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In article <strobel.720409964@dirac>, strobel@dirac.phys.washington.edu (Nicolas Strobel) writes:
> Some of the math libraries coming out recently have been including "knot
> sequences" in their spline routines (cubic and B-spline). Can anyone give
> me a "non-technical" explanation of what "knots" are? Thanks!
> 
> nick
> strobel@dirac.phys.washington.edu


Subject: Re: splines with knots
Newsgroups: sci.math.num-analysis
Distribution: na
Keywords: knot sequence splines
Summary: On the meaning of knots in splines.
References: <strobel.720409964@dirac>

In article <strobel.720409964@dirac>, strobel@dirac.phys.washington.edu (Nicolas Strobel) writes:
> Some of the math libraries coming out recently have been including "knot
> sequences" in their spline routines (cubic and B-spline). Can anyone give
> me a "non-technical" explanation of what "knots" are? Thanks!
> 
> nick
> strobel@dirac.phys.washington.edu


Roughly speaking, the following statements are true.

. Splines are piecewise polynomials.
. Knots Are the locations where the pieces are joined (or tied together, hence
  the word knot)
. Alternatively, knots are points where discontinuities are located.
. Discontinuities start with the highest order derivative.
. The multiplicity of a knot is the number of its discontinuities. For example,
  discontinuities at X in derivatives N & N-1 make for a knot of multiplicity 2.
. For a spline in a 1 dimensional space a knot is a point. In a 2 dimensional
  space it might be a line or a curve, etc.

For more information on splines see pages 61-71 of "Numerical Methods, Software,
And Analysis" by John R. Rice - from which most of the above summary derives.