make a copy of your rig and remove the animation (unlink the action on the duplicate). Flip your original rig by going into Object mode and setting scale in X-axis to -1.0 on the object. Add a Copy Rotation constraint for each bone of the duplicate rig that will target the opposite bone in the original rig - ie Image orientation and animation using quaternions . United States Patent 4797836 . Abstract: A method for orientating and animating video images using quaternions to provide smooth, predictable rotations in a digital video effect device. Euler angles for a new orientation are input by an operator and are converted into an appropriate quaternion. For incremental orientation changes the.

### Quaternions and spatial rotation - Wikipedi

Sie können die Position und Ausrichtung des Bipeds neben den Quaternion-Kurven im Labor und dem Kurven-Editor auch mithilfe der Euler-Kurven regulieren. Die Verwendung des Controllers Euler-XYZ ist eine effiziente Möglichkeit, Ihr Biped zu animieren, da Sie Bezier-Tangenten verwenden können, um die Interpolation Ihrer XYZ-Kurven (Quaternion-Kurven haben keine Tangenten) zu ändern Quaternion interpolation in Blender is an area that many people would like to see improved. This thread is meant to discuss low-level, behind-the-scenes improvements to Blender. Recently there was a discussion on the topic per email between Brecht van Lommel ( @brecht ), Stefan Werner ( @StefanW) and Mark Theriault from Tangent Animation, and me

3D Animation Quaternion Visualization. 팔로우 조회 수: 83(최근 30일) Sven Dietrich 9 Sep 2020. 추천 . 0 ⋮ 추천. 0. 댓글: Sven Dietrich 14 Sep 2020 I have to to visualize/animate some IMU data to see how the rotation looks like and to know which axes I must analyse in the following steps. Until now I analysed the movement with rotations on the axes, but it looks wron, because. Animation Nodes. Docs » User Guide » Nodes » Rotation » Quaternion Math; Edit on GitHub; Quaternion Math¶ Description¶ This node carries 13 quaternion math operation: Add - Adds input quaternion A to input quatrnion B. Subtract - Subtracts input quaternion B from input quaternion A. Combine Rotation - Hamilton product of input quaternion A by input quaternion B. Rotation Difference.

### QuaternionAnimation Klasse (System

A fully featured, pythonic library for quaternion representation, manipulation, 3D animation and geometry. Please visit the pyquaternion homepage for full information and the latest documentation. Designed for Python 2.7+ and 3.0+ Example: Smooth animation with interpolation between random orientations using the pyquaternion module. Quickstar In the demo above, before the animation has begun, Quaternions were invented in 1843 by William Hamilton, who was so inspired by his discovery that he carved the formula into a bridge nearby. Just as a complex number in 2D contains a real and imaginary component, a quaternion in 4D contains three imaginary components, x, y and z (sometimes a, b and c), and a real component, w (sometimes d. One of the most useful aspects of quaternions that we game programmers are concerned with is the fact that it's easy to interpolate between two quaternion orientations and achieve smooth animation.

### Tutorial 17 : Rotation

Quaternions, Interpolation, and Animation Quaternions, their mathematical properties, and how they can be used to rotate objects. Quaternions, Interpolation, and Animation Published on Oct 5, 2011. Hi all, this is one of those I'm pretty sure someone has already come up with a solution to this, but I can't seem to find it kind of things. It's a situation so common that either someone has solved this already, or there is no solution, but there's a work-around. Basically, the situat Quaternions, their mathematical properties, and how they can be used to rotate objects

Shoemake, Ken, Quaternion Calculus for Animation, SIGGRAPH Course Notes, Math for SIGGRAPH, 1989. Blow, Jonathan, Hacking Quaternions, Game Developer, March 2002. Busser, Thomas. PolySlerp: A fast and accurate polynomial approximation of spherical linear interpolation (Slerp), Game Developer, February 2004. Demo Demo Essential Math for Games * Demo z y x o z z y x x´ o x´ y. Quaternionen Eugenia Schwamberger Inhalt : Komplexe Zahlen Quaternionen Einheitsquaternionen Rotation mit Quaternionen Beispiel Matrix Conversion Anhang A: Körper, Schiefkörper Anhang B: Vektorprodukt, Skalarprodukt Literatur Komplexe Zahlen Definition Es sei C = R*R - das kartesische Produkt. An Stelle des geordnetes Paar (x, y) schreiben wir x + iy C für x, y R. Grafische Darstellung. Quaternion Dot Products n The dot product of two quaternions works in the same way as the dot product of two vectors: n The angle between two quaternions in 4D space is half the angle one would need to rotate from one orientation to the other in 3D space p⋅q = p 0q 0 + p 1q 1 + p 2q 2 + p 3q 3 = p q cosϕ CSE/EE 474 35 Quaternion Multiplicatio ### animation - How to convert Quaternions keyframes to Euler

