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CHSUCB BID 02/02/02BID 02/02/02
ParameterizedSculpture Design
Carlo H. Séquin
University of California, Berkeley
CHSUCB Designs I worked on:Designs I worked on:
CHSUCB Sculpture DesignSculpture Design
How can we use the visualization power offered by computer graphics and by computer-controlled rapid prototyping for the design of geometrical sculptures?
CHSUCB ““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 ?
CHSUCB ““Hyperbolic Hexagon II” (wood)Hyperbolic Hexagon II” (wood)
Brent Collins
CHSUCB Scherk’s 2nd Minimal SurfaceScherk’s 2nd Minimal Surface
Normal“biped”saddles
Generalization to higher-order saddles(monkey saddle)
CHSUCB Closing the LoopClosing the Loop
straight
or
twisted
CHSUCB Sculpture Generator, GUI Sculpture Generator, GUI
CHSUCB Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process
Armature for the "Hyperbolic Heptagon"
Mockup for the "Saddle Trefoil"
Time-consuming ! (1-3 weeks)
CHSUCB A Simple Scherk-Collins ToroidA Simple Scherk-Collins Toroid
Parameters:(genome)
branches = 2 stories = 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
CHSUCB Also a Scherk-Collins ToroidAlso a Scherk-Collins Toroid
branches = 1 stories = 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
CHSUCB A Scherk Tower A Scherk Tower (on its side)(on its side)
branches = 7 stories = 3 height = 0.2 flange = 1.00 thickness = 0.04 rim_bulge = 0 warp = 0 twist = 0 azimuth = 0 textr_tiles = 2 detail = 6
CHSUCB 180º Arch = Half a Scherk Toroid180º Arch = Half a Scherk Toroid
branches = 8 stories = 1 height = 5 flange = 1.00 thickness = 0.06 rim_bulge = 1.25 warp = 180 twist = 0 azimuth = 0 textr_tiles = e detail = 12
CHSUCB V-artV-art
VirtualGlassScherkTowerwithMonkeySaddles
(Radiance 40 hours)
Jane Yen
CHSUCB Séquin’s “Minimal Saddle Trefoil”Séquin’s “Minimal Saddle Trefoil”
Stereo-lithography master
CHSUCB
Minimal Trefoils -- cast and Minimal Trefoils -- cast and finished by Steve Reinmuthfinished by Steve Reinmuth
CHSUCB Slices through “Minimal Trefoil”Slices through “Minimal Trefoil”
50% 10%23%30%
45% 5%20%27%
35% 2%15%25%
CHSUCB Emergence of the “Heptoroid” (1)Emergence of the “Heptoroid” (1)
Assembly of the precut boards
CHSUCB Another Joint SculptureAnother Joint Sculpture
“Heptoroid”carved by Brent Collins
CHSUCB 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
CHSUCB Rapid Prototyping by FDMRapid Prototyping by FDM
CHSUCB Various “Scherk-Collins” SculpturesVarious “Scherk-Collins” Sculptures
CHSUCB Parameterized Sculpture FamiliesParameterized Sculpture Families
Within the domain of a sculpture generator, vary selectively 1 to 3 parameters, and create the resulting instances:
Scherk Collins toroids “Trefoil Family”
Pax Mundy “Viae Globi”
CHSUCB Family of Symmetrical TrefoilsFamily of Symmetrical Trefoils
W=2
W=1
B=1 B=2 B=3 B=4
CHSUCB Close-up of Some TrefoilsClose-up of Some Trefoils
B=1 B=2 B=3
Varying the number of branches B (the order of the saddles).
CHSUCB Higher-order Trefoils Higher-order Trefoils (4th order saddles)(4th order saddles)
W=1 (Warp) W=2
CHSUCB 9-story Intertwined Double-Toroid9-story Intertwined Double-Toroid
Bronzeinvestment casting from wax original made on 3D Systems’“Thermojet”
CHSUCB
Inspiration: Inspiration:
Brent Collins’ Brent Collins’
“Pax Mundi”“Pax Mundi”
CHSUCB Sculptures by Naum GaboSculptures by Naum Gabo
Pathway on a sphere:
Edge of surface is like seam of tennis ball;
2-period Gabo curve.
CHSUCB 2-period Gabo curve2-period Gabo curve
Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used.
CHSUCB 4-period Gabo curve4-period Gabo curve
Same construction as for as for 2-period curve
CHSUCB ““Pax Mundi” RevisitedPax Mundi” Revisited
Can be seen as:
Amplitude modulated, 4-period Gabo curve
CHSUCB SLIDE-UI for “Pax Mundi” ShapesSLIDE-UI for “Pax Mundi” Shapes
CHSUCB Parameterized Sculpture DesignParameterized Sculpture Design
3 Phases: Discover and distill out the key paradigm
Define the most appropriate set of parameters
Develop generalizations of the paradigm
The Program is the Design, is the Artwork!
CHSUCB Via Globi 3 (Stone)Via Globi 3 (Stone)
Wilmin Martono
CHSUCB ““Maloja” -- FDM partMaloja” -- FDM part
A rather winding Swiss mountain pass road in the upper Engadin.
CHSUCB ““Stelvio”Stelvio”
An even more convoluted alpine pass in Italy.
CHSUCB ““Altamont”Altamont”
Celebrating American multi-lane highways.
CHSUCB ““Lombard”Lombard”
A very famous crooked street in San Francisco
CHSUCB ConclusionsConclusions
Design as an aesthetic optimizationin the purely geometrical realm.
The computer can also bean amplifier / acceleratorfor the creative process.
CHSUCB Questions ?Questions ?
THE ENDTHE END
CHSUCB EXTRASEXTRAS
CHSUCB Another Inspiration by B. CollinsAnother Inspiration by B. Collins
CHSUCB Collin’s Conceptual DesignCollin’s Conceptual Design
SWEEP CURVE (FOR DOUBLE CYLINDER)IS COMPOSED OF 4 IDENTICAL SEGMENTS,FOLLOWS THE SURFACE OF A SPHERE.
CHSUCB Reconstruction / Analysis (v1)Reconstruction / Analysis (v1)
AWKWARD ALIGNMENT
FROM THE FDM MACHINE
CHSUCB Further Explorations (v2: add twist)Further Explorations (v2: add twist)
CHSUCB A More Complex Design (v3)A More Complex Design (v3)
CHSUCB Fine-tuned Final(?) Version (v5)Fine-tuned Final(?) Version (v5)
CHSUCB Galapagos-6 (v6)Galapagos-6 (v6)
CHSUCB Circle Splines on the SphereCircle Splines on the Sphere
Examples from Jane Yen’s Editor Program
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