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See also: Quaternion Quaternions Define Quarters Quat Quath Quatch Quate Quatro Quatre Quatorze Quattro Quatrain Quaternity Quaternium Quatervois Quatrefoil Quaternary Quattrocento Quatrefeuille Quatercentenary

1. Introducing The Quaternions The Complex Numbers I The complex numbers C form a plane

Quaternions

2. Quaternion is a 4-tuple, which is a more concise representation than a rotation matrix

Quaternion

3. The Quaternion algebra to be introduced will also allow us to easily compose rotations

Quaternion

4. The Quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton.

Quaternions

5. Quaternions are a nice mathematical concept to use for orientation and attitude visualization for navigation designs

Quaternions

6. Quaternions are an extension of imaginary number set, commonely refered to as a hyper-complex number. A Quaternion can be thought of as a four element vector.

Quaternions, Quaternion

7. Quaternions are the things that scare all manner of mice and men. They are the things that go bump in the night

Quaternions

8. Quaternion definition is - a set of four parts, things, or persons

Quaternion

9. Components of a Quaternion ROS uses Quaternions to track and apply rotations

Quaternion, Quaternions

10. A Quaternion has 4 components (x, y, z, w)

Quaternion

11. Quaternion Interpolation Remember that there are two redundant vectors in Quaternion space for every unique orientation in 3D space What is the difference between: Slerp(t,a,b) and Slerp(t,-a,b) ? One of these will travel less than 90 degrees while the other will travel more than 90 degrees across the sphere

Quaternion

12. This paper is an attempt to summarize Quaternion Algebras

Quaternion

13. The rst part looks at their origins and certain properties of these algebras are examined, from the roots of Polynomials over the Quaternions to how to construct a Quaternion algebra and Frobenius’ theorem

Quaternions, Quaternion

14. The second part of this paper looks at applications of Quaternion algebras.

Quaternion

15. The Quaternion structure is used to efficiently rotate an object about the (x,y,z) vector by the angle theta, where: w = cos (theta/2)

Quaternion

16. Quaternion is a 4-tuple, which is a more concise representation than a rotation matrix

Quaternion

17. The Quaternion algebra to be introduced will also allow us to easily compose rotations

Quaternion

18. Quaternion definition, a group or set of four persons or things

Quaternion

19. The Quaternion functions that you use 99% of the time are: Quaternion.LookRotation, Quaternion.Angle, Quaternion.Euler, Quaternion.Slerp, Quaternion.FromToRotation, and Quaternion.identity

Quaternion

20. (The other functions are only for exotic uses.) You can use the Quaternion.operator * to rotate one rotation by another, or to rotate a vector by a rotation.

Quaternion

21. Quaternions off soudiers to be kept, entendynge after ester to brynge hym forth to the people

Quaternions

22. Quaternions were historically the first example of a hypercomplex system, arising from attempts to find a generalization of complex numbers

Quaternions

23. Quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions

Quaternion

24. Quaternions and rules for operations on them were invented by Irish mathematician Sir William Rowan Hamilton in 1843

Quaternions

25. Quaternion.fromAxisAngle(axis, angle) Sets the Quaternion by a rotation given as axis and angle

Quaternion

26. Quaternion.fromEuler(Φ, θ, ψ[, order="ZXY"]) Creates a Quaternion by a rotation given by Euler angles

Quaternion, Quot

27. Quaternion.fromBetweenVectors(u, v) Calculates the Quaternion to rotate one vector onto the

Quaternion

28. Peter was committed by Herod to the custody of four Quaternions, i.e., one Quaternion for each watch of the night ( Acts 12:4).Thus every precaution was taken against his escape from prison.

Quaternions, Quaternion

29. Quaternion supports clients in trading, risk management and finance functions

Quaternion

30. Quaternion synonyms, Quaternion pronunciation, Quaternion translation, English dictionary definition of Quaternion

Quaternion

31. Static Cesium.Quaternion.fastSlerp (start, end, t, result) → Quaternion Core/Quaternion.js 945 Computes the spherical linear interpolation or extrapolation at t using the provided Quaternions.

Quaternion, Quaternions

32. A unit Quaternion is a Quaternion qfor which N(q) = 1

Quaternion, Qfor

33. The inverse of a unit Quaternion and the product of unit Quaternions are themselves unit Quaternions

Quaternion, Quaternions

34. A unit Quaternion can be represented by q= cos + ^usin (9) where ^uas a 3D vector has length 1

Quaternion

35. However, observe that the Quaternion

Quaternion

36. This package implements Hamilton's Quaternion algebra

Quaternion

37. Quaternions have the form a+b i+c j+d k where a, b, c, and d are real numbers

Quaternions

38. Quaternions are an extension of the complex numbers, and work much the same except that their multiplication is not commutative.

