## 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.

## When did Hamilton discover quaternions?

1843

In the case of quaternions, however, we know that they were discovered by the Irish mathematician, William Rowan Hamilton on October 16*#, 1843 (we will see later how we come to be so precise). The early 19*# century was a very exciting time for Complex Analysis.

**What is the meaning of the word quaternions?**

a set of four parts

Definition of quaternion 1 : a set of four parts, things, or persons.

**What does Slerp stand for?**

In computer graphics, Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation.

### Where do quaternions come from?

Quaternions and rules for operations on them were invented by Irish mathematician Sir William Rowan Hamilton in 1843. He devised them as a way of describing three-dimensional problems in mechanics.

### How do you explain interpolation?

Interpolation is a statistical method by which related known values are used to estimate an unknown price or potential yield of a security. Interpolation is achieved by using other established values that are located in sequence with the unknown value. Interpolation is at root a simple mathematical concept.

**What is the lerp function?**

Linear interpolation, or “lerp” for short, is a technique commonly used when programming things like games or GUIs. In principle, a lerp function “eases” the transition between two values over time, using some simple math.

**What is a quaternion with no rotation?**

There is a special quaternion called the identity quaternion which corresponds to no rotation: Geometrically, we can also consider to be an identity quaternion since it corresponds to no rotation.

#### How can I rotate a quaternion using linear interpolation?

This can be accomplished by choosing a curve such as the spherical linear interpolation in the quaternions, with one endpoint being the identity transformation 1 (or some other initial rotation) and the other being the intended final rotation. This is more problematic with other representations of rotations.

#### What are the special properties of quaternions?

A special property of quaternions is that a unit quaternion (a quaternion with magnitude ) represents a rotation in 3D space. There is a special quaternion called the identity quaternion which corresponds to no rotation: Geometrically, we can also consider to be an identity quaternion since it corresponds to no rotation.

**What is the vector part of the resulting quaternion?**

The vector part of the resulting quaternion is the desired vector p′ . Mathematically, this operation carries the set of all “pure” quaternions p (those with real part equal to zero)—which constitute a 3-dimensional space among the quaternions—into itself, by the desired rotation about the axis u, by the angle θ.