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E92 -- October 2002
Art, Math, and Sculpture
Connecting Computers and Creativity
Carlo H. Séquin
EECS Computer Science Division
University of California, Berkeley
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My 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
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My Professional Focus
Computer-Aided Design
 Design
useful and beautiful objects
with the help of computers.
 Develop
(interactive) computer programs
to make these tasks easier.
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CCD Camera, Bell Labs, 1972
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Integrated Circuits: “RISC I”, 1981
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Mathematical Models
“Granny Knot”
Lattice
Berkeley
UniGrafix
(1982)
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Buildings: Soda Hall, 1992
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Mechanical Parts: “Octa-Gear”
Octahedral Gear
Design (1985)
Realization (FDM) (2000)
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Geometrical Sculpture (virtual)
(Since 1995)
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Geometrical Sculpture (real)
“Cohesion”
2002
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“Whirled White Web”
 Design
for the 2003 International
Snow Sculpture Championship
Breckenridge, CO, Jan.28 – Feb.2
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Roots of My Passion for Sculpture
My love for geometry and abstract sculpture
emerged long long before I learned to play
with computers.
Thanks to: Alexander Calder, Naum Gabo,
Max Bill, M.C. Escher, Frank Smullin, ...
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Leonardo -- Special Issue
On Knot-Spanning Surfaces: An
Illustrated Essay on Topological Art
With an Artist’s Statement by Brent Collins
George K. Francis
with Brent Collins
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Brent Collins: Early Sculptures
All photos by Phillip Geller
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My Fascination with...
Brent Collins’ Abstract Geometric Art:

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”
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Brent Collins: Stacked Saddles
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Scherk’s 2nd Minimal Surface
Normal
“biped”
saddles
Generalization to
higher-order saddles
(monkey saddle)
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“Hyperbolic 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 ?
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Closing the Loop
straight
or
twisted
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Collins - Séquin Collaboration
 Discuss
ideas on the phone
 Exchange
 Vary
sketches
the topological parameters
 But
how do you know whether it is
beautiful ? Need visual feedback.
 Making
models from paper strips
is not good enough.
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Brent Collins’ Prototyping Process
Armature for the
"Hyperbolic Heptagon"
Mockup for the
"Saddle Trefoil"
Time-consuming ! (1-3 weeks)
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Collins’ 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 marks
and 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 !
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Collins’ Fabrication Process
Lamination process to make
an overall shape that within
contains the final sculpture.
Example: “Vox Solis”
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“Sculpture Generator I”
Prototyping & Visualization tool for
Scherk-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.
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Sculpture Generator, GUI
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The Basic Element
Scherk’s 2nd
minimal surface
3-story tower,
trimmed, thickened
180 degrees
of twist added
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Toroidal Warp into Collins Ring
8-story tower
warped into a ring
360º twist added
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Edge Treatment
square, flat cut
semi-circular
bulging out
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Embellishment of Basic Shape
color
texture
background
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A 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
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Also 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
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A Scherk Tower
(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
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1-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
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180º 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
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“Hyperbolic Hexagon II” (wood)
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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.
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Slices through “Minimal Trefoil”
50%
30%
23%
10%
45%
27%
20%
5%
35%
25%
15%
2%
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Profiled Slice through the Sculpture

One thick slice
thru “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, 3/4
of one board.
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Heptoroid
( from Sculpture Generator I )
Cross-eye stereo pair
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Emergence of the “Heptoroid” (1)
Assembly of the precut boards
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Emergence of the “Heptoroid” (2)
Forming a continuous smooth edge
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Emergence of the “Heptoroid” (3)
Smoothing the whole surface
“Heptoroid”
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
Collaboration by
Brent Collins &
Carlo Séquin
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Advantages of CAD of Sculptures
 Exploration
 Instant
visualization of results
 Eliminate
 Create
 More
need for prototyping
virtual reality pictures
 Making
 Better
of a larger domain
more complex structures
optimization of chosen form
precise implementation
 Rapid
prototyping of maquettes
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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
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Competition in Breckenridge, CO
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We Can Try Again … in L.A.
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FDM Maquette of Solar Arch
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Various “Scherk-Collins” Sculptures
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Fused Deposition Modeling (FDM)
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Galapagos-6 in the Making
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Galapagos-6 (v6)
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Séquin’s “Minimal Saddle Trefoil”
 Stereo-
lithography
master
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Séquin’s “Minimal Saddle Trefoil”
 bronze
cast,
gold
plated
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Minimal Trefoils -- cast and
finished by Steve Reinmuth
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Brent Collins’ Trefoil
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New Possibilities
Developing
Parameterized,
Procedurally Generated
Sculpture Families
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Family of Symmetrical Trefoils
W=2
W=1
B=1
B=2
B=3
B=4
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Higher-order Trefoils
W=1
(4th order saddles)
W=2
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Exploring New Ideas
 Going
around the loop twice ...
… resulting in an interwoven structure.
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9-story Intertwined Double Toroid
Bronze
investment
casting
from
wax original
made on
3D Systems’
“Thermojet”
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Stepwise 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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Note:
The computer becomes
an amplifier / accelerator
for the creative process.
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Inspiration:
Brent Collins’
“Pax Mundi”
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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.
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SLIDE
SLIDE = Scene Language for
Interactive Dynamic Environments
Developed as a modular rendering pipeline
for our introductory graphics course CS184.
Primary Author: Jordan Smith

Based on OpenGL and Tcl/tk.

Good combination of interactive 3D graphics
and parameterizable procedural constructs.
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SLIDE Example: Klein Bottle
Final Project CS 184, Nerius Landys & Shad Roundy
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SLIDE Example Bug’s Life
Final Project CS 184, David Cheng and James Chow
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SLIDE 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”
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Capturing 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.
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Sculptures by Naum Gabo
Pathway on a sphere:
Edge of surface is like seam of tennis ball;
==> 2-period Gabo curve.
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2-period Gabo curve
 Approximation
with quartic B-spline
with 8 control points per period,
but only 3 DOF are used.
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4-period Gabo curve
Same construction as for as for 2-period curve
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“Pax Mundi” Revisited

Can be seen as:
Amplitude modulated,
4-period Gabo curve
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SLIDE-UI for “Pax Mundi” Shapes
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“Viae Globi” Family
L2
L3
L4
(Roads on a Sphere)
L5
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Via Globi 3 (Stone)
Wilmin Martono
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Via Globi 5 (Wood)
Wilmin Martono
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Extending the Paradigm (again)
Circle Splines on the Sphere
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”
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“Maloja”
( FDM part )
A
very winding
Swiss mountain
pass road in the
upper Engadin.
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“Stelvio”
 An
even more
convoluted
alpine pass
in Italy.
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“Altamont”
 Celebrating
American
multi-lane
highways.
“Lombard”
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A
very famous
crooked street
in San Francisco

Note that I switched
to a flat ribbon.
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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 …
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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
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Sculpture 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
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Conclusions
 Computers
are becoming important tools
– even in the field of art.
 Virtual
Prototyping can save time and
can tackle sculptures of a complexity
that 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.
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Career Advice (1)
 Find
out what you really enjoy doing.
 Find
a job that pays you to do just that !
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Career Advice (2)
 Acquire
 Stay
solid technical foundations.
flexible; keep learning new things.
 Keep
your eyes open for new opportunities.
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Questions ?
THE END