< Can you please give a detailed step-by-step

Seems yet written ;)

If you want absolutly a square grid of holes or any special gride
- draw a vertical line at the center (or any place following your wishes) to a top
- Draw your grid of lines from ground to top
- Draw a vertical cylinder at the center
- Transform / Orient / Line-Line none Copy enable
so copy your original cylinder along the lines on quarter or half quarter of the grid (very easy ! )
- then some Mirrors Symmetry
- Return all and draw your spheric object
and Boolean Diff as above
and use the Beamfarmer or other method for the vertical cylinder side
All that take 1 minute :)

Frenchy:

Thanks for the reply, but I still don't understand what you are trying to explain. First, I don't understand why you are using angled cylinders and projecting them on a flat plane. Then what am I supposed to do with the flat plane?

Hi YHWH_777,

> Thanks for all of the replies, but all of the replies are only offering a part
> of the solution. That is, you are drilling the holes on only one section of
> the object (either the half sphere at the top or the cylinder on the bottom).
> I need to the holes to cover the entire object.

Your initial image sort of suggested that you were targeting the cylinder, because of the nature of the totally regular flat pattern that you showed.

The cylinder is equal in proportion along its height, so a regular pattern like that is possible to fit on the cylinder without distorting it.

The sphere portion is much different than that - the sphere does not have a constant amount of surface area on it, as you travel vertically up the sphere it reduces in surface area, until finally collapsing at a point near the top.

So take for example this upper ring of your sphere shown in red here:




You can see there that ring of the sphere is smaller in circumference than the circumference of a circle taken from the cylinder.

That means that as you move upwards along the sphere, there is less physical area available in those regions are compared to the cylinder. So there is simply not as much area to fit the same number of holes as you travel up the sphere.

But meanwhile look at your pattern that you showed initially, notice the top line of your pattern:



The top line of your pattern that you want to match to the tip of the sphere contains 20 circles just exactly the same as the parts that you want to put on the cylinder. It's not possible to do that without shrinking or distorting the holes because of the greatly reduced surface area in those regions.

It's sort of like you're asking how to put 5 gallons of water into a 1 gallon bucket.... You can't - it just does not fit!

Probably what you want is to have a different number of holes in the circumference as you get closer to the collapsed together point at the top of the sphere.

To get that, you probably want to create a set of cylinders like Bemfarmer shows above, but when you shift from the cylinder area to the sphere area, you will need to both reduce the number of copies of the cylinders going and also stagger them by rotating the starting one before you replicate it (using Array circular) in the top view so that the rows are also staggered more as you move upwards.

You may in fact need to just manually place the cylinders in the sphere area where you judge they have good spacing rather than trying to automatically generate them.


But anyway, the type of image that you showed initially where you have the exact same number of objects in the upper rows of your 2D pattern simply can not fit onto the reducing surface area of the sphere as it shrinks down to a single point at the top. An actual 2D pattern of it would look more like a smaller number of items in the region of the pattern that corresponds to the shrinking area. Unless you want the holes to be distorted and squished down?

- Michael

Hi YHWH_777, thanks for posting the example file.

It is possible to flow what you are showing in that example file - you would need to form the target surface as a single surface by making a longer single-segment profile curve that you revolve. Then the result would look like this:



I think that's not what you are really looking for, but it's basically what you are actually asking to create with that flat pattern having the same 12 holes in its upper area as it does in the lower area. As you can see as the pattern nears the tip of the shape where the surface collapses down to a point, the horizontal surface area becomes smaller and smaller and so it follows that the 12 circles in your pattern get squashed down more and more as you approach that area.

So you probably don't actually want to map a totally regular/uniform 2D pattern like you show in the plane there, shown in 2D the pattern that you seem to actually want would have a smaller number of larger ovoid-ish shapes for the pieces that were in the shrinking surface area zone.

It's probably easier for you to instead place cylinders as the cutting objects instead of trying to map a 2D pattern like that.

- Michael

Hi YHWH_777, how about this version here (model attached as hole_pattern_model.3dm) :



This was made generally in the same way as Bemfarmer's example above with a couple of slight differences.

But the starting row is the same with an array along a joined curve like this:





Then pick the bottom one and array it and decide how many copies you want, I used 12:



Then to get the staggering layout, select every other one and rotate it by a half increment. To do that run the Transform > Rotate command, pick the point for the center of rotation and then for the rotation angle type in 360/24 to rotate it by one-half of an array step around:



Now use Transform > Array > Circular again on all of these again with a 12 item count:



Now when you get to the top you have to use a smaller item count for those ones up there since as I described previously there is not as much physical surface area in those spots. If you were to just use a 12 count array up there the pieces would collide into one another.

