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I am using the Nurbs definition of Wikipedia. I might have missed something in the definition but I cannot understand how to know on which interval does the parametric coordinate span. Particularily for an unclamped knot vector. It seems that it is not the first knot vector value and the last knot vector value that defines the intervals for any Nurbs. So what is the rule if there is one?

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  • $\begingroup$ Can someone with great reputation create the "Nurbs" tag? $\endgroup$ – Sylvain B. Jul 16 '15 at 15:23
  • $\begingroup$ I have included the tab for NURBS ( Non-Uniform Rational B-Splines), mathematical representations of 3D geometry accurately describing any shape ( 2D line, arc, 3D curves free-form surfaces solid and hyper surfaces). Due to their flexibility and accuracy, NURBS can be useful in visualization, animation and machine manufacturing. As a superset splines may be merged into it. $\endgroup$ – Narasimham Jul 16 '15 at 17:15
  • $\begingroup$ Very good ! thanks ! $\endgroup$ – Sylvain B. Jul 17 '15 at 9:41
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For a NURBS curve with a given knot vector, the following rules are always true:

  • the number of knots = the number of control points + degree + 1.
  • the parametric range is always defined between knots[degree] to knots[number_of_control_points] where knots[] starts from index 0. This is true for all knot vectors, clamped or not.
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  • $\begingroup$ Thanks for this answer... isn't it knots[degree -1] for the beginning of the range ? This would fit better the results that I have... $\endgroup$ – Sylvain B. Jul 17 '15 at 9:48
  • $\begingroup$ The beginning of the range is knots[degree] or knots[order-1] (order = degree+1). $\endgroup$ – fang Jul 17 '15 at 16:35
  • $\begingroup$ If I consider my results (I am using OpenNurbs library), everything is coherent if I take the beginning of the range at knots[degree - 1], which is the "degree"-th element, because the knots array starts at element 0. Taking the element knots[degree] which is the element "degree+1"-th gives me strange results. But thank you for your answers... $\endgroup$ – Sylvain B. Jul 20 '15 at 9:58
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    $\begingroup$ For OpenNurbs, they omit the first knot and the last knot. Therefore, they always have number of knots = number of control points + degree -1. So, the start range will be knots[degree-1]. Please keep in mind that this is not how it is done in most softwares or textbooks that deal with NURBS. $\endgroup$ – fang Jul 21 '15 at 22:34
  • $\begingroup$ Great answer ! thanks a lot... $\endgroup$ – Sylvain B. Jul 22 '15 at 7:40

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