OpenSolid.Polyline3d

Polyline3d

Various functions for creating and working with Polyline3d values. 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 examplePolyline ==
    Polyline3d.map (Point3d.mirrorAcross Plane3d.xz) examplePolyline

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/1.0.0