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USF -- February 2001

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Computer-Aided Design V : Abstract Sculpture (virtual) ... Collins' Fabrication Process. Building the final sculpture (2-3 months) ... – PowerPoint PPT presentation

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Title: USF -- February 2001


1
USF -- February 2001
  • Art, Math, and Sculpture
  • Connecting Computers and Creativity
  • Carlo H. Séquin
  • University of California, Berkeley

2
My Professional Focus
  • Computer-Aided Design
  • Design useful and beautiful objectswith the help
    of computers.
  • Develop (interactive) computer programsto make
    these tasks easier.

3
Computer-Aided Design I Integrated Circuits
  • RISC I chip (1981)

4
Computer-Aided Design II Mathematical Models
  • Granny Knot Lattice
  • Berkeley UniGrafix (1982)

5
Computer-Aided Design III Buildings
Soda Hall, CS Dept. Berkeley (1992)
6
Computer-Aided Design IV Mechanical Parts
Octahedral Gear
  • Design (1985) Realization (FDM) (2000)

7
Computer-Aided Design V Abstract Sculpture
(virtual)
(Since 1995)
8
Computer-Aided Design V Abstract Sculpture
(virtual)
  • Scherk-Collins Tower

9
Computer-Aided Design V Abstract Sculpture
(virtual)
  • Doubly-looped Scherk-Collins saddle-chain

10
Computer-Aided Design V Abstract Sculpture
(real)
  • Bonds of Friendship(2001)
  • Fabricated by Fused Deposition Modeling
  • Currently in S.F.at Gallery 650,Delancy/Brannan

11
Roots of My Passion for Sculpture
  • My love for geometry and abstract
    sculptureemerged long long before I learned to
    play with computers.
  • Thanks to Alexander Calder, Naum Gabo,Max
    Bill, M.C. Escher, Frank Smullin, ...

12
Leonardo -- Special Issue
On Knot-Spanning Surfaces An Illustrated Essay
on Topological Art With an Artists Statement by
Brent Collins
George K. Francis with Brent Collins
13
Brent Collins Early Sculptures
All photos by Phillip Geller
14
My Fascination with...
Brent Collins 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 ?
  • gt Focus on Chains of Saddles

15
Brent Collins Stacked Saddles
16
Scherks 2nd Minimal Surface
Normal biped saddles
Generalization to higher-order saddles(monkey
saddle)
17
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 ?

18
Closing the Loop
straight or twisted
19
Collins - 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.

20
Brent Collins Prototyping Process
Mockup for the "Saddle Trefoil"
Armature for the "Hyperbolic Heptagon"
Time-consuming ! (1-3 weeks)
21
Collins 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 !

22
Collins Fabrication Process
Lamination process to make an overall shape that
withincontains the final sculpture. Example
Vox Solis
23
Sculpture Generator I
  • Prototyping Visualization 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.
  • gt VIDEO

24
Scherk-Collins Sculptures
25
The Basic Element
Scherks 2ndminimal surface
3-story tower,trimmed, thickened
180 degreesof twist added
26
Toroidal Warp into Collins Ring
8-story tower
warped into a ring
360º twist added
27
A Plethora of Shapes
28
Edge Treatment
square, flat cut
semi-circular
bulging out
29
Embellishment of Basic Shape
color
background
texture
30
VIDEO
  • 6 min

31
A Simple Scherk-Collins Toroid
  • branches 2
  • storeys 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

32
Also a Scherk-Collins Toroid
  • branches 1
  • storeys 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

33
A Scherk Tower (on its side)
  • branches 7
  • storeys 3
  • height 0.2
  • flange 1.00
  • thickness 0.04
  • rim_bulge 0
  • warp 0
  • twist 0
  • azimuth 0
  • textr_tiles 2
  • detail 6

34
1-story Scherk Tower
  • branches 5
  • storeys 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

35
180º Arch Half a Scherk Toroid
  • branches 8
  • storeys 1
  • height 5
  • flange 1.00
  • thickness 0.06
  • rim_bulge 1.25
  • warp 180
  • twist 0
  • azimuth 0
  • textr_tiles e
  • detail 12

36
Main Goal in Sculpture Generator I
  • Real-time Interactive Speed !
  • Cant afford surface optimizationto obtain true
    minimal surfaces
  • also, this would be aesthetically too limited.
  • gt Make closed-form hyperbolic approximation.

