CHSUCB CS285CS285

Sculpture Generator I

Carlo H. Séquin

University of California, Berkeley

In Collaboration with

Brent Collins

Gower, Missouri

CHSUCB Brent CollinsBrent Collins

“Genesis” – Brent Collins at BRIDGES 2000

CHSUCB Leonardo -- Special IssueLeonardo -- Special Issue

On Knot-Spanning Surfaces: An Illustrated Essay on Topological ArtWith an Artist’s Statement by Brent Collins

George K. Francis with Brent Collins

CHSUCB Brent Collins: Early SculpturesBrent Collins: Early Sculptures

All photos by Phillip Geller

CHSUCB Collins’ Abstract Geometric ArtCollins’ Abstract Geometric Art

Beautiful symmetries Graceful balance of the 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”

CHSUCB Brent Collins: Stacked SaddlesBrent Collins: Stacked Saddles

CHSUCB Scherk’s 2nd Minimal SurfaceScherk’s 2nd Minimal Surface

Normal“biped”saddles

Generalization to higher-order saddles(monkey saddle)

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 Closing the LoopClosing the Loop

straight

or

twisted

CHSUCB Collins - Séquin CollaborationCollins - Séquin Collaboration

Discuss ideas on the phone

Exchange sketches

Vary the topological parameters

But how do you know whether it is beautiful ? Need visual feedback.

Making models from paper strips is not good enough.

A key problem is making the sculpture look good from all sides !

CHSUCB Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process

Armature for the "Hyperbolic Heptagon"

Mockup for the "Saddle Trefoil"

Time-consuming ! (1-3 weeks)

CHSUCB Collins’ Fabrication ProcessCollins’ 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 marksand 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 !

CHSUCB Collins’ Fabrication ProcessCollins’ Fabrication Process

Example: “Vox Solis”

Layered laminated main shapeWood master pattern

for sculpture

CHSUCB The Need for a Prototyping ToolThe Need for a Prototyping Tool

Intriguing Conceptual Idea: “Turn the Hyperbolic Hexagon into a Heptagon” Goals: Give it more variety;

Make different hole-angles visible from one direction by adding twist before closure.

Results: Surface becomes single-sided;

The four separate edges join into a torus knot.

Question: Will it look beautiful ? What can we do if it doesn’ t ?

Perhaps more twist can save it ?

What is the best size for the holes, the flanges ?

How can we find out quickly ?

CHSUCB ““Sculpture Generator I”Sculpture Generator I”

Prototyping tool forScherk-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.

CHSUCB Generated Scherk-Collins ShapesGenerated Scherk-Collins Shapes

CHSUCB The Basic ElementThe Basic Element

Scherk’s 2ndminimal surface

3-story tower,trimmed, thickened

180 degreesof twist added

CHSUCB Toroidal Warp into Collins RingToroidal Warp into Collins Ring

8-story tower warped into a ring 360º twist added

CHSUCB A Plethora of ShapesA Plethora of Shapes

CHSUCB Edge TreatmentEdge Treatment

square, flat cut semi-circular bulging out

CHSUCB Embellishment of Basic ShapeEmbellishment of Basic Shape

color backgroundtexture

CHSUCB Sculpture Generator, GUI Sculpture Generator, GUI

CHSUCB Some of the Parameters in “SC1”Some of the Parameters in “SC1”

CHSUCB Main Goal in Sculpture Generator IMain Goal in Sculpture Generator I

Real-time Interactive Speed !

Can’t afford surface optimizationto obtain true minimal surfaces;

also, this would be aesthetically too limited.

Use closed-form hyperbolic approximation.

CHSUCB Base Geometry: One Scherk StoryBase Geometry: One Scherk Story

Hyperbolic Slices ==> Triangle Strips

Pre-computed -- then warped into toroid

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 1-story Scherk Tower1-story Scherk Tower

branches = 5 stories = 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

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 How to Obtain a How to Obtain a RealReal Sculpture ? 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.

CHSUCB Slices through “Minimal Trefoil”Slices through “Minimal Trefoil”

50% 10%23%30%

45% 5%20%27%

35% 2%15%25%

CHSUCB Profiled Slice through the SculptureProfiled Slice through the Sculpture

One thick slicethru “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, 3/4of one board.

CHSUCB Our First “Joint” SculptureOur First “Joint” Sculpture

Six monkey saddles in a ring with no twist

(like Hyperbolic Hexagon)

azimuth = –30°, flange 1.5

(aesthetics)

size, thickness (fabrication consideration)

CHSUCB ““Hyperbolic Hexagon II” (wood)Hyperbolic Hexagon II” (wood)

Brent Collins

CHSUCB Heptoroid Heptoroid ( from Sculpture Generator I )( from Sculpture Generator I )

Cross-eye stereo pair

CHSUCB Emergence of the “Heptoroid” (1)Emergence of the “Heptoroid” (1)

Assembly of the precut boards

CHSUCB Emergence of the “Heptoroid” (2)Emergence of the “Heptoroid” (2)

Forming a continuous smooth edge

CHSUCB Emergence of the “Heptoroid” (3)Emergence of the “Heptoroid” (3)

Smoothing the whole surface

CHSUCB ““Heptoroid”Heptoroid”

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 Sculpture DesignSculpture Design

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

CHSUCB FDM Maquette of Solar ArchFDM Maquette of Solar Arch

CHSUCB Breckenridge CompetitionBreckenridge Competition

2nd place

CHSUCB V-artV-art

VirtualGlassScherkTowerwithMonkeySaddles

(Radiance 40 hours)

Jane Yen

CHSUCB Fused Deposition Modeling (FDM)Fused Deposition Modeling (FDM)

CHSUCB SFF (Solid Free-form Fabrication)SFF (Solid Free-form Fabrication)

Monkey-SaddleCinquefoil

CHSUCB Various “Scherk-Collins” SculpturesVarious “Scherk-Collins” Sculptures

CHSUCB Note:Note:

The computer becomesan amplifier / acceleratorfor the creative process.

CHSUCB Questions ?Questions ?

THE ENDTHE END