The unit circle, centered on the origin with a radius of 1.

Circle2d.unit
--> Circle2d.with
-->     { centerPoint = Point2d.origin
-->     , radius = 1
-->     }

Construct a circle from its center point and radius:

exampleCircle =
    Circle2d.with
        { centerPoint =
            Point2d.fromCoordinates ( 1, 2 )
        , radius = 3
        }

The actual radius of the circle will be the absolute value of the given radius (passing radius = -2 will have the same effect as radius = 2).

Attempt to construct a circle that passes through the three given points. If the three given points are collinear, returns Nothing.

Circle2d.throughPoints
    ( Point2d.origin
    , Point2d.fromCoordinates ( 1, 0 )
    , Point2d.fromCoordinates ( 0, 1 )
    )
--> Just
-->     (Circle2d.with
-->         { centerPoint =
-->             Point2d.fromCoordinates ( 0.5, 0.5 )
-->         , radius = 0.7071
-->         }
-->     )


Circle2d.throughPoints
    ( Point2d.origin
    , Point2d.fromCoordinates ( 2, 1 )
    , Point2d.fromCoordinates ( 4, 0 )
    )
--> Just
-->     (Circle2d.with
-->         { centerPoint =
-->             Point2d.fromCoordinates ( 2, -1.5 )
-->         , radius = 2.5
-->         }
-->     )


Circle2d.throughPoints
    ( Point2d.origin
    , Point2d.fromCoordinates ( 2, 0 )
    , Point2d.fromCoordinates ( 4, 0 )
    )
--> Nothing


Circle2d.throughPoints
    ( Point2d.origin
    , Point2d.origin
    , Point2d.fromCoordinates ( 1, 0 )
    )
--> Nothing

Get the center point of a circle.

Circle2d.centerPoint exampleCircle
--> Point2d.fromCoordinates ( 1, 2 )

Get the radius of a circle.

Circle2d.radius exampleCircle
--> 3

Get the diameter of a circle.

Circle2d.diameter exampleCircle
--> 6

Get the area of a circle.

Circle2d.area exampleCircle
--> 28.2743

Get the circumference of a circle.

Circle2d.circumference exampleCircle
--> 18.8496

Get the minimal bounding box containing a given circle.

Circle2d.boundingBox exampleCircle
--> BoundingBox2d.with
-->     { minX = -2
-->     , maxX = 4
-->     , minY = -1
-->     , maxY = 5
-->     }

Convert a circle to a 360 degree arc.

Circle2d.toArc exampleCircle
--> Arc2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( 1, 2 )
-->     , startPoint =
-->         Point2d.fromCoordinates ( 4, 2 )
-->     , sweptAngle = degrees 360
-->     }

Check if a circle contains a given point.

Circle2d.contains Point2d.origin exampleCircle
--> True


exampleCircle
    |> Circle2d.contains
        (Point2d.fromCoordinates ( 10, 10 ))
--> False

Scale a circle about a given point by a given scale.

Circle2d.scaleAbout Point2d.origin 2 exampleCircle
--> Circle2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( 2, 4 )
-->     , radius = 6
-->     }


exampleCircle
    |> Circle2d.scaleAbout
        (Point2d.fromCoordinates ( 1, 2 ))
        0.5
--> Circle2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( 1, 2 )
-->     , radius = 1.5
-->     }

Rotate a circle around a given point by a given angle (in radians).

exampleCircle
    |> Circle2d.rotateAround Point2d.origin
        (degrees 90)
--> Circle2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( -2, 1 )
-->     , radius = 3
-->     }

Translate a circle by a given displacement.

exampleCircle
    |> Circle2d.translateBy
        (Vector2d.fromComponents ( 2, 2 ))
--> Circle2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( 3, 4 )
-->     , radius = 3
-->     }

Mirror a circle across a given axis.

Circle2d.mirrorAcross Axis2d.x exampleCircle
--> Circle2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( 1, -2 )
-->     , radius = 3
-->     }

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

localFrame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 2, 3 ))


Circle2d.relativeTo localFrame exampleCircle
--> Circle2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( -1, -1 )
-->     , radius = 3
-->     }

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

localFrame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 2, 3 ))


Circle2d.placeIn localFrame exampleCircle
--> Circle2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( 3, 5 )
-->     , radius = 3
-->     }