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