Degree 3 Curve with 3 ControlPoints?

As I know, the minimum number of the controlpoints of a NURBS curve is equal to its degree plus one. however, I’ve encountered in a condition that we can have a close curve in degree 3 and with 3 control points. is there any technical explanation about that ?

It’s closed, two points are fused together.

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To expand on Jim’s comment “the minimum number of the control points of a NURBS curve is equal to its degree plus one” applies to an open curve. For a closed curve the minimum number of control points equals the degree.


Hello- for periodic curves like this there are actually more control points but they a ‘wrapped’ in degree number rather than all in one location.

Periodic NURBS curve (SubD friendly)
  start = (8.333,12.500,0.000)
  end = (8.333,12.500,0.000)
  degree = 3
  control points: non-rational, count=6 (3 duplicates)
  knots: uniform (delta=66.029), domain = 0.000 to 198.087


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Thank you David !

Thank you!

Thank you Pascal!