| Author |
origami spiral tesselations
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| John Andrisan 2006-08-19, 6:50 pm |
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| Adriaan Barel 2006-08-19, 6:50 pm |
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"John Andrisan" <andrisan@pacbell.net> wrote in message
news:44e6f88c_2@cnews
> A friend of mine in an origami club in Los Angeles does 40" by 40"
> murals of single 12-arm spirals.
>
> The squares in each arm are either square origami models or sheets of
> paper, and their sizes increase by the factor 1.414 or sqrt(2). We
> learned of them in a book by Tomoko Fuse titled "Origami Quilts",
> ISBN 4-88996-068-6.
>
> Here's a tesselation design that uses 7 spirals which I plan to offer
> him today.
> john
Very nice John, but think it would look better on a different coloured
background.
--
----oooOOOooo----
Adriaan Barel
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John Andrisan wrote:
> A friend of mine in an origami club in Los Angeles does 40" by
> 40" murals of single 12-arm spirals.
> The squares in each arm are either square origami models or
> sheets of paper, and their sizes increase by the factor 1.414 or
> sqrt(2). We learned of them in a book by Tomoko Fuse titled
> "Origami Quilts", ISBN 4-88996-068-6.
> Here's a tesselation design that uses 7 spirals which I plan to
> offer him today.
I don't know how you did this (PSP tools), so please don't take it
as criticism when I ask why the blue squares have yellow
(selection?) outlines. The pattern is nice, it would look splendid
if the outlines were well defined.
Joske
--
http://members.home.nl/j.a.c.backer/
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| Joëlle 2006-08-19, 6:50 pm |
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"John Andrisan" <andrisan@pacbell.net> wrote in message
news:44e6f88c_2@cnews...
>
> A friend of mine in an origami club in Los Angeles does 40" by 40" murals
> of
> single 12-arm spirals.
>
> The squares in each arm are either square origami models or sheets of
> paper,
> and their sizes increase by the factor 1.414 or sqrt(2). We learned of
> them in a book by Tomoko Fuse titled "Origami Quilts", ISBN 4-88996-068-6.
>
> Here's a tesselation design that uses 7 spirals which I plan to offer him
> today.
> john
>
>
>
Very nice John.
I received an email some months ago, where someone had filled a page fill of
similar shapes. the circles appeared to move. I have been trying to locate
it, as I am sure you would know how that was done, but can't find it just
yet.
Your friend will be very pleased with your design I am sure.
:-)
Joëlle
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| Carrie Osmo 2006-08-19, 6:50 pm |
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John
This is a good I would prefer another background
colour. The pattern works well and is nicely
developed.
carrie
"John Andrisan" <andrisan@pacbell.net> wrote in message news:44e6f88c_2@cnews...
>
> A friend of mine in an origami club in Los Angeles does 40" by 40" murals of
> single 12-arm spirals.
>
> The squares in each arm are either square origami models or sheets of paper,
> and their sizes increase by the factor 1.414 or sqrt(2). We learned of
> them in a book by Tomoko Fuse titled "Origami Quilts", ISBN 4-88996-068-6.
>
> Here's a tesselation design that uses 7 spirals which I plan to offer him
> today.
> john
>
>
>
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| John Andrisan 2006-08-20, 6:41 pm |
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John Andrisan wrote:
> Thank you for your comments.
> As to colors and such, this was a "what if" example, and no more.
> The idea was bouncing around
> in my head and now that I have it on paper, my mind can move on
> to other things.
> I used several PSP scripts, and some trigonometry, to produce the
> single spiral shape.
> My friend uses other methods and colors, as shown below. If
> you'd like to purchase one, just let me know.
I think it's very clever of you to do these in scripts. It reminds
me a little of the spiral scripts by Mike Williams
http://www.econym.demon.co.uk/psp8scripts/index.htm
(will only work in 8 and 9)
and a barbed wire script RonV did with the help of calculations.
Your friend has a really colorful one on the photo. He looks like a
nice person.
