3d_design

updated 2008-01-02

contents:

"Engineering design is a decision making process required to optimally convert resources into systems, components or processes to meet desired needs." -- Dr. D. A. Lucca (possibly quoting someone else).

A #design describes how to apply #tools to materials.

David Cary also maintains related pages:

design news

materials

see also

[a few extremely common materials, and a few exotic materials]

supplies

Supplies: [FIXME: is this the same as #materials ? ] 

Batteries
finishing nails
wire
WD-40
superglue
Duct Tape
masking tape
scotch tape (writable with pencil)
clear contact paper
paint
spare light bulbs
ziplock bags
trash bags

tools

tools:

see also 

Screwdriver
Tape measure
hammer
scissors
pliers (needle-nose)
flashlight
Dentist's Mirror
toolbox
extension cord
power strip

furniture

see also

furniture: [FIXME: house considerations ? office space ?]

chair desk bookshelves lamp trash bucket plastic mat to go under chair

book.html#peopleware

educational aspects of toys

Origami:
reminiscent of the protein folding problem of biochemistry. A little closer (than LEGOs or wooden blocks) to the true ratio of tensile strength to compressive strength of typical building materials.
Paper airplanes:
aerodynamics (duh!) #paper_airplanes
Tetris:
a good intuitive model for crystallization (materials science). After playing Tetris, it is intuitive that faster crystallization rates result in more defects / mm^3. It makes it more intuitive that eutectic alloys have certain ratios.
Air hockey:
conservation of momentum, elastic collisions, (lack of) friction. (Physics).
Pool / Billiards:
conservation of momentum, elastic collisions (Physics).
Asteroids:
the relationship between velocity, acceleration, and position (Calculus); Newton's Laws (physics).

Pet Peeve: I despise the versions that have friction -- the ones where if you turn off your engine, you start slowing down and eventually stop. This makes it unnecessarily hard to understand Einstein's theory of relativity. The completely frictionless ones are better -- since in the real world velocity *is* truly relative.

Crystal ___(???):
Asteroids + gravity (physics); "the slingshot effect" (astrophysics physics).
wood blocks:
gravity, balance, gravitational potential energy (physics) building aesthetics (architecture) 3 D shapes and manipulation (3 D geometry; mechanical engineering) (Unfortunately, wood blocks teach the exactly the wrong thing what shapes have optimum strength -- -- a stack of blocks has zero tensile strength and practically infinite compression strength, while the strongest real building materials have very high tensile strength and lower compressive strength -- making tensegrity unnecessarily difficult to understand. Better 3D manipulatives are needed ! ). ... "the SOMA cube, invented by the Danish Author Piet Hein." http://www.fam-bundgaard.dk/SOMA/SOMA.HTM points to a "solver" program that, given the outer shape, tries to fit the available pieces together to make that shape.
Better 4D manipulatives are needed ! see video_game.html#4dtoys
Legos:
wood blocks + better tensile strength; the difference between compression and tension (physics).
Rubic's snake:
the protein folding problem. (Better protein folding analogues are needed !)
Erno Rubik's cube:
the difficulty of optimization (getting sucked into local minima), group theory (Math).

Pet peeve: Please *do not* peel the stickers off and rearrange them to "fix" the cube. They never stick back on very well, and soon fall off and are lost. Instead, if you *must* have it fixed and you don't have the patience to do that merely by twisting, *guess what's inside first*, then *take it apart* into "individual cubes". It's quite surprising how the whole thing holds together (mechanical engineering). Sure, it's "looser" after you do this, but easier-to-spin is not a bad thing. [FIXME: describe exactly how to get the 1st cube out, or link to a page that does.] http://search.dmoz.org/cgi-bin/search?search=rubik [FIXME: do I need 2 copies, 1 here, one at dav_info.html ?]

[rubik cube / typography ?] http://www.lineto.com/application.html?ID=122&dir_id=121

Rubik's Cube by Karl Dahlke http://www.eklhad.net/rubik/ has a on-line program that allows you to enter your current rubic's cube configuration, and it tells you step-by-step how to solve it. (You can download the source code to the program).

