A LineSegment2d
is a line between two points in 2D. This module contains
functionality such as:
Geometry.Types.LineSegment2d
fromEndpoints : ( Point2d, Point2d ) -> LineSegment2d
Construct a line segment from its two endpoints:
exampleLineSegment =
LineSegment2d.fromEndpoints
( Point2d.fromCoordinates ( 1, 2 )
, Point2d.fromCoordinates ( 3, 4 )
)
from : Point2d -> Point2d -> LineSegment2d
Construct a line segment from the first point to the second;
LineSegment2d.from firstPoint secondPoint
is equivalent to
LineSegment2d.fromEndpoints ( firstPoint, secondPoint )
along : Axis2d -> Basics.Float -> Basics.Float -> LineSegment2d
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 )
--> )
startPoint : LineSegment2d -> Point2d
Get the start point of a line segment.
LineSegment2d.startPoint exampleLineSegment
--> Point2d.fromCoordinates ( 1, 2 )
endPoint : LineSegment2d -> Point2d
Get the end point of a line segment.
LineSegment2d.endPoint exampleLineSegment
--> Point2d.fromCoordinates ( 3, 4 )
endpoints : LineSegment2d -> ( Point2d, Point2d )
Get the endpoints of a line segment as a tuple.
( p1, p2 ) =
LineSegment2d.endpoints lineSegment
midpoint : LineSegment2d -> Point2d
Get the midpoint of a line segment.
LineSegment2d.midpoint exampleLineSegment
--> Point2d.fromCoordinates ( 2, 3 )
length : LineSegment2d -> Basics.Float
Get the length of a line segment.
LineSegment2d.length exampleLineSegment
--> 2.8284
squaredLength : LineSegment2d -> Basics.Float
Get the squared length of a line segment. Slightly more efficient than
length
since it avoids a square root.
LineSegment2d.squaredLength exampleLineSegment
--> 8
direction : LineSegment2d -> Maybe Direction2d
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))
perpendicularDirection : LineSegment2d -> Maybe Direction2d
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))
vector : LineSegment2d -> Vector2d
Get the vector from a given line segment's start point to its end point.
LineSegment2d.vector exampleLineSegment
--> Vector2d.fromComponents ( 2, 2 )
boundingBox : LineSegment2d -> BoundingBox2d
Get the minimal bounding box containing a given line segment.
LineSegment2d.boundingBox exampleLineSegment
--> BoundingBox2d.fromExtrema
--> { minX = 1
--> , maxX = 3
--> , minY = 2
--> , maxY = 4
--> }
interpolate : LineSegment2d -> Basics.Float -> Point2d
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 )
intersectionPoint : LineSegment2d -> LineSegment2d -> Maybe Point2d
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.
intersectionWithAxis : Axis2d -> LineSegment2d -> Maybe Point2d
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
Transforming a line segment is equivalent to transforming its start and end points and forming a new line segment between the resulting points.
reverse : LineSegment2d -> LineSegment2d
Reverse a line segment, swapping its start and end points.
LineSegment2d.reverse exampleLineSegment
--> LineSegment2d.fromEndpoints
--> ( Point2d.fromCoordinates ( 3, 4 )
--> , Point2d.fromCoordinates ( 1, 2 )
--> )
scaleAbout : Point2d -> Basics.Float -> LineSegment2d -> LineSegment2d
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 )
--> )
rotateAround : Point2d -> Basics.Float -> LineSegment2d -> LineSegment2d
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 )
--> )
translateBy : Vector2d -> LineSegment2d -> LineSegment2d
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 )
--> )
translateIn : Direction2d -> Basics.Float -> LineSegment2d -> LineSegment2d
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)
mirrorAcross : Axis2d -> LineSegment2d -> LineSegment2d
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).
projectOnto : Axis2d -> LineSegment2d -> LineSegment2d
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 )
--> )
mapEndpoints : (Point2d -> Point2d) -> LineSegment2d -> LineSegment2d
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)
relativeTo : Frame2d -> LineSegment2d -> LineSegment2d
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 )
--> )
placeIn : Frame2d -> LineSegment2d -> LineSegment2d
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 )
--> )