OpenSolid.Polygon2d

Polygon2d

A Polygon2d represents a closed polygon in 2D, and is defined by a list of vertices. This module contains a variety of polygon-related functionality, such as

Computing the perimeter and area of polygons
Scaling, rotating, translating and mirroring polygons
Converting polygons between different coordinate systems

Polygons can be constructed by passing an ordered list of vertices to the Polygon2d constructor, for example

rectangle =
    Polygon2d
        [ Point2d ( 1, 1 )
        , Point2d ( 3, 1 )
        , Point2d ( 3, 2 )
        , Point2d ( 1, 2 )
        ]

The last vertex is implicitly considered to be connected back to the first vertex (you do not have to close the polygon explicitly).

Accessors

vertices : Polygon2d -> List Point2d

Get the vertices of a polygon.

Polygon2d.vertices rectangle
--> [ Point2d ( 1, 1 )
--> , Point2d ( 3, 1 )
--> , Point2d ( 3, 2 )
--> , Point2d ( 1, 2 )
--> ]

edges : Polygon2d -> List LineSegment2d

Get the edges of a polygon. This will include an edge from the last point back to the first point.

Polygon2d.edges rectangle
--> [ LineSegment2d ( Point2d ( 1, 1 ), Point2d ( 3, 1 ) )
--> , LineSegment2d ( Point2d ( 3, 1 ), Point2d ( 3, 2 ) )
--> , LineSegment2d ( Point2d ( 3, 2 ), Point2d ( 1, 2 ) )
--> , LineSegment2d ( Point2d ( 1, 2 ), Point2d ( 1, 1 ) )
--> ]

Perimeter and area

perimeter : Polygon2d -> Float

Get the perimeter of a polygon (the sum of the lengths of its edges).

Polygon2d.perimeter rectangle
--> 6

area : Polygon2d -> Float

Get the area of a polygon. This value will never be negative.

Polygon2d.area rectangle
--> 2

clockwiseArea : Polygon2d -> Float

Get the signed area of a polygon, with polygons with vertices in clockwise order considered to have positive area and polygons with vertices in counterclockwise order considered to have negative area.

Polygon2d.clockwiseArea rectangle
--> -6

counterclockwiseArea : Polygon2d -> Float

Get the signed area of a polygon, with polygons with vertices in counterclockwise order considered to have positive area and polygons with vertices in clockwise order considered to have negative area.

Polygon2d.counterclockwiseArea rectangle
--> 6

Transformations

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

scaleAbout : Point2d -> Float -> Polygon2d -> Polygon2d

Scale a polygon about a given center point by a given scale.

point =
    Point2d ( 2, 1 )


Polygon2d.scaleAbout point 2 rectangle
--> Polygon2d
-->     [ Point2d ( 0, 1 )
-->     , Point2d ( 4, 1 )
-->     , Point2d ( 4, 3 )
-->     , Point2d ( 0, 3 )
-->     ]

rotateAround : Point2d -> Float -> Polygon2d -> Polygon2d

Rotate a polygon around the given center point counterclockwise by the given angle (in radians).

Polygon2d.rotateAround Point2d.origin (degrees 90) rectangle
--> Polygon2d
-->     [ Point2d ( -1, 1 )
-->     , Point2d ( -1, 3 )
-->     , Point2d ( -2, 3 )
-->     , Point2d ( -2, 1 )
-->     ]

translateBy : Vector2d -> Polygon2d -> Polygon2d

Translate a polygon by the given displacement.

displacement =
    Vector2d ( 2, 3 )


Polygon2d.translateBy displacement rectangle
--> Polygon2d
-->     [ Point2d ( 3, 4 )
-->     , Point2d ( 5, 4 )
-->     , Point2d ( 5, 5 )
-->     , Point2d ( 3, 5 )
-->     ]

mirrorAcross : Axis2d -> Polygon2d -> Polygon2d

Mirror a polygon across the given axis.

Polygon2d.mirrorAcross Axis2d.x rectangle
--> Polygon2d
-->     [ Point2d ( 1, -1 )
-->     , Point2d ( 3, -1 )
-->     , Point2d ( 3, -2 )
-->     , Point2d ( 1, -2 )
-->     ]

Note that if a polygon's vertices were in counterclockwise order before mirroring, they will be in clockwise order afterward, and vice versa.

map : (Point2d -> Point2d) -> Polygon2d -> Polygon2d

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

Polygon2d.mirrorAcross Axis2d.x polygon

is equivalent to

Polygon2d.map (Point2d.mirrorAcross Axis2d.x) polygon

Coordinate frames

relativeTo : Frame2d -> Polygon2d -> Polygon2d

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

localFrame =
    Frame2d.at (Point2d ( 1, 2 ))


Polygon2d.relativeTo localFrame rectangle
--> Polygon2d
-->     [ Point2d ( 0, -1 )
-->     , Point2d ( 2, -1 )
-->     , Point2d ( 2, 0 )
-->     , Point2d ( 0, 0 )
-->     ]

placeIn : Frame2d -> Polygon2d -> Polygon2d

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

localFrame =
    Frame2d.at (Point2d ( 1, 2 ))


Polygon2d.placeIn localFrame rectangle
--> Polygon2d
-->     [ Point2d ( 2, 3 )
-->     , Point2d ( 4, 3 )
-->     , Point2d ( 4, 4 )
-->     , Point2d ( 2, 4 )
-->     ]

Bounds

boundingBox : Polygon2d -> Maybe BoundingBox2d

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

Polygon2d.boundingBox rectangle
--> Just
-->     (BoundingBox2d
-->         { minX = 1
-->         , maxX = 3
-->         , minY = 1
-->         , maxY = 2
-->         }
-->     )

opensolid/geometry/1.0.0