``As far as I know I am the fastest active cuber in Britain with a best average of 23.0 seconds'' -- stiff_hands http://homepage.ntlworld.com/angela.hayden/cube/cube_frontpage.html

Dominos:
"the domino effect", conversion between gravitational potential energy and kinetic energy (physics). Digital bit regeneration (communication theory).
Lemmings:
parallel processing (Computer Science).
HTML:
helps understand the difference between the 2 views of a program: design time v. run time. (Computer Science).
team sports:
teamwork, coordination, communication. (sociology, psychology) (Physics).

architecture

traditional architecture (designing buildings on the ground to support the humans inside).

related to learning.html , #design , #synergetics , #city [should I move ``city design'' info there ?], #spacecraft_design , #furniture , computer_architecture.html ,

news links:

other links:

design

Design, in general.

What I call "general design" seems to be the same as what others call "the meta-field of design" (Adam Greenfield) and "design science" (Buckminster Fuller).

See also simplicity

see also spacecraft_design

see also FUD (Fear Uncertainty and Doubt) learning.html#fud

see also general-purpose tools vs. single-purpose tools #general_purpose

general-purpose tools vs. single-purpose tools

general-purpose tools vs. single-purpose tools.

see also generalize vs. specialize dav_info.html#generalize_specialize

DAV: I am having a little cognitive dissonance here.

On one hand, I think it's really cool to have general-purpose tools. General-purpose PCs that can do lots of things never envisioned by their original designer, ... PDAs that can accept new and improved software ... multipurpose tools that do lots of stuff and still fit in your pocket (rather than having to carry around an entire tackle box of single-purpose tools) ...

On the other hand, single-purpose tools are also nice. ... telephones that ``just work'', unlike some PDA/cellphone combos that seem to crash regularly ... ... A knife that's just a knife ... ... The single purpose tools in Unix ``cut'', ``sort'', etc. ... email handling programs that just handle email, rather than displaying animated graphics and relaying virus programs to everyone else in your address book ... tools that are optimized to do one thing well, and when you have a collection of them and one does not work, all the rest of them are unaffected. (In other words, when you let someone else borrow one tool, or one tool wears out or breaks, or the batteries in one tool are drained, or you lose a tool). ... multipurpose tools often have one thing they do well, but all other secondary abilities are a compromise.

The importance of scalability/upgradeability: idea_space.html#level It's much easier to improve my collection of tools (not only in dollar cost, but in time spent learning how to use the new, improved collection) if I can simply add a simple new tool and learn how to use it, then (after I am comfortable with the new tool) discarding old tools it makes redundant. As opposed to getting a complicated new tool, spending much longer getting used to its new quirks, then trying to remember all the different functions of complicated old tools, worring that if I discard this old tool, even though most of its functions are obsoleted by the old tool, perhaps I might still need this old tool to do the 1 or 2 things that the new tool doesn't do as well -- or worse, doesn't do at all.

Occasionally one thing can be both ``simple'' and ``multifunctional'' -- graphic display hardware without complex arbitrary restrictions on what text/colors can go where ... ... paper for origami folding ... bookshelves that are smart enough *not* to make every shelf the same height, so that they can hold all different sizes of books or display objects d'art without wasting lots of space, ... dremel tools come close ... what else ?

simplicity

I think simplicity is such a important general design rule that it deserves a section all by itself.

related local pages:

synergetics

Stuff related to Buckminster Fuller (who apparently coined the word "synergy"), his World Game, and geometry. (tensegrity ?)

Related to

Other pages with long list of Buckminster Fuller links:

geometric shapes

sphere approximation

Often we want to approximate a sphere by a few points (the vertices of a polyhedron) or by a few pieces of paper (the gores of a globe).

The opposite problem is #sphere_packing.

See also #map_software for more map projections.

I've been thinking about building my own globe. Rather than approximating it with some sort of polyhedra made of flat polygons, I've been thinking about approximating it out of pieces of paper that are curved. (Unfortunately, paper can only curve in one direction ... which is what makes "map projection" so difficult -- the globe is not a developable surface ). Perhaps the intersecting cylinders illustrated by Paul Bourke would be much better than the standard thin globe gores.

sphere packing

filling space with a bunch of spheres, or filling some area with a collection of circles (possibly unequal-sized).

