Multi-knots and CV multiplicity

A multi-knot is multiple edit points at the same location in space.

CV multiplicity is multiple CVs at the same location in space.

Multi-knots are usually the result of curve or surface editing operations that require a sharp turn in a curve. You create CV multiplicity by manually placing adjacent CVs in the same location (using the Magnet tool).

Multi-knots and CVs with multiplicity are generally undesirable. Some tools (such as Rail Surface) cannot work with them, and many CAD packages do not accept models with multi-knots.

Multi-knots and CV Multiplicity achieve similar effects, even though they are different mathematically.

Multi-knots and continuity

Multi-knots eliminate one level of automatic continuity for each extra edit point.

For example, a degree 3 curve normally has curvature continuity (G2) at edit points.

If you create a multi-knot of two edit points, you lose automatic curvature continuity, so you only have tangent continuity (G1) at the multi-knot.
If you create a multi-knot of three edit points, you lose both automatic curvature and automatic tangent continuity, so you only have positional continuity (G0) at the multi-knot.

NoteOnly the intrinsic continuity is lost. As with Bezier curves, clever placement of CVs can restore continuity.

Alias only creates full multiplicity knots, that is knots which have a multiplicity equal to the degree of the curve.