The global X axis.

Axis2d.x
--> Axis2d.through Point2d.origin Direction2d.x

The global Y axis.

Axis2d.y
--> Axis2d.through Point2d.origin Direction2d.y

Construct an axis through the given origin point with the given direction.

exampleAxis =
    Axis2d.through (Point2d.meters 1 3)
        (Direction2d.degrees 30)

Construct an axis with the given direction, through the given origin point. Flipped version of through. Having both versions allow you to do different things with partial application:

-- A list of axes in different directions all passing
-- through the same origin point
List.map (Axis2d.through point) directions


-- A list of parallel axes (all having the same
-- direction) through different points
List.map (Axis2d.withDirection direction) points

Get the origin point of an axis.

Axis2d.originPoint exampleAxis
--> Point2d.meters 1 3

Get the direction of an axis.

Axis2d.direction exampleAxis
--> Direction2d.degrees 30

Convert an axis from one units type to another, by providing a conversion factor given as a rate of change of destination units with respect to source units.

Convert an axis from one units type to another, by providing an 'inverse' conversion factor given as a rate of change of source units with respect to destination units.

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

Axis2d.reverse exampleAxis
--> Axis2d.through (Point2d.meters 1 3)
-->     (Direction2d.degrees -150)

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

newOrigin =
    Point2d.meters 4 5


Axis2d.moveTo newOrigin exampleAxis
--> Axis2d.through (Point2d.meters 4 5)
-->     (Direction2d.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.

exampleAxis
    |> Axis2d.rotateAround Point2d.origin
        (Angle.degrees 90)
--> Axis2d.through (Point2d.meters -3 1)
-->     (Direction2d.degrees 120)

Rotate an axis around its own origin point by the given angle.

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

displacement =
    Vector2d.meters 2 3


Axis2d.translateBy displacement exampleAxis
--> Axis2d.through (Point2d.meters 3 6)
-->     (Direction2d.degrees 30)

Translate an axis in a given direction by a given distance.

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.through (Point2d.meters 1 -3)
-->     (Direction2d.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.meters 2 3)


Axis2d.relativeTo frame exampleAxis
--> Axis2d.through (Point2d.meters -1 0)
-->     (Direction2d.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.meters 2 3)


Axis2d.placeIn frame exampleAxis
--> Axis2d.through (Point2d.meters 3 6)
-->     (Direction2d.degrees 30)