What is the difference between two quaternions?

Using quaternions¶ The difference rotation quaternion that represents the difference rotation is defined as r ≜ p q ∗ . The distance between rotations represented by unit quaternions p and q is the angle of the difference rotation represented by the unit quaternion r = p q ∗ .

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How do quaternions describe rotation?

Quaternions are an alternate way to describe orientation or rotations in 3D space using an ordered set of four numbers. They have the ability to uniquely describe any three-dimensional rotation about an arbitrary axis and do not suffer from gimbal lock.

How do you subtract two quaternions?

Quaternions are a kind of matrix (a 1×4 matrix containing complex numbers). To append (or add) a matrix, you use matrix multiplication. There is no ‘remove/subtract’ a matrix. But you can get the effective result by appending the inverse of a matrix.

How do you find the quaternion between two quaternions?

How are you computing the difference between P2 and P1’s quaternions? To find the quaternion q’ which will transform q1 into q2, you have to find the inverse of q1, q1^’1 and left-multiply by q2.
I’m doing it like you say. I have edited my question to show the whole process to find the difference.

How do quaternions compare?

If your two quaternions are q1 and q2 , they represent the same rotation if either of these two conditions hold:

q1 is component wise approximately equal to q2 OR.
q1 is component wise approximately equal to -q2.

What is the dot product of two quaternions?

The dot-product (inner product) of two quaternions is their usual vector dot-product: ˙p· ˙q = p0q0 + pxqx + pyqy + pzqz. a vector. A unit quaternion has squared length one.

Why are quaternions used for rotations?

Quaternions are very efficient for analyzing situations where rotations in R3 are involved. A quaternion is a 4-tuple, which is a more concise representation than a rotation matrix. Its geo- metric meaning is also more obvious as the rotation axis and angle can be trivially recovered.

How do you rotate a quaternion by another quaternion?

Use the Quaternion operator * . In Unity, when you multiply two quaternions, it applies the second quaternion (expressed in global axes) to the first quaternion along the local axes produced after the first Quaternion ). So, if you want to do the equivalent of Rotate(q2, Space.

How do you add two quaternion rotations?

If you want to combine the effect of two quaternion rotations, you multiply them, not add them.

How do you know if two quaternions are equal?

If your two quaternions are q1 and q2 , they represent the same rotation if either of these two conditions hold:

q1 is component wise approximately equal to q2 OR.
q1 is component wise approximately equal to -q2.

How do you combine quaternion rotations?

To rotate a vector v=ix+jy+kz by a quaternion q you compute vq=qvq−1. So if q and q′ are two rotation quaternions, to rotate by q then q′ you calculate (vq)q′=q′qvq−1q′−1=q′qv(q′q)−1=vq′q.

Can two quaternions represent same rotation?

Any given rotation has two possible quaternion representations. If one is known, the other can be found by taking the negative of all four terms. This has the effect of reversing both the rotation angle and the axis of rotation. So if q is a rotation quaternion, then q and −q will produce the same rotation.

How do you rotate a point with quaternions?

the rotatepoint function performs the following operations:

Converts point [x,y,z] to a quaternion: u q = 0 + x i + y j + z k.
Normalizes the quaternion, q: q n = q a 2 + b 2 + c 2 + d 2.
Applies the rotation: v q = q u q q *
Converts the quaternion output, vq, back to R3

What happens when you add quaternions?

if your quats represent infinitesimal rotations, adding them together actually yields the composite rotation, provided the result is infinitesimal too (i.e. an element of that algebraic group). Quaternion addition, as opposed to multiplication, is commutative and, well, numerically fast.

How do you compare quaternions?

How to compare two quaternions?

bool RotationEquals(Quaternion r1, Quaternion r2)
{
float abs = Mathf. Abs(Quaternion. Dot(r1, r2));
if (abs >= 0. 9999999f)
return true;
return false;
}