I used 12 items for the very first ring though where it still has plenty of area, then for the next one up from that only 10 items (this one should be staggered by a rotation of 360/20 instead), and then only 5 items for the last ring.

If you don't like the spacing between items that those counts happen to produce, you may need to just manually place your cylinders to a particular spot where you like the spacing.

Hope this helps!

- Michael

<< Your initial image sort of suggested that you were targeting the cylinder, because of the nature of the totally regular flat pattern that you showed.>>

Sorry if that was confusing, but I was trying to say that I wanted the object (on the left) to be filled with evenly spaced holes. I was including the plane to give an example of how the holes should be spaced.

<< ...how about this version here...>>

Yes, that is more like what I am looking for. I'm just trying to figure out the math behind making the holes as equally spaced as possible. In your example, the holes are still unequally spaced in areas near the top of the object.

I have also been playing with using cylinders to create the holes over the past few days, but I haven't totally figured it out yet. Hopefully I'll figure it out soon.

Thanks for all of your help.

A partial attempt, incomplete.
The extrusions need to be longer...
Not sure of the best way to pack circles on a hemisphere...

Anyway, it has been good Moi practice.

Notices that when doing right to left selection highlight, the yellow highlight color often failed to remain yellow...

Is there a way to get the flowed circles to rotate "flat" on the hemisphere? If not pre-rotated, they end up radial. Maybe
there is another way?

< I don't understand why you are using angled cylinders and projecting them on a flat plane.
I don'd project on a flat plan. the Flat Plan is just the grid for start base of cylinders
In fact no need to draw line, the fonction Orient / Line-Line is sufficient for draw cylinder
from the Point snap grid toward Top

Something like this all is reversed after the drawing of cylinders

Hi YHWH_777,

> Yes, that is more like what I am looking for. I'm just trying to figure
> out the math behind making the holes as equally spaced as possible.

The math involved is likely to be extremely complex as there's a lot of constraints and variables involved.

Also there is probably no exact solution that will give the same spacing as there is on the cylinder part, so it's more of an "error minimization" type thing, and the actual things that you would probably want to minimize would be the distance between some circles measured from points on the perimeter of each circle, which is different than just distances between points on the sphere.

So the whole thing taken together trying to specify with a formula is going to be quite difficult.

Such things won't usually be solved by a single formula, it's more likely that an automated process would solve it by an iterative method where the circle for each hole would be adjusted slightly towards its neighbors and then that process repeated many times in order to distribute things.

Without some sophisticated iterative solver mechanism like that you can instead use your judgment for placing the profiles where you think they look good.


> In your example, the holes are still unequally spaced in areas near the top of the object.

Now that you have seen the technique used for that particular construction, you can adjust those steps to your liking, you could change the amount of profiles, or rotate them around individually if you want to try some other kind of spacing.

- Michael

Hi Brian,

> Is there a way to get the flowed circles to rotate "flat" on the hemisphere? If not
> pre-rotated, they end up radial. Maybe there is another way?

In the last step of Flow there are several options that you can adjust and one of them is a checkbox for "Rigid" - when that mode is enabled the objects being flowed will only be moved and rotated into their target position and not actually warped, so that may be the kind of thing that you are asking about here.

- Michael

Thank you Michael.

Here is a reference for "distributing points on a sphere."

http://cgafaq.info/wiki/Evenly_distributed_points_on_sphere

No more time to play today, have to work...
Some of the methods may be scriptable...?

Hi Brian, unfortunately the difficulty actually goes beyond just distributing things only on the sphere itself - the problem is about distributing things on the sphere that are also simultaneously equally distributed from the elements coming from the cylinder part as well...

Maybe that will yield something useful for YHWH_777 anyway though, but it's complex enough that I'm not really going to be able to dig into it more myself.

The "electrostatic repulsion" method described there is basically the same thing as the iterative solver approach which might be an approach if you were writing some custom software to solve this particular problem.

- Michael

Since you cant unroll a doubley curves surface, there wont be any linear way to array the holes. You can come close. Here is a sphere top "Smashed". Rhino tells you it is 30 % smaller though. But you could then put the objects on this and flow them properley (Well, at least close) I think that surface would have to have a bunch of tears in it to properley unroll, then you would have to figure out how to align your objeacts on that wierd shape, to match what you want.