Joske
--
http://members.home.nl/j.a.c.backer/
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| Spandex Rutabaga 2006-08-20, 6:41 pm |
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Joske wrote:
> I think it's very clever of you to do these in scripts. It reminds
> me a little of the spiral scripts by Mike Williams
>
> http://www.econym.demon.co.uk/psp8scripts/index.htm
>
> (will only work in 8 and 9)
Actually in PSP 9 the script I tested produced a deprecation
warning "integer argument expected, got float" though the script
completes.
Here's a little suggestion for you. The scripts simply use some
math to build a brush stroke comprising pixel coordinates. Instead
of using them to drive the Paintbrush you could use them to drive
the Warp Brush in one of its modes. Afterwards you can save the
result as a deformation map and just apply it to other images
without any scripting. It should be possible to get something that
is reminiscent of the Dueling Spirals deformation map that came
with PSP.
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Spandex Rutabaga wrote:
> Joske wrote:
[color=darkred]
> Actually in PSP 9 the script I tested produced a deprecation
> warning "integer argument expected, got float" though the script
> completes.
Yes, they all do that in all PSP versions, but the outcome is still
okay.
> Here's a little suggestion for you. The scripts simply use some
> math to build a brush stroke comprising pixel coordinates.
And it's the math I was referring to. I had four years of it and got
through, but thanks to my number-blindness have developed no feel
for it whatsoever. I wish I could capture more functions in math in
scripts instead of doing the simple things I do to make them work.
> Instead
> of using them to drive the Paintbrush you could use them to drive
> the Warp Brush in one of its modes. Afterwards you can save the
> result as a deformation map and just apply it to other images
> without any scripting. It should be possible to get something that
> is reminiscent of the Dueling Spirals deformation map that came
> with PSP.
It's late here and we've been working hard tonight, so I may get
this wrong. Warp an image, and save what? Or do you mean warp an
image while recording, and save the recording as a script, the
script being a kind of deformation preset as it were? Right now I
don't see how I could save Warp Tool moves performed on an image as
a deformation map. I'm sure I'm missing something... I do see that
especially the twirl settings would be similar to some of what Mike
did.
Joske
--
http://members.home.nl/j.a.c.backer/
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| Spandex Rutabaga 2006-08-20, 10:39 pm |
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Joske wrote:
> It's late here and we've been working hard tonight, so I may get
> this wrong. Warp an image, and save what? Or do you mean warp an
> image while recording, and save the recording as a script, the
> script being a kind of deformation preset as it were? Right now I
> don't see how I could save Warp Tool moves performed on an image as
> a deformation map. I'm sure I'm missing something... I do see that
> especially the twirl settings would be similar to some of what Mike
> did.
The scripts construct a brush stroke - a long list of coordinates
in a single variable. This variable is passed to the Paintbrush
command and the brush paints from coordinate to coordinate. You
can just as well pass this variable to the Warp Brush command.
When doing the warp I would pick a square image, say 1000 x 1000
pixels and simply run the script on it. If the image is of uniform
color it doesn't matter - you won't see the deformation but it will
still be there. It's safer to fill with a pattern to be sure of
seeing something. After the script has done its single long
calculated brush stroke, save the resulting deformation as a
deformation map using the Deformation Map save icon in the Tool
Options. I would run the script with the Draft Quality set to
Medium to stop the saved deformation map becoming too large. Do
not press the Final Apply checkmark icon before saving since then
the deformation (as opposed to the image) will no longer be
saveable. Next time you want to apply the saved deformation map
to some other image, open the image, start either warp tool - the
brush or mesh - and load the map. Then press the Apply button or
add more warping and then Apply. Done.
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| John Andrisan 2006-08-20, 10:39 pm |
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If you'd like I can send you a handout of about 5 pages on Yami's spirals
and the math behind them. Please ask me for a copy separately... they may
not be appropriate to post here, being rather off-the-subject.
I prepared the handout for part of Yami's presentation at the 2005 Origami
Convention in NYC in June of that year, hosted by origami-usa.org in that
city.
The scripts I did were simple ones to produce the squares in the appropriate
sizes with the growth factor specified, and create a "radial grid" or
compass rose using a specified central angle for separating the radii. I
did spirals having various numbers of arms.
I haven't tackled the problem of how to select a square and place it in the
appropriate place on the "radial grid". I may yet do that... on a
sleepless night.
john
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John Andrisan wrote:
> If you'd like I can send you a handout of about 5 pages on
> Yami's spirals and the math behind them. Please ask me for a
> copy separately... they may not be appropriate to post here,
> being rather off-the-subject.
