AAAS 2001, San Francisco Procedurally Defined Geometrical Sculptures Carlo H. Séquin University of California, Berkeley Brent Collins Gower, Missouri.

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.

CHSCHSUCBUCB

Computer-Aided Design I : Computer-Aided Design I : Integrated Circuits:Integrated Circuits: “RISC I” chip (1981)

CHSCHSUCBUCB

Computer-Aided Design II :Computer-Aided Design II :Mathematical ModelsMathematical Models

“Granny Knot” Lattice

Berkeley UniGrafix (1982)

CHSCHSUCBUCB

Computer-Aided Design III : BuildingsComputer-Aided Design III : Buildings Soda Hall, CS Dept. Berkeley (1992) Soda Hall, CS Dept. Berkeley (1992)

CHSCHSUCBUCB

Computer-Aided Design IV : Computer-Aided Design IV : Mechanical PartsMechanical Parts

Design (1985) Realization (FDM) (2000)

Octahedral Gear

CHSCHSUCBUCB

Computer-Aided Design V : Computer-Aided Design V : Abstract Sculpture (virtual)Abstract Sculpture (virtual)

(Since 1995)

CHSCHSUCBUCB

Computer-Aided Design V : Computer-Aided Design V : Abstract Sculpture (virtual)Abstract Sculpture (virtual)

Scherk-Collins Tower

CHSCHSUCBUCB

Computer-Aided Design V : Computer-Aided Design V : Abstract Sculpture (virtual)Abstract Sculpture (virtual)

Doubly-looped Scherk-Collins saddle-chain

CHSCHSUCBUCB

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 Brent Collins: Stacked SaddlesBrent Collins: Stacked 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 Closing the LoopClosing the Loop

straight

or

twisted

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 === VIDEO === === VIDEO ===

6 min

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 ““Hyperbolic Hexagon II” (wood)Hyperbolic Hexagon II” (wood)

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 Breckenridge CompetitionBreckenridge Competition

CHSCHSUCBUCB FDM Maquette of Solar ArchFDM Maquette of Solar Arch

2nd place

CHSCHSUCBUCB We Can Try Again … in L.A.We Can Try Again … in L.A.

CHSCHSUCBUCB … … or in Washington D.C.or in Washington D.C.

CHSCHSUCBUCB V-artV-art

GlassScherkTowerwithMonkeySaddles

Jane Yen

CHSCHSUCBUCB SFF Maquettes of Future SculpturesSFF Maquettes of Future Sculptures

Monkey-SaddleCinquefoil

CHSCHSUCBUCB Various “Scherk-Collins” SculpturesVarious “Scherk-Collins” Sculptures

CHSCHSUCBUCB Fused Deposition Modeling (FDM)Fused Deposition Modeling (FDM)

CHSCHSUCBUCB Looking into the FDM MachineLooking into the FDM Machine

CHSCHSUCBUCB Zooming into the FDM MachineZooming into the FDM Machine

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

CHSCHSUCBUCB

Minimal Trefoils -- cast and Minimal Trefoils -- cast and finished by Steve Reinmuthfinished by Steve Reinmuth

CHSCHSUCBUCB Brent Collins’ TrefoilBrent Collins’ Trefoil

CHSCHSUCBUCB Family of Symmetrical TrefoilsFamily of Symmetrical Trefoils

W=2

W=1

B=1 B=2 B=3 B=4

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 Brent Collins: Pax MundiBrent Collins: Pax Mundi

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 SLIDE-UI for “Pax Mundi” ShapesSLIDE-UI for “Pax Mundi” Shapes

CHSCHSUCBUCB ““Viae Globi” Family Viae Globi” Family (Roads on a Sphere)(Roads on a Sphere)

L2 L3 L4 L5

CHSCHSUCBUCB Via Globi 3 (Stone)Via Globi 3 (Stone)

Wilmin Martono

CHSCHSUCBUCB Via Globi 5 (Wood)Via Globi 5 (Wood)

Wilmin Martono

CHSCHSUCBUCB Via Globi 5 (Gold)Via Globi 5 (Gold)

Wilmin Martono

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.

CHSCHSUCBUCB Questions ?Questions ?

THE ENDTHE END

CHSCHSUCBUCB

========= SPARE ========= ========= SPARE ========= ==================================================

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

CHSCHSUCBUCB Figure-8 Knot with C-SectionFigure-8 Knot with C-Section

CHSCHSUCBUCB Conclusions (3)Conclusions (3)

What makes a CAD tool productive for this kind of work ?

Not just “virtual clay,”

partly procedural;

fewer parameters that need to be set.

Keep things aligned, joined;

guarantee symmetry, regularity,

watertight surfaces.

Interactivity is crucial !