# How do you read quaternions?

## How do you read quaternions?

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.

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.

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.

### Do we really need quaternions?

Quaternions are necessary because without them your program will suffer from gimbal lock. Gimbal lock is only an issue if you use Euler angles. 2. Quaternions use less data than vector rotations.

What is a real quaternion?

A quaternion of the form a + 0 i + 0 j + 0 k, where a is a real number, is called scalar, and a quaternion of the form 0 + b i + c j + d k, where b, c, and d are real numbers, and at least one of b, c or d is nonzero, is called a vector quaternion.

What do quaternions mean?

noun. a group or set of four persons or things. Bookbinding. four gathered sheets folded in two for binding together.

## How do you combine two quaternions?

or if you want to use Quaternions use the “*” operator to multiply them together:

1. var rotationAngle : float = 90;
2. var quatA = Quaternion. AngleAxis(rotationAngle , Vector3.
3. var quatB = Quaternion.
4. var quatC = quatA * quatB;
5. //this will be rotate 90 degrees around the z axis and 90 degrees around the y axis.
6. transform.

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

How are two quaternions combined into one rotation?

Two rotation quaternions can be combined into one equivalent quaternion by the relation: ′ = in which q′ corresponds to the rotation q 1 followed by the rotation q 2. (Note that quaternion multiplication is not commutative.) Thus, an arbitrary number of rotations can be composed together and then applied as a single rotation.

### What are quaternions and how are they used in math?

Quaternions and spatial rotation. Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions.

What’s the difference between Q1 and Q2 in quaternions?

Let’s say that your first rotation is q1 and the second is q2. You want to apply them in that order. The resulting quaternion will be q2 * q1, which will represent your composite rotation (recall that quaternions use left-hand multiplication, so q2 is being applied to q1 by multiplying from the left)

Which is an example of an infinitely many quaternion solution?

For example, the equation z 2 + 1 = 0, has infinitely many quaternion solutions, which are the quaternions z = b i + c j + d k such that b 2 + c 2 + d 2 = 1. Thus these “roots of –1” form a unit sphere in the three-dimensional space of vector quaternions.