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

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A knot vector is defined as a list of numbers that indicates the points where segments of a curve or surface join, rather than a traditional vector. It is crucial for defining the structure of NURBS (Non-Uniform Rational B-Splines) in mathematical modeling. Different mathematical contexts may use the term "knot" with varying definitions, but in this case, it relates to the points of connection in a piecewise linear approximation. The knot vector essentially represents the parameter values at which the curve changes direction. Understanding the knot vector is vital for accurately modeling and manipulating curves in design software like Rhino.
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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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