CHSCHSUCBUCB AAAS 2001, San FranciscoAAAS 2001, San Francisco
Procedurally Defined Geometrical SculpturesProcedurally Defined Geometrical Sculptures
Carlo H. Séquin
University of California, Berkeley
Brent Collins
Gower, Missouri
CHSCHSUCBUCB My Professional FocusMy Professional Focus
Computer-Aided Design
Design useful and beautiful objectswith the help of computers.
Develop (interactive) computer programsto make these tasks easier.
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Computer-Aided Design I : Computer-Aided Design I : Integrated Circuits:Integrated Circuits: “RISC I” chip (1981)
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Computer-Aided Design II :Computer-Aided Design II :Mathematical ModelsMathematical Models
“Granny Knot” Lattice
Berkeley UniGrafix (1982)
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Computer-Aided Design III : BuildingsComputer-Aided Design III : Buildings Soda Hall, CS Dept. Berkeley (1992) Soda Hall, CS Dept. Berkeley (1992)
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Computer-Aided Design IV : Computer-Aided Design IV : Mechanical PartsMechanical Parts
Design (1985) Realization (FDM) (2000)
Octahedral Gear
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Computer-Aided Design V : Computer-Aided Design V : Abstract Sculpture (virtual)Abstract Sculpture (virtual)
(Since 1995)
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Computer-Aided Design V : Computer-Aided Design V : Abstract Sculpture (virtual)Abstract Sculpture (virtual)
Scherk-Collins Tower
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Computer-Aided Design V : Computer-Aided Design V : Abstract Sculpture (virtual)Abstract Sculpture (virtual)
Doubly-looped Scherk-Collins saddle-chain
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Computer-Aided Design V : Computer-Aided Design V : Abstract Sculpture (real)Abstract Sculpture (real)
“Bonds of Friendship”(2001)
Fabricated by: Fused Deposition Modeling
Currently in S.F.:at Gallery 650,Delancy/Brannan
CHSCHSUCBUCB Roots of My Passion for SculptureRoots of My Passion for Sculpture
My love for geometry and abstract sculptureemerged long long before I learned to play with computers.
Thanks to: Alexander Calder, Naum Gabo,Max Bill, M.C. Escher, Frank Smullin, ...
CHSCHSUCBUCB Leonardo -- Special IssueLeonardo -- Special Issue
On Knot-Spanning Surfaces: An Illustrated Essay on Topological ArtWith an Artist’s Statement by Brent Collins
George K. Francis with Brent Collins
CHSCHSUCBUCB Brent Collins: Early SculpturesBrent Collins: Early Sculptures
All photos by Phillip Geller
CHSCHSUCBUCB My Fascination with...My Fascination with...
Brent Collins’ Abstract Geometric Art Beautiful symmetries Graceful balance of the saddle surfaces Superb craftsmanship Intriguing run of the edges What type of knot is formed ? Mystery: one-sided or two-sided ?
==> Focus on “Chains of Saddles”
CHSCHSUCBUCB Scherk’s 2nd Minimal SurfaceScherk’s 2nd Minimal Surface
Normal“biped”saddles
Generalization to higher-order saddles(monkey saddle)
CHSCHSUCBUCB ““Hyperbolic Hexagon” by B. CollinsHyperbolic Hexagon” by B. Collins
6 saddles in a ring
6 holes passing through symmetry plane at ±45º
“wound up” 6-story Scherk tower
What would happen, if we added more stories ?
or introduced a twist before closing the ring ?
CHSCHSUCBUCB Collins - Séquin CollaborationCollins - Séquin Collaboration
Discuss ideas on the phone
Exchange sketches
Vary the topological parameters
But how do you know whether it is beautiful ? Need visual feedback.
Making models from paper strips is not good enough.
CHSCHSUCBUCB Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process
Armature for the "Hyperbolic Heptagon"
Mockup for the "Saddle Trefoil"
Time-consuming ! (1-3 weeks)
CHSCHSUCBUCB Collins’ Fabrication ProcessCollins’ Fabrication Process
Building the final sculpture (2-3 months):
Take measurements from mock-up model,transfer parallel contours to 1” boards.
Roughly precut boards, leaving registration marksand contiguous pillars for gluing boards together.
Stack and glue together precut boards,remove auxiliary struts.
Fine-tune overall shape,sand and polish the surface.
A big investment of effort !
CHSCHSUCBUCB Collins’ Fabrication ProcessCollins’ Fabrication Process
Lamination process to make an overall shape that withincontains the final sculpture.
Example: “Vox Solis”
CHSCHSUCBUCB ““Sculpture Generator I”Sculpture Generator I”
Prototyping & Visualization tool forScherk-Collins Saddle-Chains.
