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Tor Olav Kristensen wrote:
>
> Grey Knight wrote:
> >...
> > so FAPP it *is* exact.
> I guess you mean: For All Practical POV Purposes ;)
> Tor Olav
What other type of purpose is there? ;)
--
signature{
"Grey Knight" contact{ email "gre### [at] yahoo com" }
site_of_week{ url "http://digilander.iol.it/jrgpov" }
}
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On Fri, 22 Feb 2002 10:00:51 +0000, Grey Knight <s16### [at] namtarqubacuk>
wrote:
> > I guess you mean: For All Practical POV Purposes ;)
>
> What other type of purpose is there? ;)
Of course Scientifical/Theoretical POV Purposes ;)
ABX
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I tried this with my bezier curve include file. Of course you just need
to find the derivitave of the spline function, it should give you the
tangent direction. Of course this is a lot harder than it sounds. I've
wasted half a ream calculating the derivitave of a bezier function.
Josh English
eng### [at] spiritonecom
http://www.spiritone.com/~english
Disnel wrote:
>
> Thank to all, you are right and I think, that it will be sufficient.
>
> But I wanted to ask if there is some way to get exact tangent (another
> than reimplementing POV spline in POV language, of course ;-) The answer
> is probably not.
>
> Regards
>
> Disnel
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POV is powerful enough for getting all the piecewise polynomial coefficients
from declared spline. For cubic spline we can calculate four points on every
time interval, get all four coefficients from this 4x4 linear system and
then get exact tangent function for every time interval. These coefficients
can be used outside POV.
Of course, this will be approximation too, because of limited accuracy. The
best way is just to find out these figures directly from original set of
points, but it seems that in this case we need to solve linear systems of
higher order, than 4(still possible with SDL, however).
"Disnel" <dis### [at] itamcascz> wrote in message
news:3C7### [at] itamcascz...
>
> Thank to all, you are right and I think, that it will be sufficient.
>
> But I wanted to ask if there is some way to get exact tangent (another
> than reimplementing POV spline in POV language, of course ;-) The answer
> is probably not.
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Gleb wrote:
>...
> Of course, this will be approximation too, because of limited accuracy. The
> best way is just to find out these figures directly from original set of
> points, but it seems that in this case we need to solve linear systems of
> higher order, than 4(still possible with SDL, however).
>...
I have some (slow) POV macros that will solve
linear systems with N equations and N unknowns.
Tor Olav
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"Tor Olav Kristensen" <tor### [at] hotmailcom> wrote in message
news:3C7976C9.AD9DA3D8@hotmail.com...
>
> I have some (slow) POV macros that will solve
> linear systems with N equations and N unknowns.
>
In this particular case speed is not so important,
because all calculations should be done only once for given spline.
Gleb
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Gleb wrote:
>
> "Tor Olav Kristensen" <tor### [at] hotmailcom> wrote in message
> news:3C7976C9.AD9DA3D8@hotmail.com...
> >
> > I have some (slow) POV macros that will solve
> > linear systems with N equations and N unknowns.
> >
>
> In this particular case speed is not so important,
> because all calculations should be done only once for given spline.
Ok then -
If there's anyone that is working out these
tangent functions, just tell me if you want
me to post some of my matrix macros.
Tor Olav
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