> Warp <war### [at] tagpovrayorg> wrote:
> I wonder if POV-Ray couldn't transparently calculate the radius and
> threshold values from the user-specified ones so as to match the current
> blobs [in case the default N is changed from 2 to 4].

Consider a simple situation, namely the "diatomic molecules" of my images.
There are 2*3 + 3 = 9 major visual shape parameters: the effective radius "r"
of the atoms, the positions "C1,C2" of their centers, the radius "s"
of the smallest circle that goes around the seam, and the
radius of curvature "t" of the seam in the across direction,
at its midline.

The proposed new density formula is "F(p) = S*(1 - (dist(p,C)/R)^2)^N".
Assume "N" is given. The center "C" is fixed ("C1" or "C2").  That
leaves three parameters, the influence radius "R" (same for both atoms),
the strength "S" (ditto), and the overal threshold "T".

But multiplying "S" and "T" by the same factor leaves the shape
unchanged, so there are only two real parameters: "R" and the ratio
"T/S".  These are insufficient to match the three remaining visual
parameters ("r", "s", "t").

In this simple situation, one can easily adjust "R" and "S/T" to
keep "r" and "s" fixed as "N" is changed; but then "t" will be
determined and dependent on "N".  In this case, as "N" increases
the seams will start out more gently at the edges but will become
sharper at their midline

With a little more effort one could adjust "R" and "S/T" to keep
"r" and "t" fixed.  Then the sharpness of seam at its midline
will be preserved, but its girth "s" will increase as "N" increases.

In any case, there are gazillions of POV-Ray
sources out there which use pretty complicated "blob"s and have
been carefully optimized to work with the current formula.  A
change in the formula may improve the result of some of those
images, but will surely break many others.

So, merely changing the  default "N" is not a viable alternative,
even with implicit adjustments to the other parameters.  Changing
"N" must require an explicit user choice.

On the other hand, the automatic ajustments will be very helpful
to users who wish to convert their existing order=2 blobs to order=4
blobs.  If the "R" and "S" parameters are adjusted by POV-ray so
as to preserve the efective shape parameters "r" and "s" of a
"diatomic molecule" with "dist(C1,C2) = r", then chances are that
the appearance of the user's blobs too will be improved with little
change to their overall shape.

All the best,

--stolfi

Post a reply to this message