The global X axis.

Axis2d.x
--> Axis2d.with
-->     { originPoint = Point2d.origin
-->     , direction = Direction2d.x
-->     }

The global Y axis.

Axis2d.y
--> Axis2d.with
-->     { originPoint = Point2d.origin
-->     , direction = Direction2d.y
-->     }

Construct an axis from its origin point and direction:

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

Get the origin point of an axis.

Axis2d.originPoint exampleAxis
--> Point2d.fromCoordinates ( 1, 3 )

Get the direction of an axis.

Axis2d.direction exampleAxis
--> Direction2d.fromAngle (degrees 30)

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

Axis2d.flip exampleAxis
--> Axis2d.with
-->     { originPoint =
-->         Point2d.fromCoordinates ( 1, 3 )
-->     , direction =
-->         Direction2d.fromAngle (degrees -150)
-->     }

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

newOrigin =
    Point2d.fromCoordinates ( 4, 5 )


Axis2d.moveTo newOrigin exampleAxis
--> Axis2d.with
-->     { originPoint =
-->         Point2d.fromCoordinates ( 4, 5 )
-->     , direction =
-->         Direction2d.fromAngle (degrees 30)
-->     }

Rotate an axis around a given center point by a given angle. Rotates the axis' origin point around the given point by the given angle and the axis' direction by the given angle.

Axis2d.rotateAround Point2d.origin
    (degrees 90)
    exampleAxis
--> Axis2d.with
-->     { originPoint =
-->         Point2d.fromCoordinates ( -3, 1 )
-->     , direction =
-->         Direction2d.fromAngle (degrees 120)
-->     }

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

displacement =
    Vector2d.fromComponents ( 2, 3 )


Axis2d.translateBy displacement exampleAxis
--> Axis2d.with
-->     { originPoint =
-->         Point2d.fromCoordinates ( 3, 6 )
-->     , direction =
-->         Direction2d.fromAngle (degrees 30)
-->     }

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

Axis2d.mirrorAcross Axis2d.x exampleAxis
--> Axis2d.with
-->     { originPoint =
-->         Point2d.fromCoordinates ( 1, -3 )
-->     , direction =
-->         Direction2d.fromAngle (degrees -30)
-->     }

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

frame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 2, 3 ))


Axis2d.relativeTo frame exampleAxis
--> Axis2d.with
-->     { originPoint =
-->         Point2d.fromCoordinates ( -1, 0 )
-->     , direction =
-->         Direction2d.fromAngle (degrees 30)
-->     }

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

frame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 2, 3 ))


Axis2d.placeIn frame exampleAxis
--> Axis2d.with
-->     { originPoint =
-->         Point2d.fromCoordinates ( 3, 6 )
-->     , direction =
-->         Direction2d.fromAngle (degrees 30)
-->     }