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BID 02/02/02. Parameterized Sculpture Design Carlo H. Séquin University of California, Berkeley. Designs I worked on:. Sculpture Design.
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BID 02/02/02 ParameterizedSculpture Design Carlo H. Séquin University of California, Berkeley
Sculpture Design • How can we use the visualization power offered by computer graphics and by computer-controlled rapid prototyping for the design of geometrical sculptures?
“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 ?
“Hyperbolic Hexagon II” (wood) Brent Collins
Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles(monkey saddle)
Closing the Loop straight or twisted
Brent Collins’ Prototyping Process Mockup for the "Saddle Trefoil" Armature for the "Hyperbolic Heptagon" Time-consuming ! (1-3 weeks)
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
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
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
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
V-art VirtualGlassScherkTowerwith MonkeySaddles(Radiance 40 hours) Jane Yen
Séquin’s “Minimal Saddle Trefoil” • Stereo-lithography master
Slices through “Minimal Trefoil” 50% 30% 23% 10% 45% 27% 20% 5% 35% 25% 15% 2%
Emergence of the “Heptoroid” (1) Assembly of the precut boards
Another Joint Sculpture • “Heptoroid”carved byBrent Collins
Advantages 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
Parameterized 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”
Family of Symmetrical Trefoils W=2 W=1 B=1 B=2 B=3 B=4
Close-up of Some Trefoils B=1 B=2 B=3 Varying the number of branches B (the order of the saddles).
Higher-order Trefoils (4th order saddles) W=1 (Warp) W=2
9-story Intertwined Double-Toroid Bronze investment casting fromwax original made on3D Systems’“Thermojet”
Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis ball; 2-period Gabo curve.
2-period Gabo curve • Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used.
4-period Gabo curve Same construction as for as for 2-period curve
“Pax Mundi” Revisited • Can be seen as:Amplitude modulated, 4-period Gabo curve
Parameterized 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!
Via Globi 3 (Stone) Wilmin Martono
“Maloja” -- FDM part • A rather winding Swiss mountain pass road in the upper Engadin.
“Stelvio” • An even more convoluted alpine pass in Italy.
“Altamont” • Celebrating American multi-lane highways.
“Lombard” • A very famous crooked street in San Francisco
Conclusions Design as an aesthetic optimizationin the purely geometrical realm. The computer can also bean amplifier / acceleratorfor the creative process.
Questions ? THE END
Collin’s Conceptual Design SWEEP CURVE (FOR DOUBLE CYLINDER) IS COMPOSED OF 4 IDENTICAL SEGMENTS, FOLLOWS THE SURFACE OF A SPHERE.
Reconstruction / Analysis (v1) FROM THE FDM MACHINE AWKWARD ALIGNMENT
Circle Splines on the Sphere Examples from Jane Yen’s Editor Program