Today's puzzler: Center the pattern of pink dots around the gray circle

tylerdurden · Postby **tylerdurden** » Mon Feb 04, 2019 1:06 am

Can you center the pattern of pink dots around the gray circle?

Rules:

=)

Inspired by this topic: viewtopic.php?f=5&t=34454

Moini · Postby **Moini** » Mon Feb 04, 2019 2:27 am

Can you explain what you mean by 'center around'? It looks centered already, and the rotation centers lie in the same place. I don't know what remains to do :-(

Maybe you want the small circles' centers to touch the large circle's circumference?

Moini · Postby **Moini** » Mon Feb 04, 2019 2:30 am

And - do you want to resize the dots in the process?

tylerdurden · Postby **tylerdurden** » Mon Feb 04, 2019 2:37 am

While the rotation centers of the pattern and the large circle are coincident, the distance of the dots to the large circle is inconsistent.

An even number of dots would be easy to align using default rotation centers, an odd number, not so easy.

Moini · Postby **Moini** » Mon Feb 04, 2019 2:50 am

Yeah, I got that now, too, they're not centered.

Moini · Postby **Moini** » Mon Feb 04, 2019 2:55 am

I can do it in the alpha, does that count?

Moini · Postby **Moini** » Mon Feb 04, 2019 3:03 am

(it has a 'circle by 3 points' LPE, where you can create the circle by connecting the mid points of 3 of the dots after break-apart)

tylerdurden · Postby **tylerdurden** » Mon Feb 04, 2019 3:06 am

hmmmm.... I'd like to see that, even if it's not an official puzzle entry.

Moini · Postby **Moini** » Mon Feb 04, 2019 3:08 am

After that, it's a bit of centering and adding up numbers, and creating another circle that marks the circumference of all dots, then resizing the group of circumference plus small circles to the size of the original circle plus the size of a dot.

Moini · Postby **Moini** » Mon Feb 04, 2019 3:09 am

Probably Lazur can do it in less steps, though

Moini · Postby **Moini** » Mon Feb 04, 2019 3:18 am

Sorry for no keyboard indicator... I copy-paste a couple of times and duplicate once, that isn't captured :-(

https://framadrive.org/s/RaNbd4Yo4ptzwCj

Edit: Attached resulting file. The only additional thing I did was centering it all on the page.

Postby **brynn** » Mon Feb 04, 2019 5:01 pm

I can center the big gray dot in the center of the small pink circles, with snapping. 1 step.

To center the pink circles to the gray circle, you'd have to use Align and Distribute. 2 steps. (Center on Vertical Axis plus Center on Horizontal Axis) (Of course I could write much more clear for newbies.)

Something tells me that's not what you meant?

Polygon · Postby **Polygon** » Mon Feb 04, 2019 8:39 pm

Here are my steps:
1: select ring of pink circles
2: cmd+D to double
3: Go Transformation tab: 360°/15 (amount of circles) /2 =12°to get the doubles in-between the pinky ones: Apply.
4: Shift Select both circle rings and group them.
5: Align group and grey circle horizontally and vertically.
6: ungroup and delete doubles. Done.

Cheers

Postby **brynn** » Mon Feb 04, 2019 9:00 pm

tylerdurden wrote:Can you center the pattern of pink dots around the gray circle?

Rules:
A new pattern is not allowed, the existing pattern must be used
The alignment must be precisely concentric
The process used must be described such that the readers can successfully repeat the work
The most efficient method scores highest.

When you say a new pattern is not allowed, I assume that you can't move the pink dots, because that would make a new pattern. However, after re-reading many times, my best guess is that the goal is to actually move the pink dots and make them in a perfect circle.

Is THAT the goal?

If so, when you say "precisely concentric" do you also mean evenly spaced around the circle?

Moini · Postby **Moini** » Mon Feb 04, 2019 10:38 pm

After thinking about it some more, using Polar coordinates would be a lot faster, even, and also possible to do in Inkscape 0.92.4.
Break apart the ring of circles, then align them in the correct distance around the center of the grey circle. This uses the 'Parameterized' option of the 'Polar' tab of the 'Arrange' dialog.

To get the correct position of the center, one could use a corner of a rectangle, and snap that to the center, then read off the position from the rectangle tool's tool controls bar. This would also work in the case of transformations.

tylerdurden · Postby **tylerdurden** » Mon Feb 04, 2019 10:59 pm

brynn wrote:...Is THAT the goal?
If so, when you say "precisely concentric" do you also mean evenly spaced around the circle?