That's a very nice offer of you, but I wouldn't be able to
understand the math. Not sure if it'd be off-topic here, as some
math-savvy posters do script in math when they need to. I know RonV
can do this sort of thing to. It'd probably be a bit large though.
> I prepared the handout for part of Yami's presentation at the
> 2005 Origami Convention in NYC in June of that year, hosted by
> origami-usa.org in that city.
I had no idea there was an 'origami movement'. I see they sell
papers and kits too. Love many of those papers.
> The scripts I did were simple ones to produce the squares in the
> appropriate sizes with the growth factor specified, and create a
> "radial grid" or compass rose using a specified central angle for
> separating the radii. I did spirals having various numbers of
> arms.
It is simple to you, that's why I commented favorably.
> I haven't tackled the problem of how to select a square and place
> it in the appropriate place on the "radial grid". I may yet do
> that... on a sleepless night.
Maybe RonV could help you there? I really don't know for sure, but
he knows his math and a fair bit of programming and scripting as
well.
Joske
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| Spandex Rutabaga 2006-08-21, 6:58 pm |
| Joske wrote:
> Aha, I finally got it. Okay, just for fun and because I think you
> have a good idea here: open a new 500x200 image and fill it with a
> gradient that's light at the top and dark at the bottom (or vice
> versa if you want spooky). Then use my attached map. It's just a
> quick experiment. There should be some very nice possibilities with
> your idea.
I can't follow instructions so I made the attached instead :)
However, you should also try to copy and paste the part from
Mike's scripts that does the math and builds the stroke. Then
you can use the stroke. There are a bunch of other nice curves
you can construct using math that is not especially complicated.
This book is one source of fun stuff (well, fun for some :) One
aspect is that is shows a range of ways of constructing any
given curve so that you could in principle produce a variety of
image effects concentrating only on one type of curve.
http://www.amazon.com/gp/product/05...8267157-7852655
Another place to look would be http://mathworld.wolfram.com/
A few curve names to search for: cardioid, limacon (cedilla on
the c), astroid, nephroid, deltoid, cycloid, right strophoid,
spirals of various types, lemniscate of Bernoulli, tractrix,
catenary, conchoids, cissoids, strophoids, roulettes, pedal
curves (positive and negative) and glisettes. Once you have
the math copied to make some of these you can also use exactly
the same math to make vector shapes similar to spirograph scripts.
One example of what I mean (done manually) is attached.
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Spandex Rutabaga wrote:
> Joske wrote:
>
[color=darkred]
> I can't follow instructions
Okay. I followed yours out of a mixture of politeness and
willingness to experiment.
Joske
--
http://members.home.nl/j.a.c.backer/
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| John Andrisan 2006-08-21, 6:58 pm |
| [color=darkred]
I recognize his equations... I use them in my own geometric curves and
spirals scripts. But I add more parameters, maybe too many.
My extra parms allow me to do some interesting things like connect every
n-th point along the way rather than all of them, which gives me a sort of
"strobe" effect. I'll show you some results. as soon as I find them on my
cluttered hard-drive. My user interface for these parms is "edit and
change".
I call my script a Lissajous curve generator, after those wonderful shapes I
remember seeing on ocilliscopes in EE classes in my college days. I was a
math major with lots of electives to have fun in.
john
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| John Andrisan 2006-08-21, 6:58 pm |
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>I had no idea there was an 'origami movement'.
We're world-wide... as we say "Origami is In Creasing...".
john
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| Spandex Rutabaga 2006-08-21, 6:58 pm |
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John Andrisan wrote:
>
> We're world-wide... as we say "Origami is In Creasing...".
Ouch! :)
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| John Andrisan 2006-08-21, 6:58 pm |
| underprocessable | |
| Spandex Rutabaga 2006-08-21, 10:42 pm |
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John Andrisan wrote:
> The square one is often seen in the answer to a math puzzle about 4 spiders
> trying to get to the
> one fly in the center of the square.
