This is an alternative site for discovering Elm packages. You may be looking for the official Elm package site instead.

# OpenSolid.LinearAlgebra.Point3d

Conversion and transformation functions for `Point3d`.

toVec3 : Point3d -> Vec3

Convert a `Point3d` to a `Vec3`.

``````Point3d.toVec3 (Point3d ( 2, 1, 3 ))
--> Vector3.vec3 2 1 3
``````
fromVec3 : Vec3 -> Point3d

Convert a `Vec3` to a `Point3d`.

``````Point3d.fromVec3 (Vector3.vec3 2 1 3)
--> Point3d ( 2, 1, 3 )
``````
transformBy : Mat4 -> Point3d -> Point3d

Transform a `Point3d` by a `Mat4`;

``````Point3d.transformBy matrix point
``````

is equivalent to (but more efficient than)

``````Point3d.fromVec3 (Matrix4.transform matrix (Point3d.toVec3 point))
``````

For example:

``````point =
Point3d ( 2, 1, 3 )

matrix =
Matrix4.makeTranslate3 3 4 5

Point3d.transformBy matrix point
--> Point3d ( 5, 5, 8 )
``````
``````module OpenSolid.LinearAlgebra.Point3d
exposing
( toVec3
, fromVec3
, transformBy
)

{-| Conversion and transformation functions for `Point3d`.

@docs toVec3, fromVec3, transformBy

-}

import OpenSolid.Geometry.Types exposing (..)
import OpenSolid.Point3d as Point3d
import Math.Vector3 exposing (Vec3)
import Math.Matrix4 exposing (Mat4)

{-| Convert a `Point3d` to a `Vec3`.

Point3d.toVec3 (Point3d ( 2, 1, 3 ))
--> Vector3.vec3 2 1 3

-}
toVec3 : Point3d -> Vec3
toVec3 point =
Math.Vector3.fromTuple (Point3d.coordinates point)

{-| Convert a `Vec3` to a `Point3d`.

Point3d.fromVec3 (Vector3.vec3 2 1 3)
--> Point3d ( 2, 1, 3 )

-}
fromVec3 : Vec3 -> Point3d
fromVec3 vec =
Point3d (Math.Vector3.toTuple vec)

{-| Transform a `Point3d` by a `Mat4`;

Point3d.transformBy matrix point

is equivalent to (but more efficient than)

Point3d.fromVec3 (Matrix4.transform matrix (Point3d.toVec3 point))

For example:

point =
Point3d ( 2, 1, 3 )

matrix =
Matrix4.makeTranslate3 3 4 5

Point3d.transformBy matrix point
--> Point3d ( 5, 5, 8 )

-}
transformBy : Mat4 -> Point3d -> Point3d
transformBy matrix point =
let
{ m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44 } =
Math.Matrix4.toRecord matrix

( x, y, z ) =
Point3d.coordinates point
in
Point3d
( m11 * x + m12 * y + m13 * z + m14
, m21 * x + m22 * y + m23 * z + m24
, m31 * x + m32 * y + m33 * z + m34
)
```
```