Construct a line segment from its two endpoints:

exampleLineSegment =
    LineSegment2d.fromEndpoints
        ( Point2d.fromCoordinates ( 1, 2 )
        , Point2d.fromCoordinates ( 3, 4 )
        )

Construct a line segment from the first point to the second;

LineSegment2d.from firstPoint secondPoint

is equivalent to

LineSegment2d.fromEndpoints ( firstPoint, secondPoint )

Construct a line segment lying on the given axis, with its endpoints at the given distances from the axis' origin point.

LineSegment2d.along Axis2d.x 3 5
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 3, 0 )
-->     , Point2d.fromCoordinates ( 5, 0 )
-->     )


LineSegment2d.along Axis2d.y 2 -4
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 0, 2 )
-->     , Point2d.fromCoordinates ( 0, -4 )
-->     )

Get the start point of a line segment.

LineSegment2d.startPoint exampleLineSegment
--> Point2d.fromCoordinates ( 1, 2 )

Get the end point of a line segment.

LineSegment2d.endPoint exampleLineSegment
--> Point2d.fromCoordinates ( 3, 4 )

Get the endpoints of a line segment as a tuple.

( p1, p2 ) =
    LineSegment2d.endpoints lineSegment

Get the midpoint of a line segment.

LineSegment2d.midpoint exampleLineSegment
--> Point2d.fromCoordinates ( 2, 3 )

Get the length of a line segment.

LineSegment2d.length exampleLineSegment
--> 2.8284

Get the squared length of a line segment. Slightly more efficient than length since it avoids a square root.

LineSegment2d.squaredLength exampleLineSegment
--> 8

Get the direction from a line segment's start point to its end point. If the line segment has zero length (the start and end points are the same), returns Nothing.

LineSegment2d.direction exampleLineSegment
--> Just (Direction2d.fromAngle (degrees 45))

Get the direction perpendicular to a line segment, pointing to the left. If the line segment has zero length, returns Nothing.

LineSegment2d.perpendicularDirection exampleLineSegment
--> Just (Direction2d.fromAngle (degrees 135))

Get the vector from a given line segment's start point to its end point.

LineSegment2d.vector exampleLineSegment
--> Vector2d.fromComponents ( 2, 2 )

Get the minimal bounding box containing a given line segment.

LineSegment2d.boundingBox exampleLineSegment
--> BoundingBox2d.fromExtrema
-->     { minX = 1
-->     , maxX = 3
-->     , minY = 2
-->     , maxY = 4
-->     }

Interpolate a line segment between its start and end points; a value of 0.0 corresponds to the start point of the line segment, a value of 0.5 corresponds to its midpoint and a value of 1.0 corresponds to its end point. Values less than 0.0 or greater than 1.0 can be used to extrapolate.

LineSegment2d.interpolate exampleLineSegment 0.25
--> Point2d.fromCoordinates ( 1.5, 2.5 )


LineSegment2d.interpolate exampleLineSegment 1.5
--> Point2d.fromCoordinates ( 4, 5 )

Attempt to find the unique intersection point of two line segments. If there is no such point (the two line segments do not touch, or they overlap), returns Nothing.

-- 4 corners of a square


a =
    Point2d.fromCoordinates ( 0, 0 )


b =
    Point2d.fromCoordinates ( 1, 0 )


c =
    Point2d.fromCoordinates ( 1, 1 )


d =
    Point2d.fromCoordinates ( 0, 1 )


-- definition of some segments with those points


ab =
    LineSegment2d.from a b
...


-- searching for intersections


LineSegment2d.intersectionPoint ab bc
--> Just (Point2d.fromCoordinates ( 1, 0 ))
-- corner point b


LineSegment2d.intersectionPoint ac bd
--> Just (Point2d.fromCoordinates ( 0.5, 0.5 ))
-- diagonal crossing at square center


LineSegment2d.intersectionPoint ab cd
--> Nothing -- parallel lines


LineSegment2d.intersectionPoint ab ab
--> Nothing -- collinear lines

Note that if the endpoint of one line segment lies on the other line segment, numerical roundoff means that the intersection may or may not be found. If two segments have a shared endpoint (the two segments meet in something like a 'V', where the end point of one segment is the start point of the next), that point is guaranteed to be returned as the intersection point, but if two segments meet in a 'T' shape the intersection point may or may not be found.