I think I've seen this one with dogs starting in the corners of
a square yard, each chasing the dog to its left at a constant
speed for all the dogs. Pity the real world doesn't quite work
like the math :)
> The spiral curves are called "pursuit
> curves", and are mentioned on several math web sites.
The polygons you posted are what I was trying to get at, where
the curve appears as the envelope of the curve tangents.
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| John Andrisan 2006-08-22, 6:44 pm |
| underprocessable | |
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John Andrisan wrote:
[color=darkred]
> Here are some samples from my program.
> The first one, I call it a butterfly, is a simple spiral with
> some phase angles in the equations.
> I use this one for box top designs.
> The second one is a collection of "strobe" pictures.
> To get the square shaped one, I plot and connect points that are
> slightly less than 90 degrees apart. The pentagon shape uses
> slightly less than 72 degrees, etc.
> The square one is often seen in the answer to a math puzzle about
> 4 spiders trying to get to the
> one fly in the center of the square. The spiral curves are
> called "pursuit curves", and are mentioned on several math web
> sites.
> These are all done in vectors; one pic probably has over 500
> vectors, and it does slow
> down my 2.666 GHz Compaq. Sometimes the lights dim too.
Oh dear :-)
John, I didn't know you wrote these scripts. I will say again that
my brain cells flee in every possible direction when they 'see'
calculations (I'm also one of the last not fully used to the switch
from guilder to euro, that's how bad it is). So from where I stand
it's great when you can do this sort of more complicated work in
scripts.
I imagine the scripts behind the attached examples couldn't be used
for basic shapes for use by others like scrapbookers. They're
vector, and they'd take a long time to render. But I bet one could
think of some nice scripts if one had this sort of math in one's
fingertips.
Joske
--
http://members.home.nl/j.a.c.backer/
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| Lori Davis 2006-08-22, 6:44 pm |
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"Joske" <j.backer@home.nl> wrote in message news:44e9d271_3@cnews...
> I'm already thinking ahead, not just one spiral. Lori should love
> this too I'm sure.
>
Yes, indeed. I'm following this thread closely, even though I'm not saying
much. Can't wait to see what you come up with Joske.
BTW, I think Joe Fromm was playing around with spiral-generating scripts at
one time, but I don't know whether he ever posted any.
Lori
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Lori Davis wrote:
> "Joske wrote
[color=darkred]
> Yes, indeed. I'm following this thread closely, even though I'm
> not saying much. Can't wait to see what you come up with Joske.
> BTW, I think Joe Fromm was playing around with spiral-generating
> scripts at one time, but I don't know whether he ever posted any.
I surely would have seen them if they had been posted to public
groups.
I don't think I'm going to come up with anything, really, because I
have too many other things to do :-) But I was thinking of your
paisley pattern... not that you could actually make one of just any
(unknown because user input) material, but I do think that this
could be a tool for patterns. (For instance kaleidoscoped) gradients
would go a long way and would probably be better suited than
(unknown) pattern materials.
Joske
--
http://members.home.nl/j.a.c.backer/
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| Spandex Rutabaga 2006-08-22, 6:44 pm |
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John Andrisan wrote:
> A sample is shown below. Makes for nice peacock models.
> john
Cool indeed.
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| Spandex Rutabaga 2006-08-22, 6:44 pm |
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Joske wrote:
> I will say again that
> my brain cells flee in every possible direction when they 'see'
> calculations (I'm also one of the last not fully used to the switch
> from guilder to euro, that's how bad it is).
Oh dear. I thought all you Euros used ecumenical units (Eunits)
like fish use water. I know it can be a bit intimidating but it
you can copy a lot from Mike. The trick very often is to locate
what is called the "parametric equation" of a curve. Instead of
using some complex equation to calculate Y for a particular choice
of X, the parametric equation calculates both Y and X for a series
of values that you choose of some parameter (often using standard
trigonometric functions). That is no more than applying a recipe
to get two numbers you need instead of actually solving equations,
finding roots and all that complex math stuff. It doesn't look like
I will have time to do any "scripts to make curves" so I'm throwing
out ideas that someone (not necessarily you) might follow up.
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| Nightingail 2006-08-23, 7:05 pm |
| underprocessable | |
| Spandex Rutabaga 2006-08-23, 7:05 pm |
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Nightingail wrote:
> Attached
> shows why some fractal apps give me a headache.
