Construct a sphere from its radius and center point:

exampleSphere =
    Sphere3d.withRadius (Length.meters 3)
        (Point3d.meters 1 2 1)

If you pass a negative radius, 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.meters 1 0 0)
    (Point3d.meters -1 0 0)
    (Point3d.meters 0 1 0)
    (Point3d.meters 0 0 0.5)
--> Just <|
-->     Sphere3d.withRadius (Length.meters 1.25)
-->         (Point3d.meters 0 0 -0.75)


-- Four coplanar points (in the XY plane)
Sphere3d.throughPoints
    (Point3d.meters 1 0 0)
    (Point3d.meters -1 0 0)
    (Point3d.meters 0 1 0)
    (Point3d.meters 0 -1 0)
--> Nothing

Get the center point of a sphere.

Sphere3d.centerPoint exampleSphere
--> Point3d.meters 1 2 1

Get the radius of a sphere.

Sphere3d.radius exampleSphere
--> Length.meters 3

Get the diameter of a sphere.

Sphere3d.diameter exampleSphere
--> Length.meters 6

Get the volume of a sphere.

Sphere3d.volume exampleSphere
--> Volume.cubicMeters 113.0973

Get the surface area of a sphere.

Sphere3d.surfaceArea exampleSphere
--> Area.squareMeters 113.0973

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

Sphere3d.circumference exampleSphere
--> Length.meters 18.8496

Get the minimal bounding box containing a given sphere.

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

Check if a sphere contains a given point.

exampleSphere
    |> Sphere3d.contains (Point3d.meters 4 2 1)
--> True


exampleSphere
    |> Sphere3d.contains (Point3d.meters 4.00001 2 1)
--> False

Convert a sphere from one units type to another, by providing a conversion factor given as a rate of change of destination units with respect to source units.

Convert a sphere from one units type to another, by providing an 'inverse' conversion factor given as a rate of change of source units with respect to destination units.

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

Rotate a sphere around a given axis by a given angle.

Translate a sphere by a given displacement.

Translate a sphere in a given direction by a given distance.

Mirror a sphere across a given plane.

Find the orthographic projection of a sphere onto a plane.

Sphere3d.projectOnto Plane3d.xy exampleSphere
--> Circle3d.withRadius (Length.meters 3)
-->     Direction3d.z
-->     (Point3d.meters 1 2 0)

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

Sphere3d.projectInto SketchPlane3d.xy exampleSphere
--> Circle2d.withRadius (Length.meters 3)
-->     (Point2d.meters 1 2)

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

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