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What are quaternion rotations? (Calculations explained in 2d and 3d)


pavla writes:

Have you been hearing the term ‘Quaternion Rotations’ in Blender and wondered what they are -- or even how to control them?

What this article covers

  • Before we begin...
  • Understanding Complex Numbers in 2d
  • Understanding rotations in 3d
  • Getting Stuck into the Numbers: Quartnenion Calculations
  • Before you Go: Take-Home Challenge

So...what are quaternion rotations?

Quaternions are 3D rotations performed by the multiplication of quaternions.

Got it? Yeah, probably not...

Before explaining how these rotations work, we'll need to define a few terms first.

Before we begin...

1) In computers, everything is represented by numbers.

Numbers make up everything we do on computers (including Blender). Whether it is a character, an operation, the position of a pixel on your screen, a color... or even a number.
Blender will see all operations and input as numbers.

2) Any point in 3d space has three coordinates.

A single point P has coordinates x, y and z. For example, (3.0, 0.73, 2.5). But these coordinates can also represent a 3-dimensional vector.

A number in the form of a ‘triple’ (a, b, c) can represent a simple point, but it could also be another 'type'.

A 'type' refers to a point, but also a color, or a vector.

One type can even change into another, which is what we call 'type-switching'.

3) A triple can represent a vector type.

You may remember vectors from high school maths: a vector is like an arrow, with a direction and a length, but not a fixed position.

In our example, vector (3.0, 0.73, 2.5) is an arrow going from the origin (0, 0, 0) to point (3.0, 0.73, 2.5).

It can be placed anywhere in 3D space, it is still considered the same vector, just with a different triple. the rest of the post on the CG Cookie blog

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