CHSCHSUCBUCB E92 -- October 2002E92 -- October 2002

Art, Math, and SculptureConnecting Computers and Creativity

Carlo H. Séquin

EECS Computer Science Division

University of California, Berkeley

CHSCHSUCBUCB My Professional PathMy Professional Path

65-70: Basel: Physics – Experiment design

70-76: Bell Labs: CCD – Circuit, chip design

76-82: UCB: RISC – CPU architecture design

80-??: Graphics – Modeling & Rendering SW

82-90: VLSI CAD – CAD algorithm design

87-94: Soda Hall – Building design, VR

92-98: Architecture – ArchCAD tool design

95-??: Mech. Eng. – Develop SIF, CyberCut

96-??: Sculpture – Virtual Prototyping

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 CCD Camera, Bell Labs, 1972CCD Camera, Bell Labs, 1972

CHSCHSUCBUCB Integrated Circuits: “RISC I”, 1981Integrated Circuits: “RISC I”, 1981

CHSCHSUCBUCB Mathematical ModelsMathematical Models

“Granny Knot” Lattice

Berkeley UniGrafix (1982)

CHSCHSUCBUCB Buildings: Soda Hall, 1992Buildings: Soda Hall, 1992

CHSCHSUCBUCB Mechanical Parts: “Octa-Gear”Mechanical Parts: “Octa-Gear”

Design (1985) Realization (FDM) (2000)

Octahedral Gear

CHSCHSUCBUCB Geometrical Sculpture (virtual)Geometrical Sculpture (virtual)

(Since 1995)

CHSCHSUCBUCB Geometrical Sculpture (real)Geometrical Sculpture (real)

“Cohesion”2002

CHSCHSUCBUCB ““Whirled White Web”Whirled White Web”

Design for the 2003 International Snow Sculpture Championship Breckenridge, CO, Jan.28 – Feb.2

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...

Beautiful symmetries Graceful balance of 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”

Brent Collins’ Abstract Geometric Art:

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.

CHSCHSUCBUCB Sculpture Generator, GUI Sculpture Generator, GUI

CHSCHSUCBUCB The Basic ElementThe Basic Element

Scherk’s 2ndminimal surface

3-story tower,trimmed, thickened

180 degreesof twist added

CHSCHSUCBUCB Toroidal Warp into Collins RingToroidal Warp into Collins Ring

8-story tower warped into a ring 360º twist added

CHSCHSUCBUCB Edge TreatmentEdge Treatment

square, flat cut semi-circular bulging out

CHSCHSUCBUCB Embellishment of Basic ShapeEmbellishment of Basic Shape

color backgroundtexture

CHSCHSUCBUCB A Simple Scherk-Collins ToroidA Simple Scherk-Collins Toroid

branches = 2 storeys = 1 height = 5.00 flange = 1.00 thickness = 0.10 rim_bulge = 1.00 warp = 360.00 twist = 90 azimuth = 90 textr_tiles = 3 detail = 8

CHSCHSUCBUCB Also a Scherk-Collins ToroidAlso a Scherk-Collins Toroid

branches = 1 storeys = 5 height = 1.00 flange = 1.00 thickness = 0.04 rim_bulge = 1.01 warp = 360 twist = 900 azimuth = 90 textr_tiles = 1 detail = 20

CHSCHSUCBUCB A Scherk Tower A Scherk Tower (on its side)(on its side)

branches = 7 storeys = 3 height = 0.2 flange = 1.00 thickness = 0.04 rim_bulge = 0 warp = 0 twist = 0 azimuth = 0 textr_tiles = 2 detail = 6

CHSCHSUCBUCB 1-story Scherk Tower1-story Scherk Tower

branches = 5 storeys = 1 height = 1.35 flange = 1.00 thickness = 0.04 rim_bulge = 0 warp = 58.0 twist = 37.5 azimuth = 0 textr_tiles = 8 detail = 6

CHSCHSUCBUCB 180º Arch = Half a Scherk Toroid180º Arch = Half a Scherk Toroid

branches = 8 storeys = 1 height = 5 flange = 1.00 thickness = 0.06 rim_bulge = 1.25 warp = 180 twist = 0 azimuth = 0 textr_tiles = e detail = 12

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

CHSCHSUCBUCB How to Obtain a Real Sculpture ?How to Obtain a Real Sculpture ?

Prepare a set of cross-sectional blue prints

at equally spaced height intervals,

corresponding to the board thickness

that Brent is using for the construction.

CHSCHSUCBUCB Slices through “Minimal Trefoil”Slices through “Minimal Trefoil”

50% 10%23%30%

45% 5%20%27%

35% 2%15%25%

CHSCHSUCBUCB Profiled Slice through the SculptureProfiled Slice through the Sculpture

One thick slicethru “Heptoroid”from which Brent can cut boards and assemble a rough shape.

Traces represent: top and bottom,as well as cuts at 1/4, 1/2, 3/4of one board.

