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

Sphere3d.unit
--> Sphere3d.with
-->     { centerPoint = Point3d.origin
-->     , radius = 1
-->     }

Construct a sphere from its center point and radius:

exampleSphere =
    Sphere3d.with
        { centerPoint =
            Point3d.fromCoordinates ( 1, 2, 1 )
        , radius = 3
        }

A negative radius will be interpreted as positive (the absolute value will be used).

Attempt to construct a sphere that passes through the four given points. Returns Nothing if four given points are coplanar.

Sphere3d.throughPoints
    ( Point3d.fromCoordinates ( 1, 0, 0 )
    , Point3d.fromCoordinates ( -1, 0, 0 )
    , Point3d.fromCoordinates ( 0, 1, 0 )
    , Point3d.fromCoordinates ( 0, 0, 0.5 )
    )
--> Just <| Sphere3d.with
    { centerPoint =
        Point3d.fromCoordinates ( 0, 0, -0.75 )
        , radius = 1.25
        }


Sphere3d.throughPoints
    ( Point3d.fromCoordinates ( 1, 0, 0 )
    , Point3d.fromCoordinates ( -1, 0, 0 )
    , Point3d.fromCoordinates ( 0, 1, 0 )
    , Point3d.fromCoordinates ( 0, -1, 0 )
    )
--> Nothing

Get the center point of a sphere.

Sphere3d.centerPoint exampleSphere
--> Point3d.fromCoordinates ( 1, 2, 1 )

Get the radius of a sphere.

Sphere3d.radius exampleSphere
--> 3

Get the diameter of a sphere.

Sphere3d.diameter exampleSphere
--> 6

Get the volume of a sphere.

Sphere3d.volume exampleSphere
--> 113.0973

Get the surface area of a sphere.

Sphere3d.surfaceArea exampleSphere
--> 113.0973

Get the circumference of a sphere (the circumference of a great circle of the sphere).

Sphere3d.circumference exampleSphere
--> 18.8496

Get the minimal bounding box containing a given sphere.

Sphere3d.boundingBox exampleSphere
--> BoundingBox3d.with
-->     { minX = -2
-->     , maxX = 4
-->     , minY = -1
-->     , maxY = 5
-->     , minZ = -2
-->     , maxZ = 4
-->     }

Check if a sphere contains a given point.

Sphere3d.contains
    (Point3d.fromCoordinates ( 4, 2, 1 ))
    exampleSphere
--> True


Sphere3d.contains
    (Point3d.fromCoordinates ( 4.00001, 2, 1 ))
    exampleSphere
--> False

Scale a sphere around a given point by a given scale.

Sphere3d.scaleAbout Point3d.origin 3 exampleSphere
--> Sphere3d.with
-->     { centerPoint =
-->         Point3d.fromCoordinates ( 3, 6, 3 )
-->     , radius = 9
-->     }

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

exampleSphere
    |> Sphere3d.rotateAround Axis3d.y (degrees 90)
--> Sphere3d.with
-->     { centerPoint =
-->         Point3d.fromCoordinates ( 1, 2, -1 )
-->     , radius = 3
-->     }

Translate a sphere by a given displacement.

displacement : Vector3d
displacement =
    Vector3d.fromComponents ( 2, 1, 3 )


Sphere3d.translateBy displacement exampleSphere
--> Sphere3d.with
-->     { centerPoint =
-->         Point3d.fromCoordinates ( 3, 3, 4 )
-->     , radius = 3
-->     }

Mirror a sphere across a given plane.

Sphere3d.mirrorAcross Plane3d.xy exampleSphere
--> Sphere3d.with
-->     { centerPoint =
-->         Point3d.fromCoordinates ( 1, 2, -1 )
-->     , radius = 3
-->     }

Find the orthographic projection of a sphere onto a plane.

Sphere3d.projectOnto Plane3d.xy exampleSphere
--> Circle3d.with
-->     { centerPoint =
-->         Point3d.fromCoordinates ( 1, 2, 0 )
-->     , axialDirection = Direction3d.z
-->     , radius = 3.0
-->     }

Find the orthographic projection of a sphere into a sketch plane.

Sphere3d.projectInto SketchPlane3d.xy exampleSphere
--> Circle2d.with
-->     { centerPoint =
-->         Point2d.fromCoordinates ( 1, 2 )
-->     , radius = 3.0
-->     }

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

localFrame : Frame3d
localFrame =
    Frame3d.atPoint
        (Point3d.fromCoordinates ( 1, 2, 3 ))


Sphere3d.relativeTo localFrame exampleSphere
--> Sphere3d.with
-->     { centerPoint =
-->         Point3d.fromCoordinates ( 0, 0, -2 )
-->     , radius = 3
-->     }

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

localFrame : Frame3d
localFrame =
    Frame3d.atPoint
        (Point3d.fromCoordinates ( 1, 2, 3 ))


Sphere3d.placeIn localFrame exampleSphere
--> Sphere3d.with
-->     { centerPoint =
-->         Point3d.fromCoordinates ( 2, 4, 4 )
-->     , radius = 3
-->     }