|
![](/i/fill.gif) |
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/
Post a reply to this message
|
![](/i/fill.gif) |