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 ““Heptoroid”Heptoroid”

Collaboration byBrent Collins &Carlo Séquin

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 Design: “Solar Arch”Sculpture Design: “Solar Arch”

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 Competition in Breckenridge, COCompetition in Breckenridge, CO

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

CHSCHSUCBUCB FDM Maquette of Solar ArchFDM Maquette of Solar Arch

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

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

CHSCHSUCBUCB Galapagos-6 in the MakingGalapagos-6 in the Making

CHSCHSUCBUCB Galapagos-6 (v6)Galapagos-6 (v6)

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 New PossibilitiesNew Possibilities

Developing Parameterized,

Procedurally Generated Sculpture Families

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 around the loop twice ...

… 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 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 Note:Note:

The computer becomesan amplifier / acceleratorfor the creative process.

CHSCHSUCBUCB

Inspiration: Inspiration:

Brent Collins’ Brent Collins’

“Pax Mundi”“Pax Mundi”

CHSCHSUCBUCB Keeping up with Brent ...Keeping up with Brent ...

A warped “Scherk tower” is not able to describe a shape like “Pax Mundi.”

Need a broader paradigm !

Use the SLIDE modeling environment(developed at U.C. Berkeley by J. Smith);it provides a nice combination of procedural modeling and interactivity.

CHSCHSUCBUCB SLIDESLIDE

SLIDE = Scene Language for Interactive Dynamic Environments

Developed as a modular rendering pipelinefor our introductory graphics course CS184.

Primary Author: Jordan Smith

Based on OpenGL and Tcl/tk.

Good combination of interactive 3D graphicsand parameterizable procedural constructs.

CHSCHSUCBUCB SLIDE Example: Klein BottleSLIDE Example: Klein Bottle

Final Project CS 184, Nerius Landys & Shad Roundy

CHSCHSUCBUCB SLIDE Example Bug’s LifeSLIDE Example Bug’s Life

Final Project CS 184, David Cheng and James Chow

CHSCHSUCBUCB SLIDE as a Design ToolSLIDE as a Design Tool

SLIDE has been enhanced to serve as a procedural modeling (CAD) tool.

Recently added:

Spline curves and surfaces

Morphing sweeps along such curves

3D warping module (Sederberg, Rockwood)

Many types of subdivision surfaces

These are key elements for “Sculpture Generator II”

CHSCHSUCBUCB Capturing the ParadigmCapturing the Paradigm

The first task

when trying to construct a generator

for a new family of sculptures

is to understand and define

its underlying logic.

CHSCHSUCBUCB Sculptures by Naum GaboSculptures by Naum Gabo

Pathway on a sphere:

Edge of surface is like seam of tennis ball;

==> 2-period Gabo curve.

CHSCHSUCBUCB 2-period Gabo curve2-period Gabo curve

Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used.

CHSCHSUCBUCB 4-period Gabo curve4-period Gabo curve

Same construction as for as for 2-period curve

CHSCHSUCBUCB ““Pax Mundi” RevisitedPax Mundi” Revisited

Can be seen as:

Amplitude modulated, 4-period Gabo curve

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 Extending the Paradigm (again)Extending the Paradigm (again)

Examples from Jane Yen’s Editor Program.This is a special purpose CAD program to draw nice loopy curves onto a sphere.

“Roads on a Sphere” or “Viae Globi”

Circle Splines on the SphereCircle Splines on the Sphere

CHSCHSUCBUCB ““Maloja” Maloja”

( FDM part )( FDM part )

A very winding Swiss mountain pass road in the upper Engadin.

CHSCHSUCBUCB ““Stelvio”Stelvio”

An even more convoluted alpine pass in Italy.

CHSCHSUCBUCB ““Altamont”Altamont”

Celebrating American multi-lane highways.

CHSCHSUCBUCB ““Lombard”Lombard”

A very famous crooked street in San Francisco

Note that I switched to a flat ribbon.

CHSCHSUCBUCB Who am I ? (1)Who am I ? (1)

Am I an Artist ?

What is “ART” these days ??

Cute ideas

Emotional outpours

The obsession to be novel

The goal to shock and offend

A medium for political statements …

CHSCHSUCBUCB Who am I ? (2)Who am I ? (2)

I am a Designer -- and an Engineer ! ( and proud of it. )

In design tasks you have:

Specified goals

Ways to evaluate a design

The drive to optimize your design

CHSCHSUCBUCB Sculpture EngineeringSculpture Engineering

The “Whirled White Web” is the result of such an activity. It had to be based on a shared design with B. Collins Complexity comparable to other successful designs or, preferably, slightly higher Must be executable in snow and ice Should look dramatic, intriguing, pleasing …

Lots of engineering work ahead: Design plan of attack, using CAD and graphics Prepare stencils to make implementation easier

CHSCHSUCBUCB ConclusionsConclusions

Computers are becoming important tools – even in the field of art.

Virtual Prototyping can save time and can tackle sculptures of a complexitythat manual techniques could not conquer.

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 Career Advice (1)Career Advice (1)

Find out what you really enjoy doing.

Find a job that pays you to do just that !

CHSCHSUCBUCB Career Advice (2)Career Advice (2)

Acquire solid technical foundations.

Stay flexible; keep learning new things.

Keep your eyes open for new opportunities.

CHSCHSUCBUCB Questions ?Questions ?

THE ENDTHE END