Regina supplies some 3-D geometry classes, such as Vector3D. These are intended for visualisation, not exact arithmetic, and they come with the following notes and caveats:

They use floating-point arithmetic, which makes them susceptible to floating-point errors. There is no rigorous management of error bounds, and so any results that use these classes (such as, for example, the projection from a floating-point 3-D spatial link to an exact combinatorial link diagram) should be treated as inexact.
Further to this: equality testing (e.g., testing whether two points coincide, or whether a given point lies on a given line, or whether two lines are parallel) is especially difficult, and should be avoided where possible.
Regina uses a right-handed coordinate system.