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OpenSolid.Interop.WebGLMath.Vector3d

Transformation functions for Vector3d.

transformBy : Float4x4 -> Vector3d -> Vector3d

Transform a Vector3d by a Float4x4; note that

vector
    |> Vector3d.transformBy matrix

is similar to but not in general equivalent to

vector
    |> Vector3d.components
    |> Matrix4.transform matrix
    |> Vector3d.fromComponents

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.fromComponents ( 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.fromComponents ( -1, 2, 3 )
module OpenSolid.Interop.WebGLMath.Vector3d exposing (transformBy)

{-| Transformation functions for `Vector3d`.

@docs transformBy

-}

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


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

    vector
        |> Vector3d.transformBy matrix

is similar to but _not_ in general equivalent to

    vector
        |> Vector3d.components
        |> Matrix4.transform matrix
        |> Vector3d.fromComponents

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.fromComponents ( 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.fromComponents ( -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.fromComponents
        ( m11 * x + m12 * y + m13 * z
        , m21 * x + m22 * y + m23 * z
        , m31 * x + m32 * y + m33 * z
        )