Cool Maps

[2004-01-24:DavidCary I moved this from http://rdrop.com/~cary/html/3d_design.html#maps to http://visual.wiki.taoriver.net/moin.cgi/EarthMap ; this is now an old archive]

contents:

See also:

maps with driving directions

weather maps

other online maps

(and a few of the most interesting paper maps ... should I split out paper maps into their own category ?) (also photographs of Earth, Luna, and other planets)

map_software

[FIXME: merge with other heading of same name]

map software

ready-to-run mapping software; and (non-image) raw map data. See #sphere_approximation for other "projections" and other ideas and algorithms that might be useful for mapping software

city information

finding interesting places on Earth

other map stuff

automobile design

flying car

skyhook design

skyhooks, space elevators, beanstalks, etc.

also Loftstrom loops.

Designing a skyhook has some similarities to #spacecraft_design , yet in other ways it's completely different than any artifact ever built before.

"space elevator" appears stationary (perhaps with minor vibrations) to someone standing on Earth (or whatever planet it is installed on). The "skyhook" appears to spin; typically one end comes down to (near) the planet surface, grabs the cargo, then pulls back out ... and releases it somewhere out in space. "rotavators, which are basically rotating shorter space elevators in lower orbits"

spacecraft design

serious design proposals. spaceships, Dyson spheres, Ringworld, space stations, ...

see also #skyhook

These are pretty long-term designs. For already-implemented and near-term designs, see Orbital Mechanics astro_links.html#orbit .

see also design in general.

see nanotech.html for a promising manufacturing technique.

[FIXME: comb out the skyhook info, make separate skyhook section] [FIXME: comb out satellite info, move to Orbital Mechanics]

see astro_links.html for some related devices that have already been put in space.

see lunh2o.html for info on the Lunar Prospector. satellite

trebuchet design

trebuchet design

siege engine enthusiasts

What exactly is the complicated multi-pulley-like contraption one sees attached to the top of the throwing arm on the trebuchet by Mr. Doucleff and the trebuchet that Mark uses while playing AOE ? Doucleff doesn't explain anything (why should he ? he has a trebuchet !) and the Radlinski trebuchet apparently doesn't have this feature. Does this optional feature really help improve range ? David Cary is almost tempted to build his own and find out.

Anyone who builds a trebuchet is just a teensy bit scary link_farm.html#people_that_scare_me .

TRIZ

Sounds like an interesting concept.

the "triangle function" t(x)

Some nifty theorems regarding what David Cary calls the "triangle function" t(x).

LATE BREAKING NEWS: I've just discovered that what I call t(), others call "sigmaI": "sigmaI which is like factorial but adds instead of multiplies".

Dr. Math uses T(n) notation for Triangular Numbers http://mathforum.org/dr.math/faq/faq.number.glossary.html#triangular

[FIXME: is there a better place to put my geometry ramblings ?]

tiling; packed 2D barcodes

[FIXME: tilings are generally thought of as 2D ... so move to the rest of my 2D stuff at machine_vision ? ... but DAV is interested in tiling 3D objects, in particular the sphere.]

Circle-like objects on square grid and on a hex grid

Often we want each module of a bar code to be "compact", so the foreground/background characteristics don't change much over the whole area (i.e., so we can use a single threshold per module even in the face of a linearly changing background gradient; or we can use a simple linear adjustment gradient even in the face of a non-linear background gradient). However, we also want to be able to tile (tesselate) these modules over a large area.

Also, we also want a QAM constellation to be "compact". If we spent the money to get a linear amplifier capable of getting a certain distance from the 0 point on the constellation, we might as well use *all* the points inside that constellation. [FIXME: cross link to ham radio]

Starting with a grid of pixels, I define a "circle-like object" to be a subset of pixels, such that given any pixel in the subset (or more particularly, the pixel in the subset furthest from the center point), every pixel in the grid that is the same or smaller distance from the center point is also in the subset.

(I see that Steve Waterman has extended this idea to 3D, producing Waterman polyhedra and applying some of them to polyhedral maps of Earth Waterman polyhedron: Cartography )

I know there are at least 3 kinds of circle-like objects: centered on corner of pixel, centered on middle of pixel, and centered on edge of pixel. I suspect there are other types as well, that are even less symmetric.

Some "circles" centered on center of pixel have a "sharp" single-pixel bump, which doesn't look very circular to me.

Here are all the circle-like objects of a square grid that are either centered on corner of pixel, or centered on middle of pixel, up to 81 pixels, sorted by area: (are there any that have outer pixels close to 12 sided polygon?) 

