Christopher James Huff wrote:
> Anton Sherwood <new### [at] ogrenu> 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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