Construct a 3d ellipsoid from its axes and X, Y and Z radii. If you pass a negative radius, the absolute value will be used.

exampleEllipsoid =
    Ellipsoid3d.with
        { axes = Frame3d.atPoint (Point3d.meters 2 1 3)
        , xRadius = Length.meters 5
        , yRadius = Length.meters 3
        , zRadius = Length.meters 4
        }

Get the geometric center of an ellipsoid.

Get the X, Y and Z axes of an ellipsoid as a Frame3d.

Get the X axis of an ellipsoid.

Get the Y axis of an ellipsoid.

Get the Z axis of an ellipsoid.

Get the direction of the ellipsoid's X axis.

Get the direction of the ellipsoid's Y axis.

Get the direction of the ellipsoid's Z axis.

Get the radius of an ellipsoid along its X axis.

Ellipsoid3d.xRadius exampleEllipsoid
--> Length.meters 5

Get the radius of an ellipsoid along its Y axis.

Ellipsoid3d.yRadius exampleEllipsoid
--> Length.meters 3

Get the radius of an ellipsoid along its Z axis.

Ellipsoid3d.zRadius exampleEllipsoid
--> Length.meters 4

Get the volume of an ellipsoid.

Get the minimal bounding box containing a given ellipsoid.

Ellipsoid3d.boundingBox exampleSphere
--> BoundingBox3d.from
-->     (Point3d.meters -3 -2 -1)
-->     (Point3d.meters 7 4 7)

Check if an ellipsoid contains a given point.

Project an ellipsoid onto an axis, returning the range of projected distances along that axis.

Scale an ellipsoid about a given point by a given scale.

Rotate an ellipsoid around a given axis by a given angle.

Translate an ellipsoid by a given displacement.

Translate an ellipsoid in a given direction by a given distance.

Mirror an ellipsoid across a given plane. Note that this will flip the handedness of the ellipsoid's axes.

Convert an ellipsoid 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 an ellipsoid 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.

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

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