Attempt to find the unique intersection point of a line segment with an axis. If there is no such point (the line segment does not touch the axis, or lies perfectly along it), returns Nothing.

lineSegment =
    LineSegment2d.fromEndpoints
        ( Point2d.fromCoordinates ( 1, -1 )
        , Point2d.fromCoordinates ( 4, 1 )
        )


LineSegment2d.intersectionWithAxis Axis2d.x lineSegment
--> Just (Point2d.fromCoordinates ( 2.5, 0 ))


LineSegment2d.intersectionWithAxis Axis2d.y lineSegment
--> Nothing

Reverse a line segment, swapping its start and end points.

LineSegment2d.reverse exampleLineSegment
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 3, 4 )
-->     , Point2d.fromCoordinates ( 1, 2 )
-->     )

Scale a line segment about the given center point by the given scale.

point =
    Point2d.fromCoordinates ( 1, 1 )


LineSegment2d.scaleAbout point 2 exampleLineSegment
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 1, 3 )
-->     , Point2d.fromCoordinates ( 5, 7 )
-->     )

Rotate a line segment counterclockwise around a given center point by a given angle (in radians).

exampleLineSegment
    |> LineSegment2d.rotateAround Point2d.origin
        (degrees 90)
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( -2, 1 )
-->     , Point2d.fromCoordinates ( -4, 3 )
-->     )

Translate a line segment by a given displacement.

displacement =
    Vector2d.fromComponents ( 1, 2 )


exampleLineSegment
    |> LineSegment2d.translateBy displacement
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 2, 4 )
-->     , Point2d.fromCoordinates ( 4, 6 )
-->     )

Translate a line segment in a given direction by a given distance;

LineSegment2d.translateIn direction distance

is equivalent to

LineSegment2d.translateBy
    (Vector2d.withLength distance direction)

Mirror a line segment across an axis.

LineSegment2d.mirrorAcross Axis2d.y exampleLineSegment
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( -1, 2 )
-->     , Point2d.fromCoordinates ( -3, 4 )
-->     )

Note that the endpoints of a mirrored segment are equal to the mirrored endpoints of the original segment, but as a result the normal direction of a mirrored segment is the opposite of the mirrored normal direction of the original segment (since the normal direction is always considered to be 'to the left' of the line segment).

Project a line segment onto an axis.

LineSegment2d.projectOnto Axis2d.x exampleLineSegment
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 1, 0 )
-->     , Point2d.fromCoordinates ( 3, 0 )
-->     )


LineSegment2d.projectOnto Axis2d.y exampleLineSegment
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 0, 2 )
-->     , Point2d.fromCoordinates ( 0, 4 )
-->     )

Transform the start and end points of a line segment by a given function and create a new line segment from the resulting points. Most other transformation functions can be defined in terms of mapEndpoints; for example,

LineSegment2d.projectOnto axis

is equivalent to

LineSegment2d.mapEndpoints (Point2d.projectOnto axis)

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

localFrame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 1, 2 ))


LineSegment2d.relativeTo localFrame exampleLineSegment
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 0, 0 )
-->     , Point2d.fromCoordinates ( 2, 2 )
-->     )

Take a line segment considered to be defined in local coordinates relative to a given reference frame, and return that line segment expressed in global coordinates.

localFrame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 1, 2 ))


LineSegment2d.placeIn localFrame exampleLineSegment
--> LineSegment2d.fromEndpoints
-->     ( Point2d.fromCoordinates ( 2, 4 )
-->     , Point2d.fromCoordinates ( 4, 6 )
-->     )