Multiplicity is a property of knots that refers to the number of control points associated to a knot. On a cubic curve, a knot can have a multiplicity of 1, 2, or 3. On a surface, each knot curve has two multiplicities: one in the U direction and one in V. All knots along a knot curve must have the same multiplicity in the corresponding direction.
Knots with a multiplicity greater than 1 are sometimes called multiknots. Multiknots allow for greater control over the trace of the curve through the knot, at the expense of smoothness.
A knot with a multiplicity of 1 has C2 continuity (curvature).
A knot with multiplicity 3 has C0 continuity (position) if the three control points are not lined up. It is like a Bézier point, with one control point exactly at the position of the knot on the curve and the other two control points acting like tangent handles. You can manipulate these knots on curves in a Bézier-like manner — see Using the Tweak Curve Tool.
You can set the multiplicity of knots on curves as described in Setting Knot Multiplicity, and on surfaces as described in Adding Knot Curves.
Except where otherwise noted, this work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