 Shape Pixels(area) ; pixels(perimeter)
 (distance from midpoint to center of outermost pixel)

   o  1 ; 1 tesselating

  oo
  oo 4 = 2^2 ; 4 tesselating
     (0.707 or less)

   o
  ooo 5; 4 tesselating
   o  (1 or less)

  ooo
  ooo 9 = 3^2 ; 8 tesselating
  ooo (1.41 or less)

   oo
  oooo
  oooo 12 = 2^2 + 4*2 ; 8 tesselating
   oo  (1.58 or less)

    o
   ooo
  ooooo 13 = 3^2 + 4 ; 8 tesselating
   ooo  (2 or less)
    o

  oooo
  oooo 16 = 4^2 ; 12 tesselating
  oooo 16QAM
  oooo (2.12 or less)

   ooo
  ooooo
  ooooo 21 = 3^2 + 4*2 ; 12 non-tesselating
  ooooo (2.24 or less) 
   ooo smallest non-tesselating circle-like object

     oo
    oooo
   oooooo
   oooooo 24: 4^2 + 4*2 ; 12 tesselating
    oooo  (2.55 or less)
     oo

  ooooo
  ooooo
  ooooo 25 = 5^2 ; 16 tesselating
  ooooo the largest circle-like object that is also a perfect square.
  ooooo (2.83 or less)

     o
   ooooo
   ooooo
  ooooooo 29 = 5^2 + 4*1 ; 16 non-tesselating
   ooooo  (3 or less)
   ooooo  the smallest that has any 1:2 slopes (also has *no* 1:1 slopes)
     o

    oooo
   oooooo
   oooooo
   oooooo 32: 4^2 + 4x4 ; 16 non-tesselating
   oooooo (the common 32-point constellation for 32QAM)
    oooo  (2.92 or less)

    ooo
   ooooo
  ooooooo
  ooooooo 37 = 5^2 + 4*3 ; 16 non-tesselating
  ooooooo  (3.16 or less)
   ooooo
    ooo

     oo
    oooo
   oooooo
  oooooooo
  oooooooo 40 = 4^2 + 4*4 + 4*2 ; 16 tesselating
   oooooo  (3.53 or less)
    oooo   Is this the largest circle-like object that is also tesselating?
     oo

     oo
   oooooo
   oooooo
  oooooooo
  oooooooo 44 = 6*6 + 4*2 ; 20 (or only 12, if you use convex hull)
   oooooo  the 2nd smallest that has any 1:2 slopes (also has *no* 1:1 slopes)
   oooooo  (3.54 or less -- notice the very little difference from above)
     oo    non-tesselating

   ooooo
  ooooooo
  ooooooo
  ooooooo  45 = 5^2 + 4*5 ; 20
  ooooooo  (3.61 or less)
  ooooooo
   ooooo

    oooo
   oooooo
  oooooooo
  oooooooo
  oooooooo 52 = 6*6 + 4*4 (has no 1:2 slopes) ; 20
  oooooooo (3.81 or less)
   oooooo
    oooo

      o
    ooooo
   ooooooo
   ooooooo
  ooooooooo  49 = 5^2 + 4*5 + 4*1 ; 20
   ooooooo   the third smallest with any 1:2 slopes
   ooooooo   (4 or less)
    ooooo
      o

     ooo
    ooooo
   ooooooo
  ooooooooo
  ooooooooo  57 = 5^2 + 4*5 + 4*3 ; 20
  ooooooooo  (4.12 or less)
   ooooooo
    ooooo
     ooo

   oooooo
  oooooooo
  oooooooo
  oooooooo 60 = 6^2 + 4*6 ; 24
  oooooooo (4.30 or less)
  oooooooo
  oooooooo
   oooooo

     ooo
   ooooooo
   ooooooo
  ooooooooo
  ooooooooo  61 = 7^2 + 4*3 ; 20
  ooooooooo  the 4th smallest with any 1:2 slopes
   ooooooo   (4.24 or less)
   ooooooo
     ooo

  64 = 8^2
  64QAM
  is unfortunately not a "circle-like object".
  (radius 6.36, but does not include several points closer than that).
  The following shows how to arrange more points into a smaller circle.