Quaternions

39. I can't see the page in Google Books, but what you apparently have there is the logarithm of a unit Quaternion $\mathbf q$, which has scalar part $\cos(\theta)$ and vector part $\sin(\theta)\vec{n}$ where $\vec{n}$ is a unit vector

Quaternion

40. Since the logarithm of an arbitrary Quaternion $\mathbf q=(s,\;\;v)$ is defined as

Quaternion

41. Examples of how to use “Quaternion” in a sentence from the Cambridge Dictionary Labs

Quaternion

42. A Quaternion can be used to represent a rotation in 3 dimensions

Quaternion

43. If we are rotating through t radians about a unit vector (x1,y1,z1) then the rotation can be represented by multiplying by the following Quaternion: q = cos(t/2) + i ( x1 * sin(t/2)) + j (y1 * sin(t/2)) + k ( z1 * sin(t/2)) This is a Quaternion with the following elements:

Quaternion

44. Public static Quaternion Euler (Vector3 euler); Description Returns a rotation that rotates z degrees around the z axis, x degrees around the x axis, and y degrees around the y axis.

Quaternion

45. Quaternions add a fourth element to the [ x, y, z] values that define a vector, resulting in arbitrary 4-D vectors.However, the following example illustrates how each element of a unit Quaternion relates to an axis-angle rotation, where q represents a unit Quaternion (x, y, z, w), axis is normalized, and theta is the desired counterclockwise (CCW) rotation around the axis.

Quaternions, Quaternion

46. • (poetry) Quaternion is a poetry style in which the theme is divided into four parts More crossword answers

Quaternion

47. We found 6 answers for the crossword clue Quaternion

Quaternion

48. A Quaternion number is represented in the form a + b i + c j + d k, where a, b, c, and d parts are real numbers, and i, j, and k are the basis elements, satisfying the equation: i 2 = j 2 = k 2 = ijk = −1.

Quaternion

49. The set of Quaternions, denoted by H, is defined within a four-dimensional vector space over the …

Quaternions

50. And indicates Quaternion conjugation

Quaternion

51. Note the above Quaternion multiplication results in a Quaternion with the real part, , equal to 0

Quaternion

52. Feel free to become a mega tier supporter for the price of $50, this will grant you all perks the low-tier & medium-tier & high-tier & ultra high-tier grants you & the "Patron Tier 5" role as well as the ability to get access to an exclusive Quaternion Entertainment merch after 3 months of consecutive payments.

Quot, Quaternion

53. Get a new Quaternion using eulerAngles to define the rotation

Quaternion

54. Quaternion is a cross-platform desktop IM client for the Matrix protocol

Quaternion

55. Most of talking around Quaternion happens in the room of its parent project, Quotient: #quotient:matrix.org.

Quaternion, Quotient

56. The dual-Quaternion has been around since 1882 [CLIF82] but has gained less attention compared to Quaternions alone

Quaternion, Quaternions

57. Comparable to Quaternions the dual-Quaternions have had a taboo associated with them, whereby students avoid Quaternion and hence dual …

Quaternions, Quaternion

58. Quaternion definition: a generalized complex number consisting of four components , x = x 0 + x 1 i + x 2 j + x Meaning, pronunciation, translations and examples

Quaternion

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Dictionary

QUATERNION [kwəˈtərnēən, kwäˈternēən]

NOUN
quaternion (noun) · quaternions (plural noun)

  • a complex number of the form w + xi + yj + zk, where w, x, y, z are real numbers and i, j, k are imaginary units that satisfy certain conditions.
  • a set of four people or things.

Frequently Asked Questions

What does quaternion mean?

Quaternion, [N] [E] a military term signifying a guard of four soldiers, two of whom were attached to the person of a prisoner, while the other two kept watch outside the door of his cell. ( Acts 12:4 )

What are the functions of quaternion?

The Quaternion functions that you use 99% of the time are: Quaternion.LookRotation, Quaternion.Angle, Quaternion.Euler, Quaternion.Slerp, Quaternion.FromToRotation, and Quaternion.identity. (The other functions are only for exotic uses.) You can use the Quaternion.operator * to rotate one rotation by another, or to rotate a vector by a rotation.

How do you use the quaternion.operator?

You can use the Quaternion.operator * to rotate one rotation by another, or to rotate a vector by a rotation. Note that Unity expects Quaternions to be normalized. The identity rotation (Read Only). Returns or sets the euler angle representation of the rotation. Returns this quaternion with a magnitude of 1 (Read Only).

What is the difference between unity and quaternions?

Quaternions are used to represent rotations. They are compact, don't suffer from gimbal lock and can easily be interpolated. Unity internally uses Quaternions to represent all rotations. They are based on complex numbers and are not easy to understand intuitively.

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