OpenSolid.Polyline3d

Polyline3d

A Polyline3d represents a sequence of vertices connected by line segments. Polylines can be constructed by passing an ordered list of vertices to the Polyline3d constructor, for example

examplePolyline =
    Polyline3d
        [ Point2d ( 0, 0, 0 )
        , Point2d ( 1, 0, 0 )
        , Point2d ( 1, 2, 0 )
        , Point2d ( 1, 2, 3 )
        ]

Accessors

vertices : Polyline3d -> List Point3d

Get the vertices of a polyline.

Polyline3d.vertices examplePolyline
--> [ Point3d ( 0, 0, 0 )
--> , Point3d ( 1, 0, 0 )
--> , Point3d ( 1, 2, 0 )
--> , Point3d ( 1, 2, 3 )
--> ]

segments : Polyline3d -> List LineSegment3d

Get the individual segments of a polyline.

Polyline3d.segments examplePolyline
--> [ LineSegment3d ( Point3d ( 0, 0, 0 ), Point3d ( 1, 0, 0 ) )
--> , LineSegment3d ( Point3d ( 1, 0, 0 ), Point3d ( 1, 2, 0 ) )
--> , LineSegment3d ( Point3d ( 1, 2, 0 ), Point3d ( 1, 2, 3 ) )
--> ]

Length

length : Polyline3d -> Float

Get the overall length of a polyline (the sum of the lengths of its segments).

Polyline3d.length examplePolyline
--> 6

Transformations

Transforming a polyline is equivalent to transforming each of its vertices.

scaleAbout : Point3d -> Float -> Polyline3d -> Polyline3d

Scale a polyline about the given center point by the given scale.

point =
    Point3d ( 1, 0, 0 )


Polyline3d.scaleAbout point 2 examplePolyline
--> Polyline3d
-->     [ Point3d ( -1, 0, 0 )
-->     , Point3d ( 1, 0, 0 )
-->     , Point3d ( 1, 4, 0 )
-->     , Point3d ( 1, 4, 6 )
-->     ]

rotateAround : Axis3d -> Float -> Polyline3d -> Polyline3d

Rotate a polyline around the given axis by the given angle (in radians).

Polyline3d.rotateAround Axis3d.z (degrees 90) examplePolyline
--> Polyline3d
-->     [ Point3d ( 0, 0, 0 )
-->     , Point3d ( 0, 1, 0 )
-->     , Point3d ( -2, 1, 0 )
-->     , Point3d ( -2, 1, 3 )
-->     ]

translateBy : Vector3d -> Polyline3d -> Polyline3d

Translate a polyline by the given displacement.

displacement =
    Vector3d ( 1, 2, 3 )


Polyline3d.translateBy displacement examplePolyline
--> Polyline3d
-->     [ Point3d ( 1, 2, 3 )
-->     , Point3d ( 2, 2, 3 )
-->     , Point3d ( 2, 4, 3 )
-->     , Point3d ( 2, 4, 6 )
-->     ]

mirrorAcross : Plane3d -> Polyline3d -> Polyline3d

Mirror a polyline across the given plane.

Polyline3d.mirrorAcross Plane3d.xz examplePolyline
--> Polyline3d
-->     [ Point3d ( 0, 0, 0 )
-->     , Point3d ( 1, 0, 0 )
-->     , Point3d ( 1, -2, 0 )
-->     , Point3d ( 1, -2, 3 )
-->     ]

projectOnto : Plane3d -> Polyline3d -> Polyline3d

Project (flatten) a polyline onto the given plane.

Polyline3d.projectOnto Plane3d.xz examplePolyline
--> Polyline3d
-->     [ Point3d ( 0, 0, 0 )
-->     , Point3d ( 1, 0, 0 )
-->     , Point3d ( 1, 0, 0 )
-->     , Point3d ( 1, 0, 3 )
-->     ]

map : (Point3d -> Point3d) -> Polyline3d -> Polyline3d

Transform each vertex of a polyline by the given function. All other transformations can be defined in terms of map; for example,

Polyline3d.mirrorAcross Plane3d.xz polyline

is equivalent to

Polyline3d.map (Point3d.mirrorAcross Plane3d.xz) polyline

Coordinate frames

relativeTo : Frame3d -> Polyline3d -> Polyline3d

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

localFrame =
    Frame3d.at (Point3d ( 1, 2, 3 ))


Polyline3d.relativeTo localFrame examplePolyline
--> Polyline3d
-->     [ Point3d ( -1, -2, -3 )
-->     , Point3d ( 0, -2, -3 )
-->     , Point3d ( 0, 0, -3 )
-->     , Point3d ( 0, 0, 0 )
-->     ]

placeIn : Frame3d -> Polyline3d -> Polyline3d

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

localFrame =
    Frame3d.at (Point3d ( 1, 2, 3 ))


Polyline3d.placeIn localFrame examplePolyline
--> Polyline3d
-->     [ Point3d ( 1, 2, 3 )
-->     , Point3d ( 2, 2, 3 )
-->     , Point3d ( 2, 4, 3 )
-->     , Point3d ( 2, 4, 6 )
-->     ]

Sketch planes

projectInto : SketchPlane3d -> Polyline3d -> Polyline2d

Project a polyline into a given sketch plane. Conceptually, this projects the polyline onto the plane and then expresses the projected polyline in 2D sketch coordinates.

Polyline3d.projectInto Plane3d.xy examplePolyline
--> Polyline2d
-->     [ Point2d ( 0, 0 )
-->     , Point2d ( 1, 0 )
-->     , Point2d ( 1, 2 )
-->     , Point2d ( 1, 2 )
-->     ]

Bounds

boundingBox : Polyline3d -> Maybe BoundingBox3d

Get the minimal bounding box containing a given polyline. Returns Nothing if the polyline has no vertices.

Polyline3d.boundingBox examplePolyline
--> Just
-->     (BoundingBox3d
-->         { minX = 0
-->         , maxX = 1
-->         , minY = 0
-->         , maxY = 2
-->         , minZ = 0
-->         , maxZ = 3
-->         }
-->     )

opensolid/geometry/1.0.3