Okay, this note may get a little complicated so forgive me if I confuse you.
I have written a macro that makes stacks of rings of spheres as seen in the
attached image. The macro adjusts the radius of the spheres in a ring
dependant on the radius of the ring because I wanted to make sure that all
spheres are tangential (touching each other at a tangent).
Now, what I would like to do is at the top of the "cylinder of spheres" is
start to make the rings, but so that every stack of it fits the profile i
have drawn in. Figuring out what the radius of the ring should be and the y
value of the ring is very difficult for me--especially since the sphere's
radius changes as the ring's radius gets smaller. I have attempted to
figure this out and in the second attached image you can see my initial
approach.
Initially I have thought to define a "path" for the profile by a polynomial
equation. I would then input an x-coordinate value into the function with
the equation and I would get a y-coordinate as an output. The problem is
that when you actually go and make this a macro, how can I determine the
change in the x value so it will give me the correct y value and STILL have
the sphere be tangential? In other words how do I determine the
x-coordinate to input into the function that gives me the appropriate y
value? Well I imagined that the change in x could be (as shown in the
diagram):
radius1*(sin theta1) + radius2(sin theta2)
I have figured out how to determine the radius for each sphere of any ring
size, but I simply can not figure out how to determine the "thetas" of which
to use for my equation. Am I way off? Is there an easier way to do this?
F. Audet has put up his Apple code which does something similar, and I have
looked at it, but I am trying to understand how I can figure the math so
that I can become more adept at making what I want. Thanks for your time
and help I appreciate it a great deal since it has helped me realize the
images I see in my head :)
Arie
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Attachments:
Download 'pathSpheres.jpg' (43 KB)
Download 'cylinderSpheres.jpg' (63 KB)
Preview of image 'pathSpheres.jpg'
![pathSpheres.jpg](/povray.binaries.images/attachment/%3C3bd2d492%40news.povray.org%3E/pathSpheres.jpg?preview=1)
Preview of image 'cylinderSpheres.jpg'
![cylinderSpheres.jpg](/povray.binaries.images/attachment/%3C3bd2d492%40news.povray.org%3E/cylinderSpheres.jpg?preview=1)
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