Degree 3 Curve with 3 ControlPoints?

Rhino
1

Hello.
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 ?

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2

It’s closed, two points are fused together.

1 Like
3

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.

2 Likes
4

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

-Pascal

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5

Thank you David !

6

Thank you!

7

Thank you Pascal!