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Tessellation for the chop

tessellation laser cutter image file Escher

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#1
hawksmoor

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Dear Geeks,

I want to send a laser cutter engineer an accurate image file so he can cut me 100 identical, tessellating shapes out of 4mm plywood.  The problem is that the pattern I want to use is taken from an image found online of a hand drawn pencil piece by M.C Escher. The image you see below is beautiful but not mathematically perfect and if one of those fishes is cut out it will not tessellate 100% accurately.  Is there brain enough and a program which can help to pull the lines slightly to create a perfectly tessellating fish? I'm sure there must be somewhere.  I've tried myself but I don't have a clue, I've offered the puzzle to more technical-minded friends and they failed too.  Anyone have any ideas, please? 

 

E20-MC-Escher-No-20-Fish-1938.jpg

 


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#2
paws

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Hi hawksmoor, and welcome to our forums

:welcome:

 

If you are seeking a "perfectly tessellated plane" using an irregular curved object, then a degree of either overlap or space is inevitable.....and this may defeat your objective.

 

Have you considered the position of licensing and copyright?

 

The original artwork cannot just be used as you wish without obtaining the correct permissions...

 

It might be wise to consult with the folks below before proceeding:

 

Regards

paws

 

The M.C. Escher Company B.V.

The M.C. Escher Company B.V. is the worldwide, exclusive representative of the M.C. Escher Copyrights. In this capacity The M.C. Escher Company oversees the use of works by M.C. Escher, either commercially or in publications. The M.C. Escher Company also holds all copyrights to M.C. Escher's spoken and written words and is owner of the Registered Trademark M.C. Escher®

The M.C. Escher Company B.V.
P.O.Box 101
3740 AC Baarn
the Netherlands
Tel: + 31-(0)35-541.80.41
Fax: +31-(035)-541.17.66
Email: [email protected]


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#3
dsenette

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i agree with paws on the copyright position. especially if it's for commercial use.

 

as to ACTUALLY getting the fishies to tessellate, how certain are you that they don't actually tessellate?

 

unfortunately, the only method I could think of for refining the image in such a way to ensure proper tessellation would be manual. like. literally cutting out fishies out of paper till you get the desired result, then digitizing that.

 

get the most perfect fishie, print out a bunch, line them up correctly on a cutting surface, then trim the overlaps and stuff till all the pieces are exactly the same....which....btw is why most tessellation patterns are geometric.


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#4
dsenette

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for something hand drawn by a madman, they're actually surprisingly close

 

fishies.png


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#5
dsenette

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https://www.thingive...com/thing:26121 huh, looks like someone beat us both to the refinement. they also have the cut files and such included there. thingiverse is USUALLY fairly good with deleting blatant copyright violations as well.


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