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# Unity normal vector to Quaternion

### axis - Convert a Unit Vector to a Quaternion - Stack Overflo

6.) The conjugate of a vector quaternion is its negative. X * = {0, -x} = -X. 7.) The quaternion norm is |A| = √(A⊗A *) = √( a0² + a.a) 8.) A unit quaternion is one that has a norm of 1. 9.) A unit three-vector x = {x 1, x 2, x 3} with x. x = 1 is expressible as a unit vector quaternion X = { 0, x}, |X| = 1. 10. using UnityEngine; public class Example : MonoBehaviour { void Start () { // A rotation 30 degrees around the y-axis Vector3 rotationVector = new Vector3 (0, 30, 0); Quaternion rotation = Quaternion.Euler (rotationVector); } Unity internally uses Quaternions to represent all rotations. They are based on complex numbers and are not easy to understand intuitively. You almost never access or modify individual Quaternion components (x,y,z,w); most often you would just take existing rotations (e.g. from the Transform ) and use them to construct new rotations (e.g. to smoothly interpolate between two rotations) So if thats the case to get the Quat from the normal you'd do Quaternion.LookRotation( hit.normal, Vector3.back ); And then using that in your smoothing how you have now instead of the from to. If that doesnt look right, try Vector3.forward, up, down, left, right and you should find one that works

### Unity - Scripting API: Quaternion

1. // the second argument, upwards, defaults to Vector3.up Quaternion rotation = Quaternion.LookRotation(relativePos, Vector3.up); transform.rotation = rotation; } } See Also: SetLookRotation . Is something described here not working as you expect it to
2. you can get a DIRECTIONAL VECTOR pointing in the direction of a quaternion by rotating a forward vector like this: Vector3 worldDirection = rotation * Vector3.forward; see : https://docs.unity3d.com/ScriptReference/Quaternion-operator_multiply.htm
3. The unit quaternion can now be written in terms of the angle θ and the unit vector u = q/kqk: q = cosθ +usinθ. R v = 0 + v Pure Quaternions R Quaternions 3 4 v Using the unit quaternion q we deﬁne an operator on vectors v ∈ R3: L q(v) = qvq∗ = (q2 0−kqk 2)v +2(q · v)q +2q (q ×v). (3) Here we make two observations. First, the.
4. The vector part of a unit quaternion represents the radius of the 2-sphere corresponding to the axis of rotation, and its magnitude is the cosine of half the angle of rotation. Each rotation is represented by two unit quaternions of opposite sign, and, as in the space of rotations in three dimensions, the quaternion product of two unit quaternions will yield a unit quaternion. Also, the space of unit quaternions is flat in any infinitesimal neighborhood of a given unit quaternion
5. You should then use the rotation matrix like any other 3D transformation matrix; it will rotate points around the origin as described by the quaternion it came from. The quaternion's X, Y, and Z do represent the axis of the rotation, but the quaternion also encodes the magnitude of the rotation, in a not-particularly-straightforward way. If your package includes functions that return a quaternion, it should also include functions that turn its quaternions into rotation matrices; you should.
6. Quaternions differ from Euler angles in that they use imaginary numbers to define a 3D rotation. While this may sound complicated (and arguably it is), Unity has great builtin functions that allow you to switch between Euler angles and quaterions, as well as functions to modify quaternions, without knowing a single thing about the math behind them. Converting Between Euler and Quaternion

### Normal. Direction - Unity Foru

• And thank you for taking the time to help us improve the quality of Unity Documentation. Close. Your name Your email Suggestion * Submit suggestion. Cancel. public static Vector3 Normalize (Vector3 value); Description. Makes this vector have a magnitude of 1. When normalized, a vector keeps the same direction but its length is 1.0. Note that this function will change the current vector. If you.
• This representation is a higher-dimensional analog of the gnomonic projection, mapping unit quaternions from a 3-sphere onto the 3-dimensional pure-vector hyperplane. It has a discontinuity at 180° ( π radians): as any rotation vector r tends to an angle of π radians, its tangent tends to infinity
• Turn your 3-vector into a quaternion by adding a zero in the extra dimension. [0,x,y,z]. Now if you multiply by a new quaternion, the vector part of that quaternion will be the axis of one complex rotation, and the scalar part is like the cosine of the rotation around that axis. This is the part you want, for a 3D rotation
• A unit quaternion is a quaternion of norm one. Dividing a non-zero quaternion q by its norm produces a unit quaternion U q called the versor of q : U q = q ‖ q ‖ . {\displaystyle \mathbf {U} q={\frac {q}{\lVert q\rVert }}.
• 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 GameObject, Asset or Project Settings, allowing you to inspect and edit the values. More info See in Glossary to make it easy for you to edit. Euler angles and quaternions Euler angles. Euler angles are represented by three.
• Suppose that I have an orientation Quaternion Q, I can compute its forward vector from V = Q * Vector3.forward easily.. Inversely, suppose that I have its forward vector V, how do I compute Q? I know that is not possible, please tell me what's needed beside V, in order to compute Q.. Motivation behind the problem: I have a forward direction of a game object, I want to find out its up direction.

### Rotation formalisms in three dimensions - Wikipedi

Vectors in Unity; Quaternions in Unity: An ode to Quaternions: A quaternion is like a vector, but with a w To construct one, use an axis and an angle, that's what we do. For rotations it must be normal, or otherwise its pure. So we normalise, divide by length, just to be sure. To invert a normal quaternion, we negate x, y and z . Multiply quaternion, vector, inverse quaternion and it rotates. Rotates a vector by a quaternion. quaternion. Creates a vector4 representing a quaternion. resample_linear. rint. Rounds the number to the closest whole number. shl. Bit-shifts an integer left. shr. Bit-shifts an integer right. shrz. Bit-shifts an integer right. sign. Returns -1, 0, or 1 depending on the sign of the argument. sin. Returns the sine of the argument. sinh. Returns the hyperbolic. A surface with a rational ﬁeld of unit normal vectors is called a Pytha-gorean normal vector (PN) surface, and such a surface clearly has rational offsets. Based on a dual approach PN surfaces were derived in  as the envelope of a two-parametric family of tangent planes with unit rational normals. Unfortu-nately, dual construction leads in general to rational surfaces and no algebraic. I am new to the OpenCV, C++, and general to coding. I somehow managed to get Euler's angles from rvec (with some major help). But I have a 180 degree flip in x (sometimes also z) axis. Also is it possible to get quaternion rotation from rvec or rotation matrix? would appreciate a detailed answer as I am very new to this where e is the unit vector along the axis of the minimal rotation between the two quaternions and the asterisk on the right side denotes the quaternion product. You always want theta to be less.    Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchang Convert unit-quaternion to 3-vector. Parameters. q - unit-quaternion. Returns. a unique 3-vector. Return type. ndarray(3) Returns a unique 3-vector representing the input unit-quaternion. The sign of the scalar part is made positive, if necessary by multiplying the entire quaternion by -1, then the vector part is taken That this is necessary is because a unit quaternion and it's derivative are normal to one another. (Any constant length vector and its time derivative are normal to one another.) An additive step in the direction of that derivative necessarily takes the quaternion away from the unit 3-sphere dimensional vector space into itself, we can ﬁnd a matrix representation of each. We will avoid some headaches in the following analysis if we do so. Let the quaternion u be represented by the real vector (u 0,u 1,u 2,u 3)T. Note that the norm of the quaternion is easily related to this dot product of the real vector with itself:

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