How do we interpolate between two quaternions representing rotations? For instance we may want to fill in some gaps between calculated rotations to make an animation less jerky. if q is the quaternion which rotates from qa to qb then: qb = qa * q multiplying both sides by conj(qa) gives: q = conj(qa) * qb The real part of a multiplication is Using Quaternion.LookRotation() and Animator.SetLookAtPosition() methods to make characters follow an object with their gaze. Sometimes you need a character to look at an object in the game, for instance, at the camera. To do so, we can use two methods: Quaternion.LookRotation and Animator.SetLookAtPosition (). We will cover both in this recipe (the second one is covered in the There's more. Creates a vector4 representing a quaternion from an angle and axis. The angle is specified in radians. vector4 quaternion (vector angleaxis) Creates a vector4 representing a quaternion from a combined angle/axis. This is the normalized rotation axis multiplied by the rotation angle in radians. There used to be a fourth form that took a rotation vector. It has been renamed to eulertoquaternion.

Bildorientierung und -animation unter Verwendung von Quaternionen Download PDF Info Publication number EP0268984B1. quaternions Prior art date 1986-11-19 Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.) Expired - Lifetime Application number. When I was teaching game animation, I tried to teach my students to always use Quaternion controllers with TCB interpolators. Using Quaternion controllers with TCB interpolators gives you less control over the interpolation but when you use Quaternion interpolation it always uses SLERP function which selects the shortest arc from the source rotation to the destination. This means you can. How to utilize the quaternion system to manage the rotation of game objects. My Learning. Pathways. Guided learning journeys. Embark on a guided experience where you unlock free assets, prepare to get Unity Certified, and earn shareable badges to demonstrate your learning to future employers. 1352. Unity Essentials. Pathway. Foundational +600 XP. 2 Weeks. Designed for anyone new to Unity, this.

3D Animation & Đồ họa chuyển động Projects for $250 -$750. I have an inertial measurement unit (IMU) that outputs its orientation in quaternions or Euler angles at 100Hz. I use the IMU to measure motion for five minutes at a time and would like to be able to. Choose Animation > Convert Euler Rotation to Quaternion from the Animation panel. If you select an object that already has Euler rotation fcurves, the curves are simply converted to quaternion. 3. Key rotations as usual and the resulting fcurves will be quaternion. Setting keys for one rotation axis creates corresponding keys on the other two rotation axes. 4. Edit the timing and interpolation. unity3d documentation: Intro to Quaternion vs Euler. Example. Euler angles are degree angles like 90, 180, 45, 30 degrees. Quaternions differ from Euler angles in that they represent a point on a Unit Sphere (the radius is 1 unit) We use Quaternion system to rotate 3D objects in ARCore and Sceneform (pretty much in all game engines) We don't prefer Euler's angle rotation because of a problem called Gimbal Lock; Typical Quaternion takes 4 parameters. 3 Vectors and one Scalar. We practically don't use raw Quaternion representation. Instead we use Quaternion axis angle representation, rest Sceneform takes care. This. 3D Animation Quaternion Visualization. Learn more about animation, quaternion, visualization, 3d MATLAB, Robotics System Toolbox, Aerospace Toolbox, Simulin  Add animation using quaternion interpolation. Budget \$14-15 USD. Freelancer. Jobs. C++ Programming. Add animation using quaternion interpolation. Add animation using quaternion interpolation. Skills: C++ Programming, OpenGL. See more: upload photo add animation, end dental animation using studio max, add images using php, quaternion slerp, quaternion interpolation python, quaternion slerp. If this animation is the first in a composition chain /// this value will be the snapshot value if one is available or the /// base property value if it is not; otherise this value will be the /// value returned by the previous animation in the chain with an /// animationClock that is not Stopped. /// /// /// This value is the suggested destination value provided to the animation /// to be. Quaternions provide an easy way to nicely interpolate between two rotation values, and avoid the gimbal lock and direction changes caused by interpolating Euler angles. They can easily be converted to and from rotation matrices, Euler angles, and angle-axis rotations. A quaternion is represented by a vector of 4 floats (x, y, z, and w). Any rotation in three dimensions is a rotation by some. IMAGE ORIENTATION AND ANIMATION USING QUATERNIONS . European Patent Application EP0268984 . Kind Code: A3 . Abstract: Abstract of EP0268984 A method for orientating and animating video images using quaternions to provide smooth, predictable rotations in a digital video effect device. Euler angles for a new orientation are input by an operator and are converted into an appropriate quaternion. Rethinking Quaternions: Theory and Computation Synthesis Lectures on Computer Graphics and Animation, Band 13: Amazon.de: Goldman, Ron, Barsky, Brian: Fremdsprachige Büche The animation curves in this mode are not intuitive, so they are also difficult to understand and edit. The following formula applies (provided that the quaternion is normalized): $$W = \cos(\frac{a}{2})$$, where a is actually the rotation angle we are looking for. That is: $$a = 2 \arccos{W}$$. Other Considerations¶ In axis-angle and quaternion modes we can lock rotations in interactive.

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