View source for Type:FloatQ

A ''FloatQ'' is a floating point representation of a [https://en.wikipedia.org/wiki/Quaternion Quaternion], used to represent rotations on things such as [[Slot]]s.

== Overview ==

The underlying mathematics of a quaternions are complicated and are beyond the scope of this article. That said, [[Resonite]] provides plenty of helpers to make working with them more intuitive.

Quaternions are internally made up of '''four''' components: '''X''', '''Y''', '''Z''', and '''W'''. Since these values are not easy to understand directly, Resonite will usually show quaternions by converting them to and from 3-component [https://en.wikipedia.org/wiki/Euler_angles Euler angles]. 

Quaternion multiplication is '''[https://en.wikipedia.org/wiki/Anticommutative_property not commutative!]''' Multiplying one '''FloatQ''' by another will rotate the second '''FloatQ''' by the first one, order is important.

== In ProtoFlux ==

=== Rotations With Math ===

[[ProtoFlux]] has specific nodes for working with quaternions, primarily under the [[:Category:ProtoFlux:Math:Rotation]] category.

=== Rotations With Matrices ===

There is a section in [[ProtoFlux]] that can let you compose or decompose a rotation using matrices, and that category is [[:Category:ProtoFlux:Operators:Matrix]].

== Examples ==
[[File:FloatQ Rotation Example.png|alt=Screenshot of Protoflux]]

The above [[ProtoFlux|Protoflux]] is rotating a [[Type:Float3|Float3]] vector 90° counter-clockwise around the Y-axis using a FloatQ. This transforms a vector facing towards +X into one towards -Z. Note that the X-component of the output vector is written in [[wikipedia:Scientific_notation|scientific notation]] representing 0.00000005960464. This very small number is the result of precision errors.

[[File:FloatQ Rotation Example 2.png|alt=Frotoflux Screenshot]]

The above Protoflux is first rotating a vector 90° counter-clockwise around the Y-axis and then 90° counter-clockwise around the X-axis. This results in a vector facing towards +Y. The order of the operands is important when rotating a floatQ as it is '''not commutative'''. See below for an example.

[[File:FloatQ Rotation Example 3.png]]

If the operands were swapped, the result would not be different from the first example. To understand this, think of rotating a vector facing towards +X around the X-axis first. The result is the same.

== Further Reading ==

=== Videos ===

A video showing how it looks like visually when working with quaternions:
<youtube>d4EgbgTm0Bg</youtube>

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