Construct a line segment from its two endpoints:

exampleLineSegment =
    LineSegment2d.fromEndpoints
        ( Point2d.meters 1 2
        , Point2d.meters 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 given its start point and the vector from its start point to its end point;

LineSegment2d.fromPointAndVector point vector

is equivalent to

LineSegment2d.fromEndpoints
    ( point
    , point |> Point2d.translateBy vector
    )

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
    (Length.meters 3)
    (Length.meters 5)
--> LineSegment2d.fromEndpoints
-->     ( Point2d.meters 3 0
-->     , Point2d.meters 5 0
-->     )

Get the start point of a line segment.

Get the end point of a line segment.

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.meters 2 3

Get the length of a line segment.

LineSegment2d.length exampleLineSegment
--> Length.meters 2.8284

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.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.degrees 135)

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

LineSegment2d.vector exampleLineSegment
--> Vector2d.meters 2 2

Get the minimal bounding box containing a given line segment.

LineSegment2d.boundingBox exampleLineSegment
--> BoundingBox2d.from
-->     (Point2d.meters 1 2)
-->     (Point2d.meters 3 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.meters 1.5 2.5


LineSegment2d.interpolate exampleLineSegment 1.5
--> Point2d.meters 4 5

If you just need to interpolate between two points, you don't have to construct a line segment first - you can use Point2d.interpolateFrom directly.

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.meters 0 0


b =
    Point2d.meters 1 0


c =
    Point2d.meters 1 1


d =
    Point2d.meters 0 1


-- definition of some segments with those points


ab =
    LineSegment2d.from a b
...


-- searching for intersections


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


LineSegment2d.intersectionPoint ac bd
--> Just (Point2d.meters 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.meters 1 -1
        , Point2d.meters 4 1
        )


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


LineSegment2d.intersectionWithAxis Axis2d.y lineSegment
--> Nothing

Measure the distance of a line segment along an axis. This is the range of distances along the axis resulting from projecting the line segment perpendicularly onto the axis.

Note that reversing the line segment will not affect the result.

Measure the distance of a line segment from an axis. If the returned interval:

• is entirely positive, then the line segment is to the left of the axis
• is entirely negative, then the line segment is to the right of the axis
• contains zero, then the line segment crosses the axis

Note that reversing the line segment will not affect the result.

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

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

Rotate a line segment counterclockwise around a given center point by a given angle.

Translate a line segment by a given displacement.

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

Mirror a line segment across an axis. 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.

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)

Convert a line segment 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 a line segment 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.

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

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.