Hi there,
This may or may not be a stupid question, but I was wondering how I would find references for my designs. I Understand circle packing and tiling perfectly, but I have no idea how to figure out the reference points for them. Is there some mathematical problem needed to do that, or what?
Finding references for my designs
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Re: Finding references for my designs
I'm not positive, but I think that one of Robert Lang's free tools will help with finding references... You'll have to search or wait for someone who has used them...
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cowburger13
Re: Finding references for my designs
I think there is another way besides reference finder.
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FlareglooM
- Senior Member
- Posts: 433
- Joined: January 30th, 2009, 3:15 pm
Re: Finding references for my designs
Robert Lang has written an article titled "Origami and Geometric Constructions". I think it covers some reference finding. (crossing diagonals, Fujimoto's construction etc)
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FlareglooM
- Senior Member
- Posts: 433
- Joined: January 30th, 2009, 3:15 pm
Re: Finding references for my designs
At least that is for finding the folds that go through point you want. If you need to calculate the point itself, so for example the center of one of the circles you used, I think you can just use stuff like sine and cosine.
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FlareglooM
- Senior Member
- Posts: 433
- Joined: January 30th, 2009, 3:15 pm
Re: Finding references for my designs
Just to be sure, before I make an explanation. (if it's possible, haven't checked yet)
Are you having trouble:
1. Finding the folds that run through a point (basically what Reference Finder does)
2. If you have made a packing, finding/calculating the coordinates of the centers of the circles.
Are you having trouble:
1. Finding the folds that run through a point (basically what Reference Finder does)
2. If you have made a packing, finding/calculating the coordinates of the centers of the circles.
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FlareglooM
- Senior Member
- Posts: 433
- Joined: January 30th, 2009, 3:15 pm
Re: Finding references for my designs
I was thinking I would make an elaborate explanation for you, but that is basically redoing Robert Lang's work so that's not what I am going to do.
This is the article I mentioned before (link on Lang's site doesn't really work for me so here is a different one): Origami and Geometric Constructions
(Click for PDF)
What my advice to you is: Start at page 4 at Binary Divisions and read up till the end of page 13.
The section about Binary Divisions and Binary Folding Algorithm covers converting fractions to binary numbers. These binary numbers represent folds you need to make. It is important that you understand that, since it is provides a good basis for the Crossing Diagonals. When you have arrived at page 12, the start of the Crossing Diagonals section formula 11 is kind of postulated. If you want the full derivation for that I can provide you that. (it is a couple of lines). See if you can follow that section till the end of page 13 (after example of folding thirds, note: I think p must be equal to 2 here in the example)
If you have questions about these pages when reading you can ask me questions, I understand as far as I know most of those pages. (haven't read more, I will if you want to continue understanding the rest. I myself also find it interesting
)
I also might have confused you with that finding the folds can be simply done by using sine and cosine. It is not possible afaik, sorry for that if that it is the case. The use of only sine and cosine is possible for the 2nd option in my previous post, but I think you know that already, since you can make packings.
Well this was it for now, good luck and ofcourse you can always ask me questions
This is the article I mentioned before (link on Lang's site doesn't really work for me so here is a different one): Origami and Geometric Constructions
(Click for PDF)
What my advice to you is: Start at page 4 at Binary Divisions and read up till the end of page 13.
The section about Binary Divisions and Binary Folding Algorithm covers converting fractions to binary numbers. These binary numbers represent folds you need to make. It is important that you understand that, since it is provides a good basis for the Crossing Diagonals. When you have arrived at page 12, the start of the Crossing Diagonals section formula 11 is kind of postulated. If you want the full derivation for that I can provide you that. (it is a couple of lines). See if you can follow that section till the end of page 13 (after example of folding thirds, note: I think p must be equal to 2 here in the example)
If you have questions about these pages when reading you can ask me questions, I understand as far as I know most of those pages. (haven't read more, I will if you want to continue understanding the rest. I myself also find it interesting
) I also might have confused you with that finding the folds can be simply done by using sine and cosine. It is not possible afaik, sorry for that if that it is the case. The use of only sine and cosine is possible for the 2nd option in my previous post, but I think you know that already, since you can make packings.
Well this was it for now, good luck and ofcourse you can always ask me questions
