"Arie L. Stavchansky" wrote:
> While muddling around, I have come up with this.  You can start
> see the effect I am after, but this is truly a linear inclination. 
> I am looking to acheive a curved inclination all the while my
> spheres remain tangential.  I just can't get enough of this stuff.

Hooked, eh?

If you want to keep the spheres one size (or roughly so),
you'll have to abandon the equal spacing of the green lines.

	r0 = radius of the spheres of the previous tier
	R0 = radius of the circle containing their centers
	n0 = how many are in that tier

	p(R) = your profile curve
	P(R) = its first derivative

In the next tier, as a first approximation,
	r1 = r0
	R1 = R0 - 2*r0 / sqrt(1+(P(R0))^2)	// i hope; i'm tired!
	n1 = round(n0*R1/R0)

This won't be an exact fit, but there are techniques for improving it
(which, unfortunately, are beyond my intelligence at this hour).


...
What is your desired profile curve, by the way?
For a different look, I might try adapting what others have called a
"Fibonacci spiral" (really the Fermat spiral with golden sector
sampling).


-- 
Anton Sherwood

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