-
1. Re: Geometric shapes repeated into infinity
Bert_Philippus Apr 21, 2011 10:50 AM (in response to ecofugal)Experiment with the Transform EFFECT, located under Effect>Distort&Transform>Transform, then play with rotation, scaling and number-of-copies. You can also load multiple such transformations on top of each other.
-
2. Re: Geometric shapes repeated into infinity
Jacob Bugge Apr 21, 2011 11:16 AM (in response to Bert_Philippus)Bert.
-
3. Re: Geometric shapes repeated into infinity
Bert_Philippus Apr 21, 2011 12:27 PM (in response to Jacob Bugge) -
4. Re: Geometric shapes repeated into infinity
Jacob Bugge Apr 21, 2011 2:43 PM (in response to Bert_Philippus)Our spirits rise.
-
5. Re: Geometric shapes repeated into infinity
CarlosCanto Apr 21, 2011 10:31 PM (in response to ecofugal) -
6. Re: Geometric shapes repeated into infinity
[Jongware] Apr 22, 2011 4:22 AM (in response to CarlosCanto)Yeah, that's what I got too.
Why is it the copies are created underneath the original object!? You cannot use a fill here, can you? I tried to make the alternating black/white fills by doing 1 copy only, expand & fill with black, then group and re-transform. Didn't work as intended ...
-
7. Re: Geometric shapes repeated into infinity
Bert_Philippus Apr 22, 2011 6:14 AM (in response to [Jongware])You could start with the smallest triangle and reverse your settings, of course...
-
8. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 22, 2011 6:36 AM (in response to [Jongware])group and re-transform. Didn't work as intended ...
There's nothing to prevent you from using a fill. It's just that you didn't think the problem out right.
What you forgot to do was to halve the scaling percentage and rotate value (because you had two triangles grouped, not just one).
The other method is to start with the smallest unit and use a scaling percentage of more than 100.
If you do it that way with a group of 2 objects you will have to double the scaling percentage and rotate value in the transform.
This was done the latter way. I started of with a 1mm square, rotate-copied by 25.5°, coloured it yellow and sent behind and then scaled by 134.35%.
Grouped and then transformed with 45° rotate and 268.7% scale.
-
9. Re: Geometric shapes repeated into infinity
CarlosCanto Apr 22, 2011 7:27 AM (in response to Steve Fairbairn) -
10. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 22, 2011 7:32 AM (in response to CarlosCanto)But that way you have to recolour everything manually, right?
Use my way with 2 grouped objects and everything colours itself and you don't need to expand appearance.
-
11. Re: Geometric shapes repeated into infinity
CarlosCanto Apr 22, 2011 9:07 AM (in response to Steve Fairbairn)yes, of course coloring would have to be manual, this is just a usage example, your method is great for a two-color pattern no need to expand.
-
12. Re: Geometric shapes repeated into infinity
Wade_Zimmerman Apr 22, 2011 10:03 AM (in response to Steve Fairbairn)Actually Steve if you look at that particular example you used you only have to do one color (red) as a transform and make the other only only once as the color will be seen through the transparent shapes form by the first one the same thing would be true if you made three colors in which case you do it twice l though it might be easy for many to just use the way you describe it.
-
13. Re: Geometric shapes repeated into infinity
Mike Gondek2 Apr 22, 2011 11:59 AM (in response to CarlosCanto)Carlos,
A dumb question maybe, but how did you get your lines to exactly touch the edge, as the size of the triangle makes a difference. Did you use geometry and calculate the sides. Or did you find a way to chaneg the center anchor point. Both of these use your settings, but come out different.
I drew my triangle using the octagon tool and hit cursor down until I got 3 sides.
If I play with the settings I can get something close, but but only 2 sides touching, not 3.
-
14. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 22, 2011 12:39 PM (in response to Wade_Zimmerman)you only have to do one color (red) as a transform
No Wade, that's not right.
Red and yellow are interlaced so you get yellow-red-yellow-red-yellow-red and so on in a stack.
