Is there a limit for maximum amount of control points in natural spline?

Gleb

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Please ask your question in povray.general.

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In article <3ca71790$1@news.povray.org> , "Gleb" <gk1### [at] sotonacuk> wrote:

> Is there a limit for maximum amount of control points in natural spline?

Yes, the amount of free memory.

    Thorsten

____________________________________________________
Thorsten Froehlich, Duisburg, Germany
e-mail: tho### [at] trfde

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Thorsten Froehlich wrote in message <3ca722d1$1@news.povray.org>...
>In article <3ca71790$1@news.povray.org> , "Gleb" <gk1### [at] sotonacuk> wrote:
>
>> Is there a limit for maximum amount of control points in natural spline?
>
>Yes, the amount of free memory.

Not quite.  Strictly speaking, it's the amount of free memory, or the
largest number that can be stored in a long integer, whichever comes first.
(or in practical terms, the amount of free memory).

--
Mark

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"Mark Wagner" <mar### [at] gtenet> wrote in message
news:3ca7ee05@news.povray.org...
>
> Not quite.  Strictly speaking, it's the amount of free memory, or the
> largest number that can be stored in a long integer, whichever comes
first.
> (or in practical terms, the amount of free memory).

Thank you, Mark, this is what I wanted to know.
I'm also curious how stable is the current natural splines implementation,
when handling huge amount of control points, because it seems that there
are some matrix calculations involved, which possibly can be unstable
above some limit. Is it correct?

Gleb

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Gleb <gk1### [at] sotonacuk> wrote:
>> Not quite.  Strictly speaking, it's the amount of free memory, or the
>> largest number that can be stored in a long integer, whichever comes
> first.
>> (or in practical terms, the amount of free memory).

> Thank you, Mark, this is what I wanted to know.

  You will never reach the largest number limit in your PC (unless you have
more than 4 gigabytes of memory), so it really is just the amount of free
memory that is the limit.

> I'm also curious how stable is the current natural splines implementation,
> when handling huge amount of control points, because it seems that there
> are some matrix calculations involved, which possibly can be unstable
> above some limit. Is it correct?

  What do you mean by stability?
  I don't understand how the implementation can become unstable for a bigger
number of control points.

-- 
#macro N(D)#if(D>99)cylinder{M()#local D=div(D,104);M().5,2pigment{rgb M()}}
N(D)#end#end#macro M()<mod(D,13)-6mod(div(D,13)8)-3,10>#end blob{
N(11117333955)N(4254934330)N(3900569407)N(7382340)N(3358)N(970)}//  - Warp -

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"Warp" <war### [at] tagpovrayorg> wrote in message
news:3ca86c65@news.povray.org...
>   What do you mean by stability?

When small variation of the control points values(rounding errors, in fact)
should lead to small variation in the spline function(spline polinomial
coefficients).
With calculation on big matrices it is not always true.

>   I don't understand how the implementation can become unstable for a
bigger
> number of control points.

Simple example: we have one big number and a whole lot of very small,
the result depends of the order of summarizing because of rounding errors.

Atb,

Gleb

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Gleb wrote in message <3ca86b79@news.povray.org>...
>
>"Mark Wagner" <mar### [at] gtenet> wrote in message
>news:3ca7ee05@news.povray.org...
>>
>> Not quite.  Strictly speaking, it's the amount of free memory, or the
>> largest number that can be stored in a long integer, whichever comes
>first.
>> (or in practical terms, the amount of free memory).
>
>Thank you, Mark, this is what I wanted to know.
>I'm also curious how stable is the current natural splines implementation,
>when handling huge amount of control points, because it seems that there
>are some matrix calculations involved, which possibly can be unstable
>above some limit. Is it correct?

I just use standard Gaussian elimination on a tridiagonal system of
equations to get the coefficients, so there might be a numeric stability
problem for some combinations of control points.  It's not likely to show up
for realistic sets of control points, though.

--
Mark

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