A LineSegment2d
is a line between two points in 2D. This module contains
functionality such as:
Geometry.Types.LineSegment2d units coordinates
fromEndpoints : ( Point2d units coordinates, Point2d units coordinates ) -> LineSegment2d units coordinates
Construct a line segment from its two endpoints:
exampleLineSegment =
LineSegment2d.fromEndpoints
( Point2d.meters 1 2
, Point2d.meters 3 4
)
from : Point2d units coordinates -> Point2d units coordinates -> LineSegment2d units coordinates
Construct a line segment from the first point to the second;
LineSegment2d.from firstPoint secondPoint
is equivalent to
LineSegment2d.fromEndpoints ( firstPoint, secondPoint )
fromPointAndVector : Point2d units coordinates -> Vector2d units coordinates -> LineSegment2d units coordinates
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
)
along : Axis2d units coordinates -> Quantity Basics.Float units -> Quantity Basics.Float units -> LineSegment2d units coordinates
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
--> )
startPoint : LineSegment2d units coordinates -> Point2d units coordinates
Get the start point of a line segment.
endPoint : LineSegment2d units coordinates -> Point2d units coordinates
Get the end point of a line segment.
endpoints : LineSegment2d units coordinates -> ( Point2d units coordinates, Point2d units coordinates )
Get the endpoints of a line segment as a tuple.
( p1, p2 ) =
LineSegment2d.endpoints lineSegment
midpoint : LineSegment2d units coordinates -> Point2d units coordinates
Get the midpoint of a line segment.
LineSegment2d.midpoint exampleLineSegment
--> Point2d.meters 2 3
length : LineSegment2d units coordinates -> Quantity Basics.Float units
Get the length of a line segment.
LineSegment2d.length exampleLineSegment
--> Length.meters 2.8284
direction : LineSegment2d units coordinates -> Maybe (Direction2d coordinates)
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)
axis : LineSegment2d units coordinates -> Maybe (Axis2d units coordinates)
Construct an axis collinear with a given line segment; the origin point of the axis will be the
start point of the line segment and the direction of the axis will be the direction of the line
segment. Returns Nothing
if the line segment has zero length.
perpendicularDirection : LineSegment2d units coordinates -> Maybe (Direction2d coordinates)
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)
vector : LineSegment2d units coordinates -> Vector2d units coordinates
Get the vector from a given line segment's start point to its end point.
LineSegment2d.vector exampleLineSegment
--> Vector2d.meters 2 2
boundingBox : LineSegment2d units coordinates -> BoundingBox2d units coordinates
Get the minimal bounding box containing a given line segment.
LineSegment2d.boundingBox exampleLineSegment
--> BoundingBox2d.from
--> (Point2d.meters 1 2)
--> (Point2d.meters 3 4)
interpolate : LineSegment2d units coordinates -> Basics.Float -> Point2d units coordinates
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.
intersectionPoint : LineSegment2d units coordinates -> LineSegment2d units coordinates -> Maybe (Point2d units coordinates)
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.
intersectionWithAxis : Axis2d units coordinates -> LineSegment2d units coordinates -> Maybe (Point2d units coordinates)
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
signedDistanceAlong : Axis2d units coordinates -> LineSegment2d units coordinates -> Quantity.Interval.Interval Basics.Float units
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.
signedDistanceFrom : Axis2d units coordinates -> LineSegment2d units coordinates -> Quantity.Interval.Interval Basics.Float units
Measure the distance of a line segment from an axis. If the returned interval:
Note that reversing the line segment will not affect the result.
These transformations generally behave just like the ones in the Point2d
module.
reverse : LineSegment2d units coordinates -> LineSegment2d units coordinates
Reverse a line segment, swapping its start and end points.
scaleAbout : Point2d units coordinates -> Basics.Float -> LineSegment2d units coordinates -> LineSegment2d units coordinates
Scale a line segment about the given center point by the given scale.
rotateAround : Point2d units coordinates -> Angle -> LineSegment2d units coordinates -> LineSegment2d units coordinates
Rotate a line segment counterclockwise around a given center point by a given angle.
translateBy : Vector2d units coordinates -> LineSegment2d units coordinates -> LineSegment2d units coordinates
Translate a line segment by a given displacement.
translateIn : Direction2d coordinates -> Quantity Basics.Float units -> LineSegment2d units coordinates -> LineSegment2d units coordinates
Translate a line segment in a given direction by a given distance.
mirrorAcross : Axis2d units coordinates -> LineSegment2d units coordinates -> LineSegment2d units coordinates
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).
projectOnto : Axis2d units coordinates -> LineSegment2d units coordinates -> LineSegment2d units coordinates
Project a line segment onto an axis.
mapEndpoints : (Point2d unitsA coordinatesA -> Point2d unitsB coordinatesB) -> LineSegment2d unitsA coordinatesA -> LineSegment2d unitsB coordinatesB
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)
at : Quantity Basics.Float (Quantity.Rate units2 units1) -> LineSegment2d units1 coordinates -> LineSegment2d units2 coordinates
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.
at_ : Quantity Basics.Float (Quantity.Rate units1 units2) -> LineSegment2d units1 coordinates -> LineSegment2d units2 coordinates
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.
relativeTo : Frame2d units globalCoordinates { defines : localCoordinates } -> LineSegment2d units globalCoordinates -> LineSegment2d units localCoordinates
Take a line segment defined in global coordinates, and return it expressed in local coordinates relative to a given reference frame.
placeIn : Frame2d units globalCoordinates { defines : localCoordinates } -> LineSegment2d units localCoordinates -> LineSegment2d units globalCoordinates
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.