The global XY plane, centered at the origin with a normal in the positive Z direction.

Plane3d.xy
--> Plane3d.through Point3d.origin Direction3d.z

The global YZ plane, centered at the origin with a normal in the positive X direction.

Plane3d.yz
--> Plane3d.through Point3d.origin Direction3d.x

The global ZX plane, centered at the origin with a normal in the positive Y direction.

Plane3d.zx
--> through Point3d.origin Direction3d.y

Construct a plane through the given point, with the given normal direction.

xyPlane =
    Plane3d.through Point3d.origin Direction3d.z

Construct a plane with the given normal direction, through the given point. Flipped version of through.

plane =
    Plane3d.withNormalDirection Direction3d.y
        (Point3d.fromCoordinates ( 2, 1, 3 ))

Attempt to construct a plane passing through the three given points. The origin point of the resulting plane will be equal to the first given point, and the normal direction will be such that the three given points are in counterclockwise order around it according to the right-hand rule. If the three given points are collinear, returns Nothing.

Plane3d.throughPoints
    (Point3d.fromCoordinates ( 2, 0, 0 ))
    (Point3d.fromCoordinates ( 3, 0, 0 ))
    (Point3d.fromCoordinates ( 4, 1, 1 ))
--> Just
-->     (Plane3d.through
-->         (Point3d.fromCoordinates ( 2, 0, 0 ))
-->         (Direction3d.fromAzimuthAndElevation
-->             (degrees -90)
-->             (degrees 45)
-->         )
-->     )


Plane3d.throughPoints
    (Point3d.fromCoordinates ( 2, 0, 0 ))
    (Point3d.fromCoordinates ( 3, 0, 0 ))
    (Point3d.fromCoordinates ( 4, 0, 0 ))
--> Nothing

Get the origin point of a plane.

Plane3d.originPoint Plane3d.xy
--> Point3d.origin

Get the normal direction of a plane.

Plane3d.normalDirection Plane3d.xy
--> Direction3d.z

Construct an axis from the origin point and normal direction of a plane.

Plane3d.normalAxis Plane3d.zx
--> Axis3d.y

Shift a plane in its own normal direction by the given (signed) distance.

Plane3d.offsetBy 1.0 Plane3d.zx
--> Plane3d.withNormalDirection Direction3d.y
-->     (Point3d.fromCoordinates ( 0, 1, 0 ))


Plane3d.offsetBy -2.0 Plane3d.xy
--> Plane3d.withNormalDirection Direction3d.z
-->     (Point3d.fromCoordinates ( 0, 0, -2 ))

Reverse a plane's normal direction while leaving its origin point unchanged.

Plane3d.reverseNormal Plane3d.xy
--> Plane3d.through Point3d.origin
-->     Direction3d.negativeZ

Rotate a plane around an axis by a given angle.

Plane3d.rotateAround Axis3d.y (degrees 90) Plane3d.xy
--> Plane3d.yz

Translate a plane by a given displacement. Applies the given displacement to the plane's origin point and leaves its normal direction unchanged.

plane =
    Plane3d.withNormalDirection Direction3d.z
        (Point3d.fromCoordinates ( 1, 1, 1 ))


displacement =
    Vector3d.fromComponents ( 1, 2, 3 )


Plane3d.translateBy displacement plane
--> Plane3d.withNormalDirection Direction3d.z
-->     (Point3d.fromCoordinates ( 2, 3, 4 ))

Translate a plane in a given direction by a given distance;

Plane3d.translateIn direction distance

is equivalent to

Plane3d.translateBy
    (Vector3d.withLength distance direction)

Move a plane so that it has the given origin point but unchanged normal direction.

newOrigin =
    Point3d.fromCoordinates ( 1, 2, 3 )


Plane3d.moveTo newOrigin Plane3d.xy
--> Plane3d.through newOrigin Direction3d.z

Mirror one plane across another. The plane to mirror across is given first and the plane to mirror is given second.

plane =
    Plane3d.withNormalDirection Direction3d.z
        (Point3d.fromCoordinates ( 1, 2, 3 ))


Plane3d.mirrorAcross Plane3d.xy plane
--> Plane3d.withNormalDirection Direction3d.negativeZ
-->     (Point3d.fromCoordinates ( 1, 2, -3 ))

Take a plane defined in global coordinates, and return it expressed in local coordinates relative to a given reference frame.

referenceFrame =
    Frame3d.atPoint
        (Point3d.fromCoordinates ( 1, 1, 1 ))


plane =
    Plane3d.withNormalDirection Direction3d.z
        (Point3d.fromCoordinates ( 0, 0, 2 ))


Plane3d.relativeTo referenceFrame plane
--> Plane3d.withNormalDirection Direction3d.z
-->     (Point3d.fromCoordinates ( -1, -1, 1 ))

Take a plane defined in local coordinates relative to a given reference frame, and return that plane expressed in global coordinates.

referenceFrame =
    Frame3d.atPoint
        (Point3d.fromCoordinates ( 1, 1, 1 ))


plane =
    Plane3d.withNormalDirection Direction3d.z
        (Point3d.fromCoordinates ( 1, 2, 3 ))


Plane3d.placeIn referenceFrame plane
--> Plane3d.withNormalDirection Direction3d.z
-->     (Point3d.fromCoordinates ( 2, 3, 4 ))