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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
)
```