Construct a polygon from a list of its vertices:

rectangle =
    Polygon2d.fromVertices
        [ Point2d.fromCoordinates ( 1, 1 )
        , Point2d.fromCoordinates ( 3, 1 )
        , Point2d.fromCoordinates ( 3, 2 )
        , Point2d.fromCoordinates ( 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).

Get the vertices of a polygon.

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

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

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

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

Polygon2d.perimeter rectangle
--> 6

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

Polygon2d.area rectangle
--> 2

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

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

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

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

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

point =
    Point2d.fromCoordinates ( 2, 1 )


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

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

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

Translate a polygon by the given displacement.

displacement =
    Vector2d.fromComponents ( 2, 3 )


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

Mirror a polygon across the given axis.

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

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

Polygon2d.mirrorAcross axis

is equivalent to

Polygon2d.mapVertices (Point2d.mirrorAcross axis)

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

localFrame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 1, 2 ))


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

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.atPoint (Point2d.fromCoordinates ( 1, 2 ))


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