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BID 02/02/02

Parameterized Sculpture Design

Carlo H. Séquin University of California, Berkeley

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Designs I worked on:

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Sculpture Design

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How can we use the visualization power offered by computer graphics and by computer-controlled rapid prototyping for the design of geometrical sculptures?

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“Hyperbolic Hexagon” by B. Collins

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6 saddles in a ring

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6 holes passing through symmetry plane at ±45º

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= “wound up” 6-story Scherk tower

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What would happen,

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if we added more stories ?

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or introduced a twist before closing the ring ?

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“Hyperbolic Hexagon II” (wood) Brent Collins

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Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles (monkey saddle)

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Closing the Loop straight or twisted

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Sculpture Generator, GUI

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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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A 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

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Also 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

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A Scherk Tower (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

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180º 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

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V-art Virtual Glass Scherk Tower with Monkey Saddles (Radiance 40 hours) Jane Yen

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Séquin’s “Minimal Saddle Trefoil”

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Stereo lithography master

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Minimal Trefoils -- cast and finished by Steve Reinmuth

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Slices through “Minimal Trefoil” 50% 30% 23% 10% 45% 27% 20% 5% 35% 25% 15% 2%

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Emergence of the “Heptoroid” (1)

Assembly of the precut boards

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Another Joint Sculpture

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“Heptoroid” carved by Brent Collins

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Advantages of CAD of Sculptures

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Exploration of a larger domain

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Instant visualization of results

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Eliminate need for prototyping

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Create virtual reality pictures

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Making more complex structures

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Better optimization of chosen form

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More precise implementation

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Rapid prototyping of maquettes

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Rapid Prototyping by FDM

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Various “Scherk-Collins” Sculptures

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Parameterized Sculpture Families Within the domain of a sculpture generator, vary selectively 1 to 3 parameters, and create the resulting instances:

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Scherk Collins toroids

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“Trefoil Family”

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Pax Mundy

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“Viae Globi”

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Family of Symmetrical Trefoils

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

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Close-up of Some Trefoils

B=1 B=2 B=3 Varying the number of branches B (the order of the saddles).

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Higher-order Trefoils (4th order saddles) W=1 (Warp) W=2

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9-story Intertwined Double-Toroid Bronze investment casting from wax original made on 3D Systems’ “Thermojet”

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Inspiration: Brent Collins’ “Pax Mundi”

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Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis ball;

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2-period Gabo curve.

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2-period Gabo curve

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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

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Can be seen as: Amplitude modulated, 4-period Gabo curve

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SLIDE UI for “Pax Mundi” Shapes

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Parameterized Sculpture Design 3 Phases:

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Discover and distill out the key paradigm

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Define the most appropriate set of parameters

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Develop generalizations of the paradigm

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The Program is the Design, is the Artwork!

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Via Globi 3 (Stone) Wilmin Martono

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“Maloja” -- FDM part

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

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“Stelvio”

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An even more convoluted alpine pass in Italy.

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“Altamont”

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Celebrating American multi-lane highways.

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“Lombard”

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A very famous crooked street in San Francisco

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Conclusions Design as an aesthetic optimization in the purely geometrical realm.

The computer can also be an amplifier / accelerator for the creative process.

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Questions ?

THE END

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EXTRAS

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Another Inspiration by B. Collins

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Collin’s Conceptual Design

SWEEP CURVE (FOR DOUBLE CYLINDER) IS COMPOSED OF 4 IDENTICAL SEGMENTS, FOLLOWS THE SURFACE OF A SPHERE.

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Reconstruction / Analysis (v1)

FROM THE FDM MACHINE AWKWARD ALIGNMENT

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Further Explorations (v2: add twist)

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A More Complex Design (v3)

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Fine-tuned Final(?) Version (v5)

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Galapagos-6 (v6)

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Circle Splines on the Sphere Examples from Jane Yen’s Editor Program