Multiplicity

 
 
 

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.

     

Multiplicity = 1

Multiplicity = 2

Multiplicity = 3

You can set the multiplicity of knots on curves as described in Setting Knot Multiplicity, and on surfaces as described in Adding Knot Curves.

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