OpenSolid.Axis2d

Axis2d

An Axis2d represents an infinitely long straight line in 2D and is defined by an origin point and direction. Axes have several uses, such as:

Mirroring across the axis
Projecting onto the axis
Measuring distance along the axis

Axes can by constructed by passing a record with originPoint and direction fields to the Axis2d constructor, for example:

exampleAxis =
    Axis2d
        { originPoint = Point2d ( 1, 3 )
        , direction = Direction2d ( 0.8, 0.6 )
        }

Predefined axes

x : Axis2d

The global X axis.

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

y : Axis2d

The global Y axis.

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

Accessors

originPoint : Axis2d -> Point2d

Get the origin point of an axis.

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

direction : Axis2d -> Direction2d

Get the direction of an axis.

Axis2d.direction exampleAxis
--> Direction2d ( 0.8, 0.6 )

Transformations

flip : Axis2d -> Axis2d

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

Axis2d.flip exampleAxis
--> Axis2d
-->     { originPoint = Point2d ( 1, 3 )
-->     , direction = Direction2d ( -0.8, -0.6 )
-->     }

moveTo : Point2d -> Axis2d -> Axis2d

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

newOrigin =
    Point2d ( 4, 5 )


Axis2d.moveTo newOrigin exampleAxis
--> Axis2d
-->     { originPoint = Point2d ( 4, 5 )
-->     , direction = Direction2d ( 0.8, 0.6 )
-->     }

rotateAround : Point2d -> Float -> Axis2d -> Axis2d

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
-->     { originPoint = Point2d ( -3, 1 )
-->     , direction = Direction2d ( -0.6, 0.8 )
-->     }

translateBy : Vector2d -> Axis2d -> Axis2d

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

displacement =
    Vector2d ( 2, 3 )


Axis2d.translateBy displacement exampleAxis
--> Axis2d
-->     { originPoint = Point2d ( 3, 6 )
-->     , direction = Direction2d ( 0.8, 0.6 )
-->     }

mirrorAcross : Axis2d -> Axis2d -> Axis2d

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
-->     { originPoint = Point2d ( 1, -3 )
-->     , direction = Direction2d ( 0.8, -0.6 )
-->     }

Coordinate frames

Functions for transforming axes between local and global coordinates in different coordinate frames.

relativeTo : Frame2d -> Axis2d -> Axis2d

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

originPoint =
    Point2d ( 2, 3 )


Axis2d.relativeTo (Frame2d.at originPoint) exampleAxis
--> Axis2d
-->     { originPoint = Point2d ( -1, 0 )
-->     , direction = Direction2d ( 0.8, 0.6 )
-->     }

placeIn : Frame2d -> Axis2d -> Axis2d

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

originPoint =
    Point2d ( 2, 3 )


Axis2d.placeIn (Frame2d.at originPoint) exampleAxis
--> Axis2d
-->     { originPoint = Point2d ( 3, 6 )
-->     , direction = Direction2d ( 0.8, 0.6 )
-->     }

Sketch planes

placeOnto : SketchPlane3d -> Axis2d -> Axis3d

Take an axis defined in 2D coordinates within a particular sketch plane and return the corresponding axis in 3D.

Axis2d.placeOnto SketchPlane3d.xy exampleAxis
--> Axis3d
-->     { originPoint = Point3d ( 2, 3, 0 )
-->     , direction = Direction3d ( 0.8, 0.6, 0 )
-->     }


Axis2d.placeOnto SketchPlane3d.zx exampleAxis
--> Axis3d
-->     { originPoint = Point3d ( 3, 0, 2 )
-->     , direction = Direction3d ( 0.6, 0, 0.8 )
-->     }

opensolid/geometry/1.0.0