What is a Knot Vector and How Do You Define It?

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SUMMARY

The knot vector is defined as a list of numbers that represent the points where different segments of a curve join, specifically in the context of Non-Uniform Rational B-Splines (NURBS). In the discussion, it is clarified that the knot vector is not a real vector but rather a sequence that indicates the parameterization of the curve. The example provided illustrates a simple knot vector as (b0, b1, b2, b3), which corresponds to the points of intersection of the curve segments.

PREREQUISITES
  • Understanding of Non-Uniform Rational B-Splines (NURBS)
  • Familiarity with basic mathematical concepts related to curves
  • Knowledge of parameterization in graphical representations
  • Experience with Rhino 3D software for practical applications
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  • Research the mathematical foundations of NURBS and their applications
  • Explore how to define and manipulate knot vectors in Rhino 3D
  • Learn about different types of knot vectors and their implications on curve continuity
  • Investigate the relationship between knot vectors and spline interpolation techniques
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This discussion is beneficial for graphic designers, 3D modelers, and software developers working with NURBS in applications like Rhino 3D, as well as mathematicians interested in spline theory.

mymachine
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Could someone show me which one is called by the knot vector and how to define it?

Thank you
 

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There are a number of different definitions of "knot" in different types of mathematics. From your graph it appears that you are approximating a function by a "broken line". In this case the "knots" are the points at which the different line segments join so your "knot vector" is simply (b0, b1, b2, b3).
 

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