Quaternion

A quaternion type. Used for rotations in three dimensions.

Building

{ vector : Vector

, scalar : Float

}

Quaternion is a combination of a 3-vector and a scalar.

quaternion : Float -> Float -> Float -> Float -> Quaternion

Construct a quaternion given its four components. The first argument is the scalar component, the rest are the vector components.

identity : Quaternion

The identity quaternion corresponds to no rotation.

identity == quaternion 1 0 0 0

xRotation : Float -> Quaternion

Create a quaternion corresponding to a rotation about the x axis by the given angle. Rotation is counter-clockwise.

q = xRotation (degrees 90)
v = vector 0 1 0 -- y axis


rotate q v == vector 0 0 1 -- rotated into z axis

yRotation : Float -> Quaternion

Create a quaternion corresponding to a rotation about the y axis by the given angle.

zRotation : Float -> Quaternion

Create a quaternion corresponding to a rotation about the z axis by the given angle.

rotationFor : Vector -> Vector -> Quaternion

Given two vectors, return the quaternion that would rotate the first vector to the second vector. The lengths of the vectors are ignored. If one or both vectors are zero, return the identity quaternion.

fromAxisAngle : Vector -> Float -> Maybe Quaternion

Create a quaternion given an axis and angle of rotation. The length of the axis is ignored, but returns Nothing if the axis is the zero vector.

fromVector : Vector -> Quaternion

Convert a rotation vector to a quaternion. A rotation vector's direction is the axis of rotation, and its length is the angle of rotation.

toVector : Quaternion -> Vector

Convert a quaternion to a rotation vector.

Working With Rotations

similar : Quaternion -> Quaternion -> Bool

Returns true if two quaternions represent the same rotation.

Rotation depends on the direction that a quaternion points in, but not its length.

The zero quaternion is only similar to itself.

mul : Quaternion -> Quaternion -> Quaternion

Multiply two quaternions.

compose : Quaternion -> Quaternion -> Quaternion

Multiplication with the operands flipped.

This can make multiplication easier to use along with the pipe operators |> and <|

compose p q == mul q p

conjugate : Quaternion -> Quaternion

The conjugate of a quaternion.

rotate : Quaternion -> Vector -> Vector

Rotate a vector by a quaternion.

The quaternion does not have to be a unit quaternion. The vector length will be preserved.

If given the zero quaternion, no rotation will be performed.

reverseRotate : Quaternion -> Vector -> Vector

Rotate vector in the opposite direction. reverseRotate q v == rotate (conjugate q) v

Interop

encode : Quaternion -> Value

Convert to a Json Value.

decode : Decoder Quaternion

A Json Decoder for vectors encoded with encode.

toMat4 : Quaternion -> Mat4

Convert to an elm-linear-algebra Mat4

Lesser Math

These functions are not as useful if you are just using quaternions to handle 3D rotations.

equal : Quaternion -> Quaternion -> Bool

Returns true when two quaternions are about equal (within 10^-5).

getW : Quaternion -> Float

Get scalar component.

getX : Quaternion -> Float

Get first vector component.

getY : Quaternion -> Float

Get second vector component.

getZ : Quaternion -> Float

Get third vector component.

lengthSquared : Quaternion -> Float

The square of the length.

length : Quaternion -> Float

The length, or norm, of the quaternion.

add : Quaternion -> Quaternion -> Quaternion

Add two quaternions.

If you are trying to combine rotations, you should to use mul or compose instead.

scale : Float -> Quaternion -> Quaternion

Multiply all of the quaternion's components by a factor.

nphollon/geo3d/2.0.3

Quaternion

Building

Working With Rotations

Interop

Lesser Math

Modules