There aren't any transparent objects and I think compounds in this example would just confuse the issue.
The reason I used a square rather than a triangle was just to get easier calculations, but I could've done it with triangles just the same.
-
15. Re: Geometric shapes repeated into infinity
Wade_Zimmerman Apr 22, 2011 12:45 PM (in response to Steve Fairbairn)When I get back to my studio I will look at and see if I can explain or demonstrate whether I am right or wrong.
-
16. Re: Geometric shapes repeated into infinity
CarlosCanto Apr 22, 2011 12:47 PM (in response to Mike Gondek2)Hi Mike, no I didn't use math, I just eyeballed it. The first two examples I posted I started matching the OP triangle size. In the below sample I started with a random size triangle, then I set the angle (-5 for instance), scaled (1 copy) to 90%, then started moving right and down to manually center both triangles as shown below.
Since the copy is not exactly inside the original, I'll keep scaling till it fits, and nudging up/down/right/left as necessary.
-
17. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 22, 2011 1:44 PM (in response to Wade_Zimmerman) -
18. Re: Geometric shapes repeated into infinity
ecofugal Apr 22, 2011 5:45 PM (in response to ecofugal)wow, what a great response! Thank you so much.
I have tried it with the triangle and it worked beautifully. (still needed a bit of tweaking)
I had the same problem as Mike with one corner of the triangle out of alignment.
Definitely beats eyeballing each one which i did orginally.
Here are a few more i am going to work on. will post my efforts soon.
-
19. Re: Geometric shapes repeated into infinity
Wade_Zimmerman Apr 22, 2011 11:01 PM (in response to ecofugal)It appears i was wrong about one shape behind the art However I was able to do this with one shape and two fills.
Although this is original it has not been researched as such and I would not want Adobe or myself
with someone who is a licentious litigated hence the watermark making it unique.Of course I could do a tone of variations all just as applicable to a ton of different things. As art of any kind for almost any purpose.
Anyway if you fool around with the transform tools there are possibilities.
-
20. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 23, 2011 2:59 AM (in response to ecofugal)I fiddled around with the triangle a bit. There's no need for guesswork if you know where the centre is.
Do this by copying a side, rotating it by 90° and making a guide of it. Do the same with another side. Where the guides intersect is the centre (Not the same as the centre of the bounding box). Now draw a no fill, no stroke circle with the same radius as, or greater than, that of the triangle. Group. Now when you rotate, the triangle will turn around its own geometrical centre and no guesswork. You can use the same method for any polygon that has an odd number of sides (where the geometrical centre and the centre of the bounding box do not coincide). Like this:
In this case the rotation of the copy (red) was 3.25° and the scale 110%.
Now for the transform. Reckon that this is just about as good as it gets:
The transform rotate angle of the red+yellow group was 6.5°and the scale 120%.
Note that the circles are still there; you just can't see them. They are what keep the centre of rotation in the right place.
-
21. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 23, 2011 3:50 AM (in response to ecofugal)You can do it with any regular polygon using the circle technique for polygons with an odd number of sides.
Here's a pentagon:
On the original pair the scale was 110%, rotate 8.857°.
Transform scale 120%, rotate 17.714°.
You see the relationship between the figures. Scale integer above 100% doubles (10 becomes 20), rotate angle doubles.
-
22. Re: Geometric shapes repeated into infinity
Jacob Bugge Apr 23, 2011 4:43 AM (in response to ecofugal)ecofugal,
The following way of creating rotated regular polygons with inward/outward scaling is accurate. You may:
For regular polygons with an odd number of sides (for regular polygons with an even number of sides skip to 0):
-2) Place the polygon with its centre at X=Y=0 or create a copy in front and Object>Path>Average to get the centre;
-1) Create a no stroke no fill circle with D = 2*R with its centre at the centre of 1) (Smarts Guides are your friends) and Group;
0) Now you have the polygon/group of polygon+circle;
With 0) selected (all angles are in degrees):
1) Choose a rotation angle RA;
2) Object>Distort & Transform>Transform with Scale Horizontal/Vertical = S (see below) and Rotate Angle = RA, number of copies as desired.