The problem is:
The pattern of dots (which are already properly spaced in a circle) is not centered around the gray circle. There is less space between the dots and the circle near the top than there is near the bottom. This is due to the odd number of circles.

Polygon's solution seems the most elegant... duplicate to create an even number of circles in the pattern. Center. Delete the doubles. (I failed miserably, trying to simply flip the pattern.)

I used a geometric process of finding the true center of the pattern. It works, but not nearly as simple as Polygon's solution.
(my capture software was interfering with my mouse pointer, so there are a lot of extra clicks.)

Postby **druban** » Wed Feb 06, 2019 4:23 pm

Because whoever created this evil puzzle made the little circles have a total of 76 nodes instead of 75 or 60 Polygon's very logical method is almost but not absolute. two circles have 6 nodes and one circle has 4. there are more nodes on the tops of the circles than on the bottoms so even after making an even number of circles the center of the group as a whole is biased North by a tiny amount.... !!

Lazur · Postby **Lazur** » Wed Feb 06, 2019 5:40 pm

Hmm why am I just seeing this now?

Anyway, here goes my two cents.

draw star with 15 spikes
snap its top spike to to the bottom most node of the top dot
set its rotation/object origin to that exact node
pull down a horizontal guide line for the snapping target of another node in the circle of dots
scale the star until it snaps while holding shift
change the number of spokes to 16
reset the object origin and scale up the star manually
group it with the dots
use the align and distribute panel to align it with whatever object horizontally/vertically

Well not some streamlined solution but at least you don't have to deal with the digit limit of fraction angles -like, if there were 17 dots to start the puzzle with.

Edit: here is a screen capture of the process:
video

Postby **druban** » Wed Feb 06, 2019 7:30 pm

1. draw 2 sides of equilateral triangle connecting three appropriate nodes of pink circles AB & BC,
2. draw 2 medians
3. snap gray circle center to intersection of medians D

Shown as an equilateral triangle to make it easy to understand, but actually the intersection of the perpendicular bisectors of any two chords is the center of the circle

: Align_Puzzle.png (48.76 KiB) Viewed 4980 times

As an interesting side observation if one tries to find the center of each one of the small 5 node circles, one encounters the same problem as the original puzzle and so there is an endless recursion possible...

Polygon · Postby **Polygon** » Wed Feb 06, 2019 7:35 pm

druban wrote:Because whoever created this evil puzzle made the little circles have a total of 76 nodes instead of 75 or 60 Polygon's very logical method is almost but not absolute. two circles have 6 nodes and one circle has 4. there are more nodes on the tops of the circles than on the bottoms so even after making an even number of circles the center of the group as a whole is biased North by a tiny amount.... !!

The explanation is pretty easy: As long as edges of the small circles at North/East/South/West the bounding box will be a square - no matter how many points they are made of.
But this can´t happen with 15 resp. 30 circles as the second number needs to be divisible by 4 and aligned NESW. Just in this case you´ll receive a totally squared bounding box which is needed for the proper alignment.

Lazur · Postby **Lazur** » Thu Feb 07, 2019 7:26 am

druban wrote:1. draw 2 sides of equilateral triangle connecting three appropriate nodes of pink circles AB & BC,
2. draw 2 medians
3. snap gray circle center to intersection of medians D

YES.

My previous method was a bit overcomplicated.

Guessing it's because I hardly using the rotation centre as a snapping target thus the align on horizontal/vertical axises is my preferred drawing habit. Or just too sleepy again.

So, here goes another one, basically following that direction:

grab a guideline and snap it to two of the innermost nodes of the dots
double click on it and rotate relative 90°
snap it to the according other inner node in the purple layout of dots
repeat the steps with two other nodes as a start, preferably one closest to 90° in the layout
snap rotation centre of the dots to the guide intersection
snap one of the object with its centre to the other's

In a nutshell.

Here is the screen capture:
video

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Today's puzzler: Center the pattern of pink dots around the gray circle

Today's puzzler: Center the pattern of pink dots around the gray circle

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Re: Today's puzzler: Center the pattern of pink dots around the gray circle

Re: Today's puzzler: Center the pattern of pink dots around the gray circle

Re: Today's puzzler: Center the pattern of pink dots around the gray circle

Re: Today's puzzler: Center the pattern of pink dots around the gray circle

Re: Today's puzzler: Center the pattern of pink dots around the gray circle

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