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On Tue, 11 Feb 2003, James Coburn wrote:
> I am currently working on a project that requires me to spline (preferrably
> Non-Uniform B-Spline) interpolate through several sets of data points in 3
> dimensions. I have looked into several algorithms and software packages
> that will calculate these splines, but they all seem to require a knot
> vector. I have not been able to create one that will make the line pass
> through all control points including the end points.
>
> Is there another algorithm or program for creating this knot sequence?
There's an infinity of knot sequences which will do what you ask for. What
you're creating is a parametric curve, and loosely speaking the knot
sequence determines the parameterization of that curve. I.e. if you're
walking along the curve it determines how fast you're walking.
If you need interpolating endpoints your knot multiplicity at the ends
must equal the order of curve (= degree + 1). For a cubic curve this means
that you must have 4 identical knot values at the beginning and at the
end.
There's a number of different approaches for choosing the knots inbetween.
The easiest is to choose a uniform knot vector, but depending on your
requirements you can set up other schemes.
For a many, many more details about all this, you may want to consult :
"Curves and Surfaces for CAGD: A Practical Guide" by Gerald Farin
or
"The NURBS Book" by Les A. Piegl and Wayne Tiller
Hope this helps,
Rasmus
-----------------------------------------------------------------------------
Rasmus.Tamstorf@disney.com "A problem worthy of attack,
Walt Disney Feature Animation proves its worth by hitting back" Kumbel
-----------------------------------------------------------------------------
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> I am currently working on a project that requires me to spline (preferrably
> Non-Uniform B-Spline) interpolate through several sets of data points in 3
> dimensions. I have looked into several algorithms and software packages
> that will calculate these splines, but they all seem to require a knot
> vector. I have not been able to create one that will make the line pass
> through all control points including the end points.
>
> Is there another algorithm or program for creating this knot sequence?
There's an infinity of knot sequences which will do what you ask for. What
you're creating is a parametric curve, and loosely speaking the knot
sequence determines the parameterization of that curve. I.e. if you're
walking along the curve it determines how fast you're walking.
If you need interpolating endpoints your knot multiplicity at the ends
must equal the order of curve (= degree + 1). For a cubic curve this means
that you must have 4 identical knot values at the beginning and at the
end.
There's a number of different approaches for choosing the knots inbetween.
The easiest is to choose a uniform knot vector, but depending on your
requirements you can set up other schemes.
For a many, many more details about all this, you may want to consult :
"Curves and Surfaces for CAGD: A Practical Guide" by Gerald Farin
or
"The NURBS Book" by Les A. Piegl and Wayne Tiller
Hope this helps,
Rasmus
-----------------------------------------------------------------------------
Rasmus.Tamstorf@disney.com "A problem worthy of attack,
Walt Disney Feature Animation proves its worth by hitting back" Kumbel
-----------------------------------------------------------------------------
---------------------------------------------------------------
To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl
For information and archives: http://isb.ri.ccf.org/biomch-l
---------------------------------------------------------------