N being the number of sides/angles, half the internal angle HIT = (1 - (2/N))*90.
Using the chosen/calculated values, you get:
Inward scaling:
S = 100*(sin(HIT)/(sin(180-HIT-RA)).
Outward scaling:
S = 100*((sin(180-HIT-RA)/sin(HIT)).
Obviously, RA should not exceed 90 - HIT.
-
23. Re: Geometric shapes repeated into infinity
JETalmage Apr 23, 2011 6:21 AM (in response to Steve Fairbairn)There's no need for guesswork if you know where the centre is.
To find the center of an equilateral polygon, just average the positions of the vertices:
1. Draw the polygon.
2. Copy. PasteInFront.
3. Object>Path>Average>Both.
That's the center.
JET
-
24. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 23, 2011 7:16 AM (in response to Jacob Bugge)Good for mathematicians, but many people will prefer the more visual approach (which is quite as accurate if you do things right).
I started off by choosing an arbitrary scale percentage. Then used smart guides to find the rotation value for the back polygon of the fist pair relative to the scale percentage. I just did it with the rotate tool, holding the cursor on an anchor point and rotating until smart guides said "path". That way I knew that the sides of the front polygon were touching the corners of the back one.
Just make a note of the scale and rotation values. Then for the transform double the rotation value and the part of the scale figure that exceeds 100.
So if the original scale value for the first pair was 110% then the scaling in the transform will be 120% (horizontal and vertical).
Likewise if the original rotation value was 8.854°, the rotation value for the transform will be twice that, or 17.714°.
-
25. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 23, 2011 7:21 AM (in response to JETalmage)There's no need for guesswork if you know where the centre is.
There never was any guesswork, at least not on my behalf. I explained how to find the centre of a triangle and the same thing applies to any regular polygon with an odd number of sides. Make a no-fill, no-stroke circle with the same radius as the polygon like I explained in an earlier posting and get the centres to coincide, Group and Bob's your uncle. :-)
-
26. Re: Geometric shapes repeated into infinity
Jacob Bugge Apr 23, 2011 9:27 AM (in response to Steve Fairbairn)Steve,
... the more visual approach (which is quite as accurate if you do things right).
Almost.
In post #20 you have 6.5 degrees and 120%; with RA = 6.5 degrees, S = 118.96% ~ 119%.
Just make a note of the scale and rotation values. Then for the transform double the rotation value and the part of the scale figure that exceeds 100.
That is also math.
-
27. Re: Geometric shapes repeated into infinity
Jacob Bugge Apr 23, 2011 9:29 AM (in response to JETalmage)James,
There is no guesswork over here. I used the Average in post #22, and Steve did it with Guides.
-
28. Re: Geometric shapes repeated into infinity
JETalmage Apr 23, 2011 9:31 AM (in response to Steve Fairbairn)There never was any guesswork
I was quoiting you, Steve.
I explained how to find the centre of a triangle
And I explained another way.
JET
-
29. Re: Geometric shapes repeated into infinity
JETalmage Apr 23, 2011 9:32 AM (in response to Steve Fairbairn)Double post due to forum error.
-
30. Re: Geometric shapes repeated into infinity
Wade_Zimmerman Apr 23, 2011 9:47 AM (in response to Jacob Bugge) -
31. Re: Geometric shapes repeated into infinity
Wade_Zimmerman Apr 23, 2011 9:48 AM (in response to Jacob Bugge)Double post
-
32. Re: Geometric shapes repeated into infinity
Wade_Zimmerman Apr 23, 2011 2:00 PM (in response to JETalmage).Very weird postings it shows up a=on my browser and then disappears then returns.
-
33. Re: Geometric shapes repeated into infinity
Jacob Bugge Apr 23, 2011 2:19 PM (in response to ecofugal)James, Wade,
Latest post before this, I wrote and posted and got a message saying that an unexpected error had occurred. I was about to try to post again, but I looked at the thread, and it was actually posted.
