siggraph 2004, ozone turning a snowball inside out: mathematical visualization at the 12-foot scale...
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![Page 1: SIGGRAPH 2004, OZONE Turning a Snowball Inside Out: Mathematical Visualization at the 12-foot Scale Alex Kozlowski & Carlo H. Séquin: U.C. Berkeley Dan](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d6d5503460f94a4cd5c/html5/thumbnails/1.jpg)
SIGGRAPH 2004, OZONESIGGRAPH 2004, OZONE
Turning a Snowball Inside Out:
Mathematical Visualization at the 12-foot Scale
Alex Kozlowski & Carlo H. Séquin: U.C. Berkeley
Dan Schwalbe: ComSquared Systems, Eagan, MN
Stan Wagon: Macalester College, St. Paul, MN
John M. Sullivan, Tech. University, Berlin
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““Whirled White Web”Whirled White Web”
3D-Print
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Day 1: The “Monolith”Day 1: The “Monolith”
Cut away prisms …
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End of Day 2End of Day 2
The Torus
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Day 3, pm: Flanges, Holes Day 3, pm: Flanges, Holes
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Day 4: Geometry RefinementDay 4: Geometry Refinement
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““House Cleaning”House Cleaning”
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Memories of 2003Memories of 2003
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12:40 pm -- 4212:40 pm -- 42° F° F
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12:41 pm -- 4212:41 pm -- 42° F° F
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The WinnersThe Winners
1st: Canada – B.C., 2nd: USA – Minnesota, 3rd: USA – Breckenridge
“… sacred geometry … very intricate … very 21st century !”
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““WWW” Wins Silver MedalWWW” Wins Silver Medal
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What Are We Going To Do For 2004 ?What Are We Going To Do For 2004 ?
“Turning a Snowball Inside Out”
Making a Model of the Half-way Pointof the Sphere Eversion Process
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Sphere Eversion is Possible !Sphere Eversion is Possible !
First proven by Steve Smale around 1960from complex topological arguments.
But he could not say HOW it can be done … !
Surface may pass through itself,
but no ripping, puncturing, creasing allowed,e.g., this is not an acceptable solution:
PINCH
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Sphere Eversion ProcessSphere Eversion Process
A few years later Bernard Morin, a blind mathematician, figured out how to do it.
In his honor, the half-way point,where half each of the inside and outside of the sphere shell can be seen, is called the Morin surface.
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Sphere Eversion ProcessSphere Eversion Process
You need a rather contorted move to achieve the desired goal.
Bernard Morin figured out one such path.
Charles Pugh made models from chicken wire.
Nelson Max made a first computer simulation.
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Optimal Sphere EversionOptimal Sphere Eversion
In the 1990’s John Sullivan found the most efficient way (using the least surface bending)to accomplish this eversion,and made a beautiful movie of it.
From: John Sullivan: “The Optiverse”
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The Simplest Polyhedral ModelThe Simplest Polyhedral Model
Partial cardboard model based on cuboctahedron eversion by Apéry & Denner.
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Restructured Morin surface to fit block size: (10’ x 10’ x 12’)
Shape Adaption for Snow SculptureShape Adaption for Snow Sculpture
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Make Surface “Transparent”Make Surface “Transparent”
Realize surface as a grid.
Draw a mesh of smooth lines onto the surface …
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Gridded Models for TransparencyGridded Models for Transparency
3D-Print from Zcorp SLIDE virtual model
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““Turning a Snowball Inside-Out”Turning a Snowball Inside-Out”
Carlo H. Séquin, Alex Kozlowski, John Sullivan
Dan Schwalbe, Stan Wagon
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The Final ModelThe Final Model
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Morin’s Surface EversionMorin’s Surface Eversion
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The Half-way PointThe Half-way Point
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Finish the ProcessFinish the Process
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Computer ProjectionsComputer Projections
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Horizontal Slices and ProjectionsHorizontal Slices and Projections
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Practice Block (Stan Wagon)Practice Block (Stan Wagon)
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First NightFirst Night
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Working Out Plan BWorking Out Plan B
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Working on the GridWorking on the Grid
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Day 1Day 1Day 1Day 1
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Day 1Day 1
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Shovels, Drills, Pick-axes ...Shovels, Drills, Pick-axes ...
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End of End of Day 1Day 1
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Day 2Day 2
A Template for the “ear”A Template for the “ear”
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Day 2Day 2
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Day2Day2
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End of End of Day 2Day 2
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Day 3Day 3
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Defining the GridDefining the Grid
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Carving the GridCarving the Grid
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Cleaning Out the Cross-TunnelCleaning Out the Cross-Tunnel
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Day3Day3
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End of Day 3End of Day 3
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Day 4Day 4
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Day 4Day 4
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Day 5Day 5 End of End of Day 4Day 4
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Day 5Day 5
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Day 5Day 5
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Day 5Day 5
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““Paradigm Shift” (British Columbia)Paradigm Shift” (British Columbia)
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““Year of the Dragon” (USA – Tennessee)Year of the Dragon” (USA – Tennessee)
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““Winter Oasis” (Canada – Ontario)Winter Oasis” (Canada – Ontario)
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CeremonyCeremonyHonorable Mention:“Most Ambitious Design”
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Celebration Celebration
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Day 6Day 6
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Questions ?Questions ?
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““Knot Divided”Knot Divided”
Accepted, August 5, 2004 for competition in January 2005