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Christopher James Huff wrote:
> . . . . The function I used for the blob2 object is:
>
> ((6*r - 15)*r + 10)*r*r*r
Why quintic? All we absolutely need is
f(0) = 1
f(1) = f'(1) = f''(1) = 0
for which (1-r)^3 would do; were you also trying to fit the traditional
curve?
--
Anton Sherwood, http://www.ogre.nu/
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In article <3f84f22f$1@news.povray.org>, Anton Sherwood <new### [at] ogre nu>
wrote:
> > ((6*r - 15)*r + 10)*r*r*r
>
> Why quintic?
This function is used in several other places as well, such as the
recent updates to Perlin noise. It's not something I came up with.
> All we absolutely need is
> f(0) = 1
> f(1) = f'(1) = f''(1) = 0
No, you also need f'(0) = f"(0) = 0
> for which (1-r)^3 would do; were you also trying to fit the traditional
> curve?
(1-r)^3 doesn't even remotely resemble the old-style curve. I wasn't
trying to "fit" it, but I did want something that was somewhat similar.
--
Christopher James Huff <cja### [at] earthlink net>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tag povray org
http://tag.povray.org/
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Christopher James Huff wrote:
> Anton Sherwood <new### [at] ogre nu> wrote:
>>> ((6*r - 15)*r + 10)*r*r*r
>>
>> Why quintic?
>
> This function is used in several other places as well, such as the
> recent updates to Perlin noise. It's not something I came up with.
Ah.
I imagine that would have more constraints.
>> All we absolutely need is
>> f(0) = 1
>> f(1) = f'(1) = f''(1) = 0
>
> No, you also need f'(0) = f"(0) = 0
Why? That point is never on the surface (unless, I guess, another
component with greater and opposite strength is in just the right place).
And shouldn't f''(0) be negative rather than zero?
We also want f'(t)<0 for 0<t<1, but that's almost automatic with a
polynomial of low degree that fits the other constraints. ;)
>> for which (1-r)^3 would do; were you also trying to fit
>> the traditional curve?
>
> (1-r)^3 doesn't even remotely resemble the old-style curve. I wasn't
> trying to "fit" it, but I did want something that was somewhat similar.
(1-rr)^3, then, and you get f'(0)=0 for free. ;)
...It occurs to me that my remarks may seem hostile in tone.
Please be assured that it is none of my intent.
--
Anton Sherwood, http://www.ogre.nu/
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In article <3f863fc0@news.povray.org>, Anton Sherwood <new### [at] ogre nu>
wrote:
> > (1-r)^3 doesn't even remotely resemble the old-style curve. I wasn't
> > trying to "fit" it, but I did want something that was somewhat similar.
>
> (1-rr)^3, then, and you get f'(0)=0 for free. ;)
You may be right, I will have to do more tests when I have time. I do
like the shape given by the quintic curve.
--
Christopher James Huff <cja### [at] earthlink net>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tag povray org
http://tag.povray.org/
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