      oo
    oooooo
   oooooooo
   oooooooo
  oooooooooo 68 = 6^2 + 4*6 + 4*2 ; 24
  oooooooooo the 5th-smallest with 1:2 slopes
   oooooooo  the smallest with *both* 1:2 and 1:1 slopes.
   oooooooo  (4.53 or less)
    oooooo
      oo

    ooooo
   ooooooo
  ooooooooo
  ooooooooo
  ooooooooo  69 = 7^2 + 4*5 ; 24
  ooooooooo  (4.47 or less)
  ooooooooo
   ooooooo
    ooooo

     oooo
    oooooo
   oooooooo
  oooooooooo
  oooooooooo 76 = 6^2 + 4*6 + 4*4 ; 24
  oooooooooo
  oooooooooo  
   oooooooo  (4.74 or less)
    oooooo
     oooo

     oooo
   oooooooo
   oooooooo
  oooooooooo
  oooooooooo 80 = 8^2 + 4*4 ; 28
  oooooooooo the 6th-smallest with 1:2 slopes
  oooooooooo (has no 1:1 slopes)
   oooooooo  (4.95 or less)
   oooooooo
     oooo

       o
    ooooooo
   ooooooooo
   ooooooooo
   ooooooooo
  ooooooooooo 81 = 7^2 + 4*7 + 4*1 ; 24
   ooooooooo  (5 or less)
   ooooooooo  because of the 3:4:5 triangle,
   ooooooooo  the first to add more than 8 to the area.
    ooooooo   The smallest with a 1:3 slope.
       o

Circle-like objects on a hex grid: 

centered on one pixel:

    o  1

   o o
  o o o +6 = 7
   o o


     o
  o o o o
   o o o  +6 = 13
  o o o o
     o 


    o o o
   o o o o
  o o o o o +6 = 19
   o o o o
    o o o


     o o
  o o o o o
 o o o o o o
  o o o o o  +12 = 31
 o o o o o o
  o o o o o
     o o


     o o o o
    o o o o o
   o o o o o o
  o o o o o o o +6 = 37
   o o o o o o
    o o o o o
     o o o o

centered on corner:


     o
    o o 3 tesselating

     o
    o o
   o o o +3 = 6 tesselating

   o o o
  o o o o
   o o o  +6 = 12 tesselating
    o o

     o o
    o o o
   o o o o
  o o o o o +6 = 18 non-tesselating (?)
   o o o o

     o o
  o o o o o
   o o o o
  o o o o o +3 = 21
   o o o o
      o


    o o o o
   o o o o o
  o o o o o o
   o o o o o  +6 = 27 tesselating (?)
    o o o o
     o o o

       o
    o o o o
   o o o o o
  o o o o o o
   o o o o o  +3 = 30
  o o o o o o
     o o o


      o o o
     o o o o
    o o o o o
   o o o o o o
  o o o o o o o  +6 = 36
   o o o o o o
    o o o o o


      o o o
   o o o o o o
  o o o o o o o
   o o o o o o
  o o o o o o o  +6 = 42
   o o o o o o
    o o o o o
       o o


    o o o o o
   o o o o o o
  o o o o o o o
 o o o o o o o o
  o o o o o o o  +6 = 48
   o o o o o o  (is the largest tesselating circle-like object?)
    o o o o o
     o o o o

Bonus: triangular grid.

6 unbroken equilateral unit triangles can fit in a hexagon inscribed inside a circle. But what is the area (in fractions of a unit triangle) of the little leftover circular segments? The leftovers add up to a bit more than 1 and 1/4 unit triangles. A hexagon circumscribed around a unit circle has an area equal to the total area of 8 unit triangles.

(Similarly, 4 unit squares exactly fit in a square circumscribed around a unit circle. The square inscribed in a unit circle has a diagonal of length 2*r and has an area equal to 2 unit squares. The little leftovers add up to a bit more than 1 square.)

The area of a unit square is 4/sqrt(3) unit triangles. The area of a circle A is: A = πr^2 unit squares = 4*π*r^2 / sqrt(3) unit triangles. (this is related to the "area of circle of radius r" in terms of unit triangles, as mentioned above)

The continued fraction for 4*π/sqrt(3) = [7; 3, 1, 11, 3, 1, ...] =~= 7.255197...

