The global X axis.

Axis3d.x
--> Axis3d.with
-->     { originPoint = Point3d.origin
-->     , direction = Direction3d.x
-->     }

The global Y axis.

Axis3d.y
--> Axis3d.with
-->     { originPoint = Point3d.origin
-->     , direction = Direction3d.y
-->     }

The global Z axis.

Axis3d.z
--> Axis3d.with
-->     { originPoint = Point3d.origin
-->     , direction = Direction3d.z
-->     }

Construct an axis from its origin point and direction:

exampleAxis =
    Axis3d.with
        { originPoint =
            Point3d.fromCoordinates ( 1, 2, 3 )
        , direction = Direction3d.y
        }

Construct a 3D axis lying on a sketch plane by providing a 2D axis specified in XY coordinates within the sketch plane.

axis2d =
    Axis2d.with
        { originPoint =
            Point2d.fromCoordinates ( 1, 3 )
        , direction =
            Direction2d.fromAngle (degrees 30)
        }


Axis3d.on SketchPlane3d.xy axis2d
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( 1, 3, 0 )
-->     , direction =
-->         Direction3d.with
-->             { azimuth = degrees 30
-->             , elevation = 0
-->             }
-->     }


Axis3d.on SketchPlane3d.zx axis2d
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( 3, 0, 1 )
-->     , direction =
-->         Direction3d.with
-->             { azimuth = 0
-->             , elevation = degrees 60
-->             }
-->     }

Get the origin point of an axis.

Axis3d.originPoint exampleAxis
--> Point3d.fromCoordinates ( 1, 2, 3 )

Get the direction of an axis.

Axis3d.direction exampleAxis
--> Direction3d.y

Reverse the direction of an axis while keeping the same origin point.

Axis3d.flip exampleAxis
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( 1, 2, 3 )
-->     , direction = Direction3d.negativeY
-->     }

Move an axis so that it has the given origin point but unchanged direction.

newOrigin =
    Point3d.fromCoordinates ( 3, 4, 5 )


Axis3d.moveTo newOrigin exampleAxis
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( 3, 4, 5 )
-->     , direction = Direction3d.y
-->     }

Rotate an axis around another axis by a given angle. The axis to rotate around is given first and the axis to rotate is given last.

Axis3d.rotateAround Axis3d.z (degrees 90) exampleAxis
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( -2, 1, 3 )
-->     , direction = Direction3d.negativeX
-->     }

Translate an axis by a given displacement. Applies the given displacement to the axis' origin point and leaves the direction unchanged.

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


Axis3d.translateBy displacement exampleAxis
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( 4, 5, 6 )
-->     , direction = Direction3d.y
-->     }

Mirror an axis across a plane.

Axis3d.mirrorAcross Plane3d.xy exampleAxis
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( 1, 2, -3 )
-->     , direction = Direction3d.y
-->     }

Project an axis onto a plane, returning the axis that is the 'shadow' of the given axis on the given plane. If the given axis is exactly perpendicular to the given plane, returns Nothing.

Axis3d.projectOnto Plane3d.xy exampleAxis
--> Just
-->     (Axis3d.with
-->         { originPoint =
-->             Point3d.fromCoordinates ( 1, 2, 0 )
-->         , direction = Direction3d.y
-->         }
-->     )


Axis3d.projectOnto Plane3d.xy Axis3d.z
--> Nothing

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

localFrame =
    Frame3d.atPoint
        (Point3d.fromCoordinates ( 3, 3, 3 ))


Axis3d.relativeTo localFrame exampleAxis
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( -2, -1, 0 )
-->     , direction = Direction3d.y
-->     }

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

localFrame =
    Frame3d.atPoint
        (Point3d.fromCoordinates ( 3, 3, 3 ))


Axis3d.placeIn localFrame exampleAxis
--> Axis3d.with
-->     { originPoint =
-->         Point3d.fromCoordinates ( 4, 5, 6 )
-->     , direction = Direction3d.y
-->     }

Project an axis into a given sketch plane. Conceptually, this projects the axis onto the plane and then expresses the projected axis in 2D sketch coordinates.

This is only possible if the axis is not perpendicular to the sketch plane; if it is perpendicular, Nothing is returned.

Axis3d.projectInto SketchPlane3d.xy exampleAxis
--> Just
-->     (Axis2d.with
-->         { originPoint =
-->             Point2d.fromCoordinates ( 1, 2 )
-->         , direction = Direction2d.y
-->         }
-->     )


Axis3d.projectInto SketchPlane3d.yz exampleAxis
--> Just
-->     (Axis2d.with
-->         { originPoint =
-->             Point2d.fromCoordinates ( 2, 3 )
-->         -- The global Y direction is the X
-->         -- direction of the YZ plane:
-->         , direction = Direction2d.x
-->         }
-->     )


Axis3d.projectInto SketchPlane3d.xz exampleAxis
--> Nothing