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# OpenSolid.WebGLMath.Vector3d

Transformation functions for `Vector3d`.

transformBy : Float4x4 -> Vector3d -> Vector3d

Transform a `Vector3d` by a `Float4x4`; note that

``````Vector3d.transformBy matrix vector
``````

is similar to but not in general equivalent to

``````Vector3d (Matrix4.transform matrix (Vector3d.components vector))
``````

since `Matrix4.transform` implicitly assumes that the given argument represents a point, not a vector, and therefore applies translation to it. Transforming a vector by a 4x4 matrix should in fact ignore any translation component of the matrix, which this function does. For example:

``````vector =
Vector3d ( 2, 1, 3 )

-- 90 degree rotation around the Z axis, followed by a translation
matrix =
Matrix4.makeTranslate ( 5, 5, 5 )
|> Matrix4.rotate (degrees 90) ( 0, 0, 1 )

Vector3d.transformBy matrix vector
--> Vector3d ( -1, 2, 3 )
``````
``````module OpenSolid.WebGLMath.Vector3d
exposing
( transformBy
)

{-| Transformation functions for `Vector3d`.

@docs transformBy

-}

import OpenSolid.Geometry.Types exposing (..)
import OpenSolid.Vector3d as Vector3d
import Matrix4 exposing (Float4x4)

{-| Transform a `Vector3d` by a `Float4x4`; note that

Vector3d.transformBy matrix vector

is similar to but *not* in general equivalent to

Vector3d (Matrix4.transform matrix (Vector3d.components vector))

since `Matrix4.transform` implicitly assumes that the given argument represents
a point, not a vector, and therefore applies translation to it. Transforming a
vector by a 4x4 matrix should in fact ignore any translation component of the
matrix, which this function does. For example:

vector =
Vector3d ( 2, 1, 3 )

-- 90 degree rotation around the Z axis, followed by a translation
matrix =
Matrix4.makeTranslate ( 5, 5, 5 )
|> Matrix4.rotate (degrees 90) ( 0, 0, 1 )

Vector3d.transformBy matrix vector
--> Vector3d ( -1, 2, 3 )

-}
transformBy : Float4x4 -> Vector3d -> Vector3d
transformBy matrix vector =
let
( ( m11, m12, m13, m14 ), ( m21, m22, m23, m24 ), ( m31, m32, m33, m34 ), ( m41, m42, m43, m44 ) ) =
matrix

( x, y, z ) =
Vector3d.components vector
in
Vector3d
( m11 * x + m12 * y + m13 * z
, m21 * x + m22 * y + m23 * z
, m31 * x + m32 * y + m33 * z
)
```
```