The headache comes from there being one word in French while
the rest are in English and from the funny spelling of color.
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Spandex Rutabaga wrote:
> Joske wrote:
[color=darkred]
> Oh dear. I thought all you Euros used ecumenical units (Eunits)
> like fish use water.
Not me. I still don't know what stuff is worth, and the 2.20 anchor
for the guilder is gone because the guilder wouldn't be worth now
what it was a few years ago. The only nice thing about the euro to
me is still that there are all these different coins from all the
countries.
> I know it can be a bit intimidating but it
> you can copy a lot from Mike. The trick very often is to locate
> what is called the "parametric equation" of a curve. Instead of
> using some complex equation to calculate Y for a particular choice
> of X, the parametric equation calculates both Y and X for a series
> of values that you choose of some parameter (often using standard
> trigonometric functions). That is no more than applying a recipe
> to get two numbers you need instead of actually solving equations,
> finding roots and all that complex math stuff.
> It doesn't look like I will have time to do any
> "scripts to make curves" so I'm throwing out ideas that
> someone (not necessarily you) might follow up.
Would be really nice if someone did a few more of these, I do enjoy
running them and figuring out for what the outcomes could be used.
Pity you don't have time, I hope RonV or John does.
Joske
--
http://members.home.nl/j.a.c.backer/
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| Nightingail 2006-08-24, 7:01 pm |
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Spandex Rutabaga wrote:
> The headache comes from there being one word in French while
> the rest are in English and from the funny spelling of color.
It's not as inconsistent as it appears :-) New formulas are added
separately, and the authors are of various nationalities. It's similar to
the way some of my plugins in PSP will have their settings in something
other than English.
--
Nightingail's Gallery
www.nightingail.com
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| John Andrisan 2006-08-25, 7:00 pm |
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John Andrisan wrote:
[color=darkred]
> also shows curves done with loops... I refer to them as epicycles
> and hypocycles.
> Here's a hypocycle spiral that reminds me of an orb weaver
> spider's web. I added the radii separately.
Definitely spiderish, but if the lines were harder, it's also make a
good fill pattern. I'm also thinking of umbrellas. It's really nice
you can do this.
Joske
--
http://members.home.nl/j.a.c.backer/
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| Lori Davis 2006-08-28, 6:44 pm |
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John Andrisan wrote:
>
>
> also shows curves done with loops... I refer to them as epicycles and
> hypocycles.
>
> Here's a hypocycle spiral that reminds me of an orb weaver spider's web. I
> added the radii separately.
All really nifty stuff, John.
Lori
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| John Andrisan 2006-08-31, 11:08 pm |
| underprocessable | |
| John Andrisan 2006-08-31, 11:08 pm |
| underprocessable | |
| Spandex Rutabaga 2006-08-31, 11:08 pm |
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John Andrisan wrote:
> But I find odd differences between the results that I don't yet
> understand... see attach ment 1.
The application of a gradient to a vector object is based on the
bounding box of the object. As a vector object is rotated away
from horizontal or vertical the size of the bounding box changes
and the aspect ratio changes. This might be playing a role in
your case depending on what your scripts do. Another thing to
check is how a gradient stroke works on a vector and a brush
stroke, i.e. whether the gradient direction is relative to the
orientation of the object or relative to the edges of the image
for each of these objects.
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| Spandex Rutabaga 2006-08-31, 11:08 pm |
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John Andrisan wrote:
> I've learned a lot about paint brushes along the way, and I plan to learn
> more, like tip changes. I find that the journey is usually more fun than
> the result.
You might want to create an empty layer and paint on it using the
Paint Behind blend mode. From PSP 9 Help: "Paint Behind Works on
layered images only. When a layer is selected, Paint Behind paints
behind the data currently on that layer. No paint will be visible
when the topmost layer and active layer are both fully opaque."
I guess it might be like reversing the order of your strokes.
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| John Andrisan 2006-09-01, 6:33 pm |
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>Another thing to check is how a gradient stroke works on a vector and a
brush
stroke, i.e. whether the gradient direction is relative to the
orientation of the object or relative to the edges of the image
for each of these objects.<
good ideas... another adventure for me.
john
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