That continued fraction gives us the approximations of approximate number of unit-strut triangles to approximate the total area of the unit-radius circle: 7, 22/3, 29/4, 341/47, ... 7, 7+1/3, 7+1/4, 7+12/47, ...

unsorted

general aircraft design

airplane design

paper_airplanes

Paper airplanes are one category of functional origami #origami . See also flying robots robot_links.html#flying_robots .

origami

see also #educational_toys and one of my favorite varieties of functional origami, #paper_airplanes . Alas, I haven't had any time recently to play with origami. I am more interested in pure geometry, and functional origami than with representational origami.

"modular origami"

tool closure

related to the bootstrap problem learning.html#bootstrap and robot replication computer_architecture.html#replication .

I've often wondered what set of mechanical tools it takes to get "closure" (in the software tools sense). I.e., say Ann has a bunch of tools in her garage, and (given a bunch of raw materials) she builds, say, a milling machine and some other tools to fill my (empty) garage. Then, with only raw materials going into my garage, I build another set of tools, and I give them and (a copy of) the plans I used to build them to Joe. If Joe -- using only (a) those tools, (b) those plans, and (c) some more raw materials -- can construct another milling machine and *all* the other tools in my garage, such that they are as good as or better than the tools in my garage, then this set of tools and plans has "closure". I'm not sure how raw I want to get with "raw materials"; maybe I'll accepts screws and bolts and sheet metal and car starter motors and a computer as "raw materials", and let other people worry about extracting iron from rocks. On the other hand, I want to be a little more sophisticated with "plans" and "tools", and try to make CNC mostly-automated tools.

I think it would be cool to load up a stack of sheet metal into a gizmo that would feed them one at a time (like a paper sheet feeder) and then when I came back the next day, I would have a pile of (possibly all unique) precisely cut sheet metal parts. -- DAV

John Bump http://www.frii.com/~katana/casting.html has already gotten pretty good at casting aluminum, and plans on building a entire milling machine and a airplane. I think this is a good start.

2NA (Tuna)

Nesting is the process of finding minimum waste arrangements of irregular shapes on regular stock sheets. The problem arises in a number of manufacturing applications, some of which are sheet metal fabrication, composite layup, water jet cutting, and tooling. ...

The 2NA (2-stage Nesting Algorithm) software is a set of C-language subroutines that construct approximate solutions to the 2D nesting problem. The 2NA code uses a two-stage heuristic algorithm ... Furthermore, 2NA has recently been expanded to allow "nesting in cutouts," i.e. the placement of parts inside other parts that have holes.

...

2-stage Nesting Algorithm (2NA) is Copyright © 2002 The Boeing Company.

-- http://www.boeing.com/phantom/2NA/ [FIXME: 2NA Polygon Simplification http://www.boeing.com/phantom/2NA/description/nesting1.html looks interesting ... ]

2003-05-29:DAV: started section on closure.

"Don Reinertsen"

submarine

"submarine": literally, under water.

Many various devices designed to be used under water. see also "swimming robots" robot_links.html#swim

Transatlantic cables

Alcatel Submarine Networks (ASN) http://www.alcatel.com.au/cable.htm owns one of the 5 modern submarine cable manufacturing facilities in the world. Their facility cost $120 million, and can manufacture over 6 000 Km of optical fibre cable per year. Supplied the 1996 JASURAUS cable between Australia and Asia. The built the cable for Cable & Wireless and MFS http://www.cwplc.com/press/1996/p96oct28.htm for the approximately £315 million London to New York cable (10 Gigabits/s) planned for 1998. [FIXME: bignums ?]

Transatlantic cable communications: "The Original Information Highway" http://www.rescol.ca/collections/canso/ lots of cool photographs and FAQs about the first successful transatlantic cable, (laid by the Niagra and the Agamemnon, starting in the center and ending at Newfoundland and Ireland, finished around 1858 August 5) earlier submarine cable attempts, and other related information. "...it would be a pity to kill the birds".

http://w2.siemens.de/infoshop/150_cd/business/u867-8.htm 1875: the "first direct transatlantic cable from Ireland to the U.S." is finished.

dynamic design

Some "things" don't work when they hold still, they require dynamic action.

counter-intuitive

A list of things that I've found that are counter-intuitive (at least to me). (Sometimes things that are counter-intuitive lead to counter-productive behavior).

unsorted

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