Hi Julian,
I used this article on SCARAB BEETLEs as an inspiration for curved designs for solar panels. The silicon wafer of solar cells must be kept flat so this pattern of polygons [characterized by Voronoi analysis] is what the beetle used to go around curves.
and, as you know, this is an excellent study of iridescence from Srinivasaraos’ group here at Georgia Tech.
best regards,
Jeannette
----- Original Message -----
From: "Manfred Drack" <[log in to unmask]>
To: [log in to unmask]
Sent: Thursday, September 20, 2012 3:41:28 PM
Subject: Re: Tiling eyes!
Beto,
I am not sure if I understood your argument. Why would a hexagonal
pattern preferable for motion detection? One could also think of a
rectangular patter for your case; cf. compound eyes of crustaceans
(which of course, as superposition eyes work differently).
Manfred
Am 20.09.2012 19:36, schrieb Beto Cruz:
> i think that the "reason" behind hexagonal segmentation of insect eyes
> is related to motion detection. think about a plane that is segmented in
> a hexagonal pattern.. what calls our attentions is the nucleous of seven
> hexagons, a flowe- like pattern, right, with one hexagon surrounded by
> other 6 hexagons.
>
> now consider it a visual "unity", able to capture an object..
>
> now, if that object moves from this first nucleous, all you have to do
> is to count how many other nucleous it moved from the first one, to
> calculate a distance.
>
> what i am saying is that, even if the object moved just one hexagon in
> any direction, it becomes immediately the center for the closest
> nucleous of vison..
>
> something like that.
>
>
>
> ------------------------------------------------------------------------
> *From:* Julian Vincent <[log in to unmask]>
> *To:* [log in to unmask]
> *Sent:* Thursday, September 20, 2012 1:32 PM
> *Subject:* Re: Tiling eyes!
>
> Yes - please send the link / reference. We can then compare the maths
> with the natural system, and perhaps ask sensible questions about the
> reasons behind the segmentation of insect eyes.
>
> Julian
>
>
> On 20 Sep 2012, at 16:40, Lynny wrote:
>
> > I've found a paper online which deals with hexagonal global
> parameterization of arbitary surfaces. It allows for the tiling of
> surfaces with nearly regular hexagonal patterns. Would that's be of any
> use? It's not my paper but can send you the link if you want?
> >
> > Sent from my HTC
> >
> > ----- Reply message -----
> > From: "Julian Vincent" <[log in to unmask]
> <mailto:[log in to unmask]>>
> > To: <[log in to unmask] <mailto:[log in to unmask]>>
> > Subject: Tiling eyes!
> > Date: Thu, Sep 20, 2012 15:24
> >
> >
> > Chicken wire would work if the hexagons kept constant geometry, but
> they don't. Corners tend to disappear and the size changes! So I really
> do need to know the detail.
> >
> > Julian
> >
> >
> > On 20 Sep 2012, at 15:17, Lynny wrote:
> >
> > > Thank you Julien, my apologies for not staying in touch better! Ah,
> well if you have the designer in house you will know much more about it! =)
> > >
> > > I may be going down too simple a route here but if you are wanting
> to analyse how the hexagons distort over various curvature, could you
> not set up a model using some kind of lightweight chicken wire? Not
> particularly high tech I know but might give some indication to if there
> is a pattern to the distortion?
> > >
> > > I'd be very interested in the results once you have got them.
> > >
> > > Lynn.
> > >
> > >
> > >
> > > Sent from my HTC
> > >
> > > ----- Reply message -----
> > > From: "Julian Vincent" <[log in to unmask]
> <mailto:[log in to unmask]>>
> > > To: <[log in to unmask] <mailto:[log in to unmask]>>
> > > Subject: Tiling eyes!
> > > Date: Thu, Sep 20, 2012 14:59
> > >
> > >
> > > Nice to hear from you, Lynn!
> > >
> > > I know about the BM roof - the guy who did the computation (Chris
> WIlliams) is in the Architecture Dept at Bath. But that's all
> triangulated. The interesting thing about the insect eye is that the
> basic unit is a hexagon (like a geodesic dome) which encloses the
> largest area with the shortest perimeter and thus gives the lightest
> structure (cf. Eden Centre biomes). But all these structures have even
> curvature. The uneven curvature that you get in the eye of a dragonfly
> takes you round far sharper corners. I want to see how the hexagons are
> distorted under those geometrical constraints.
> > >
> > > I'll report results, but at the moment it looks as if I'll be
> taking photos!
> > >
> > > Julian
> > >
> > > On 20 Sep 2012, at 14:52, Lynny wrote:
> > >
> > > > Hi Julian,
> > > >
> > > > I'm not sure how much use this will be but it might be worth
> having a look at the design for Norman and Fosters Great Court at the
> British Museum. The glazed roof spans in an arc from a cylinder to a
> straight edge.
> > > >
> > > > Let of know if this is the sort of lines you are going down and I
> can see if I have and additional information on it at home.
> > > >
> > > > Hope this helps.
> > > >
> > > > Thanks,
> > > >
> > > > Lynn.
> > > >
> > > > Sent from my HTC
> > > >
> > > > ----- Reply message -----
> > > > From: "Julian Vincent" <[log in to unmask]
> <mailto:[log in to unmask]>>
> > > > To: <[log in to unmask] <mailto:[log in to unmask]>>
> > > > Subject: Tiling eyes!
> > > > Date: Wed, Sep 19, 2012 16:06
> > > >
> > > >
> > > > I'm working on a project to tile a curved surface and wonder
> whether the packing pattern of ommatidia on an insect's eye would give
> some clues about what to do at the corners. I've found a few pictures,
> but I'm sure there should be more - probably in the older literature.
> Alternatively, has anyone got an algorithm for morphing (say) hexagons
> as they go round corners? Come to that, what is the supposed function of
> the packing shapes going round corners. Is it purely getting as many
> ommatidia of more than a minimum area, or are there other criteria?
> > > >
> > > > Thanks for all the replies!
> > > > Julian Vincent
> > >
> >
>
>
--
====================================
Manfred Drack, Dr. Mag.
Department of Theoretical Biology
University of Vienna
Althanstrasse 14
1090 Wien
Austria
Tel: ++43 1 4277 56706
Fax: ++43 1 4277 9567
====================================
--
--
Jeannette Yen
Professor, School of Biology
Director, Center for Biologically-Inspired Design
Georgia Institute of Technology
310 Ferst Drive
Atlanta, GA. 30332-0230
404-385-1596
404-894-0519 fax
[log in to unmask]
http://www.biology.gatech.edu/faculty/jeannette-yen/
http://www.cbid.gatech.edu/
http://www.channelone.com/onair/index.vm?releasePID=JmizffrtbqiC1iRQ5fnMyKGCbKKKLott
TEDx talk on Biologically Inspired Design for Interdisciplinary Education.
http://www.youtube.com/watch?v=PMlvUJ9_GSk
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