On Thu, 13 Apr 2000 01:15:32 +0200, Tor Olav Kristensen
<tto### [at] onlineno> wrote:

>
>Peter Popov wrote:
>> Take -2*x^3+3*x^2 in the region [0;1].

>I tried your suggestion to use the cubic spline above.

>I found that it doesn't differ much from Greg's cosine spline.
>(I used the points that he put in his sample scene file.)

>Is that the way it should be?

Well, it shares the same properties with the cosine spline (minima,
maxima, symmetry, point of inflexion) so it doesn't differ much. Both
are used in POV.

>Do you know of any other interesting polynomials for splines?

No, I don't, but I am sure the various spline macros have them.

I am interested to see if this makes any sense (untested!):

y = [-2*(x+0.5)^3+3*(x+0.5)^2-0.5]^n , where n is real

This time we're interested in the values of y for x [-0.5; 0.5]. The
spline has a minimum at [-0.5, -0.5], a maximum at [0.5, 0.5], a point
of inflexion at the origin and is an odd function. The parameter n
should control the steepness of the slope, but preserving the
smoothness of the spline and its scope.


Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] usanet
TAG      e-mail : pet### [at] tagpovrayorg

Post a reply to this message