Slider control for this one shape-family,
Control of about 12 parameters.
Main goal: Speed for interactive editing.
Geometry part is about 5,000 lines of C;
10,000 lines for display & user interface.
==> VIDEO
CHSCHSUCBUCB Base Geometry: One Scherk StoryBase Geometry: One Scherk Story
Hyperbolic Slices ==> Triangle Strips
precomputed -- then warped into toroid
CHSCHSUCBUCB Slices through the SculptureSlices through the Sculpture
One thick slicethru “Heptoroid”from which Brent can cut boards and assemble a rough shape.
Shown are top andbottom as well ascuts at 1/4, 1/2, 3/4of one board.
CHSCHSUCBUCB Our First “Joint” SculptureOur First “Joint” Sculpture
Six monkey saddles in a ring with no twist
(like Hyperbolic Hexagon)
azimuth = –30°, flange 1.5
(aesthetics)
size, thickness (fabrication consideration)
CHSCHSUCBUCB Heptoroid Heptoroid ( from Sculpture Generator I )( from Sculpture Generator I )
Cross-eye stereo pair
CHSCHSUCBUCB Emergence of the “Heptoroid” (1)Emergence of the “Heptoroid” (1)
Assembly of the precut boards
CHSCHSUCBUCB Emergence of the “Heptoroid” (2)Emergence of the “Heptoroid” (2)
Forming a continuous smooth edge
CHSCHSUCBUCB Emergence of the “Heptoroid” (3)Emergence of the “Heptoroid” (3)
Smoothing the whole surface
CHSCHSUCBUCB Advantages of CAD of SculpturesAdvantages of CAD of Sculptures
Exploration of a larger domain
Instant visualization of results
Eliminate need for prototyping
Create virtual reality pictures
Making more complex structures
Better optimization of chosen form
More precise implementation
Rapid prototyping of maquettes
CHSCHSUCBUCB Sculpture DesignSculpture Design
branches = 4 storeys = 11 height = 1.55 flange = 1.00 thickness = 0.06 rim_bulge = 1.00 warp = 330.00 twist = 247.50 azimuth = 56.25 mesh_tiles = 0 textr_tiles = 1 detail = 8 bounding box: xmax= 6.01, ymax= 1.14, zmax= 5.55, xmin= -7.93, ymin= -1.14, zmin= -8.41
CHSCHSUCBUCB SFF Maquettes of Future SculpturesSFF Maquettes of Future Sculptures
Monkey-SaddleCinquefoil
CHSCHSUCBUCB Séquin’s “Minimal Saddle Trefoil”Séquin’s “Minimal Saddle Trefoil”
Stereo-lithography master
CHSCHSUCBUCB Séquin’s “Minimal Saddle Trefoil”Séquin’s “Minimal Saddle Trefoil”
bronze cast, gold plated
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Minimal Trefoils -- cast and Minimal Trefoils -- cast and finished by Steve Reinmuthfinished by Steve Reinmuth
CHSCHSUCBUCB Higher-order Trefoils Higher-order Trefoils (4th order saddles)(4th order saddles)
W=1 W=2
CHSCHSUCBUCB Exploring New IdeasExploring New Ideas
Going twice around the loop ...
Resulting in an interwoven structure.
CHSCHSUCBUCB 9-story Intertwined Double Toroid9-story Intertwined Double Toroid
Bronzeinvestment casting from wax original made on 3D Systems’“Thermojet”
CHSCHSUCBUCB Keeping up with Brent ...Keeping up with Brent ...
A bent “Scherk tower” is not able to describe a shape like “Pax Mundi.”
Need a broader paradigm !
Use SLIDE modeling environment,it provides a nice combination of procedural modeling and interactivity.
CHSCHSUCBUCB ““Viae Globi” Family Viae Globi” Family (Roads on a Sphere)(Roads on a Sphere)
L2 L3 L4 L5
CHSCHSUCBUCB Conclusions (1)Conclusions (1)
Interactive computer graphics is a novel (to artists) medium that can play an important role -- even for traditional artists.
Virtual Prototyping can save time and can tackle sculptures of a complexitythat manual techniques could not conquer.
CHSCHSUCBUCB Conclusions (2)Conclusions (2)
The computer is not only a great visualization and prototyping tool,
It also is a generator for new ideas and
an amplifier for an artist’s inspiration.
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CHSCHSUCBUCB Stepwise Expansion of HorizonStepwise Expansion of Horizon
Playing with many different shapes and
experimenting at the limit of the domain of the sculpture generator,
stimulates new ideas for alternative shapes and generating paradigms.
Swiss Mountains
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