Did something like that happen to you two, too?
If it did, I will report it in the Forum Comments forum as a triple occurrence.
-
34. Re: Geometric shapes repeated into infinity
Jacob Bugge Apr 23, 2011 2:27 PM (in response to Wade_Zimmerman)it use to take hours to cut this stuff
Maths can be your friend. But it may take quite some pondering.
-
35. Re: Geometric shapes repeated into infinity
Steve Fairbairn Apr 23, 2011 2:34 PM (in response to Jacob Bugge)Did something like that happen to you two, too?
Yep. It happened three me three three. (??)
I was pressed the button to send and got an error message and a blank page.
But when I went back to the main page the message had been sent.
-
36. Re: Geometric shapes repeated into infinity
Jacob Bugge Apr 23, 2011 2:42 PM (in response to Steve Fairbairn)Steve,
I did as did you.
I guess James and Wade retried, and succeeded.
-
37. Re: Geometric shapes repeated into infinity
CarlosCanto Apr 23, 2011 4:47 PM (in response to ecofugal)enjoy
#target Illustrator // script.name = dupNrotateShape.jsx; // script.description = makes a polygon and duplicates itself into a spiral; // script.required = an open document; // script.parent = carlos canto // 4/23/11; // script.elegant = false; if (app.documents.length > 0) { var idoc = app.activeDocument; var sides = Number(prompt ("Enter the Polygon Sides", 3, "Dup & Rotate Shape")); if (sides>2) { var radius = Number(prompt ("Enter the Polygon Radius", 100, "Dup & Rotate Shape")); var perCent = Number(prompt ("Enter the Skew Percentage from 0% to 100%", 15, "Dup & Rotate Shape")); perCent = perCent/100; // to make 15% = 0.15 for example var copies = Number(prompt ("How many copies", 20, "Dup & Rotate Shape")); var pp = []; var ilayer = idoc.layers.add(); ilayer.name = "Dup & Rotate Shape"; idoc.defaultStrokeWidth = 0.5; idoc.defaultStroked = true; idoc.defaultFilled = true; var ipath = ilayer.pathItems.polygon (idoc.width/2, idoc.height/2, radius, sides); var swatchIndex = []; swatchIndex[0] = Math.round( Math.random() * ( doc.swatches.length - 1 ) ); swatchIndex[1] = Math.round( Math.random() * ( doc.swatches.length - 1 ) ); ipath.fillColor = doc.swatches[ swatchIndex[0] ].color; var ppCount = ipath.pathPoints.length; var j=1; var k = 0; for (m=1 ; m<=copies ; m++) { for (i=0 ; i<ppCount ; i++) { var pp1 = ipath.pathPoints[i]; k = i+j; if (i==ppCount-1) { k = 0; } var pp2 = ipath.pathPoints[k]; var pp1x = pp1.anchor[0]; var pp1y = pp1.anchor[1]; var pp2x = pp2.anchor[0]; var pp2y = pp2.anchor[1]; var pp3x = (pp2x-pp1x)*perCent + pp1x; var pp3y = (pp2y-pp1y)*perCent + pp1y; pp[i] = [pp3x, pp3y]; } var jpath = ilayer.pathItems.add(); jpath.setEntirePath(pp); jpath.closed = true; var n = m%2; jpath.fillColor = doc.swatches[ swatchIndex[n] ].color; ipath = jpath; } } else { alert ("needs to have at least 3 sides"); } } else { alert ("there are no open documents"); } -
38. Re: Geometric shapes repeated into infinity
tromboniator Apr 23, 2011 10:36 PM (in response to CarlosCanto) -
39. Re: Geometric shapes repeated into infinity
JETalmage Apr 24, 2011 7:02 AM (in response to Jacob Bugge)Did something like that happen to you two, too?
Yes. Happens all the time.
JET
