37
Hyperbolic Cross Sections
38
Base Geometry One Scherk Story
  • Hyperbolic Slices gt Triangle Strips
  • precomputed -- then warped into toroid

39
The Basic Saddle Element
  • with surface normals

40
Hyperbolic Contour Lines
  • On a straight tower and on a ring

41
How to Obtain a Real Sculpture ?
  • Prepare a set of cross-sectional blue printsat
    eaqually spaced height intervals,corresponding
    to the board thickness that Brent is using for
    the construction.

42
Slices through Minimal Trefoil
50
10
23
30
45
5
20
27
35
2
15
25
43
Profiled Slice through the Sculpture
  • One thick slicethru Heptoroidfrom 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.

44
Our 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)

45
Hyperbolic Hexagon II (wood)
46
Heptoroid ( from Sculpture Generator I )
Cross-eye stereo pair
47
Emergence of the Heptoroid (1)
Assembly of the precut boards
48
Emergence of the Heptoroid (2)
Forming a continuous smooth edge
49
Emergence of the Heptoroid (3)
Smoothing the whole surface
50
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

51
Sculpture Design Solar Arch
  • 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

52
Competition in Breckenridge, CO
53
SLA Maquette of Solar Arch
Back-lighting and photo by Philip Geller
54
FDM Maquette of Solar Arch
  • 2nd place

55
We Can Try Again in L.A.
56
or in Washington D.C.
57
V-art
VirtualGlassScherkTowerwith MonkeySaddles Ja
ne Yen
58
SFF Maquettes of Future Sculptures
Monkey- Saddle Cinquefoil
59
Various Scherk-Collins Sculptures
60
Fused Deposition Modeling (FDM)
61
Looking into the FDM Machine
62
Zooming into the FDM Machine
63
Séquins Minimal Saddle Trefoil
  • Stereo-lithography master

64
Séquins Minimal Saddle Trefoil
  • bronze cast, gold plated

65
Minimal Trefoils -- cast and finished by Steve
Reinmuth
66
Brent Collins Trefoil
67
Family of Symmetrical Trefoils
W2
W1
B1 B2 B3
B4
68
Higher-order Trefoils (4th order saddles)
W1
W2
69
Exploring New Ideas
  • Going around the loop twice ...

resulting in an interwoven structure.
70
9-story Intertwined Double Toroid
Bronze investment casting from wax original
made on 3D SystemsThermojet
71
Stepwise Expansion of Horizon
  • Playing with many different shapes and
  • experimenting at the limit of the domain of the
    sculpture generator,
  • stimulates new ideas for alternative shapes and
    generating paradigms.

Swiss Mountains
72
Brent Collins Pax Mundi
73
Keeping up with Brent ...
  • A warped Scherk tower is not able to describe
    a shape like Pax Mundi.
  • Need a broader paradigm !
  • Use the SLIDE modeling environment(developed at
    U.C. Berkeley by J. Smith)it provides a nice
    combination of procedural modeling and
    interactivity.

74
SLIDE
  • SLIDE Scene Language for Interactive Dynamic
    Environments
  • Developed as a modular rendering pipelinefor our
    introductory graphics course.
  • Primary Author Jordan Smith
  • Based on OpenGL and Tcl/tk.
  • Good combination of interactive 3D graphicsand
    parameterizable procedural constructs.

75
SLIDE Example Klein Bottle
  • Final Project CS 184, Nerius Landys Shad
    Roundy

76
SLIDE Example Bugs Life
  • Final Project CS 184, David Cheng and James Chow

77
SLIDE as a Design Tool
  • SLIDE is being enhanced currentlyto serve as a
    front-end for CyberBuild.
  • Recently added
  • Spline curves and surfaces
  • Morphing sweeps along such curves
  • 3D warping module (Sederberg, Rockwood)
  • Many types of subdivision surfaces
  • These are key elements for Sculpture Generator II

78
3D Hilbert Curves (FDM)
  • Hilbert64 and Hilbert512

79
SLIDE-UI for Knot Generation
80
SLIDE-UI for Pax Mundi Shapes
81
Viae Globi Family (Roads on a Sphere)
L2 L3 L4
L5
82
Via Globi 3 (Stone)
Wilmin Martono
83
Via Globi 5 (Wood)
Wilmin Martono
84
Via Globi 5 (Gold)
Wilmin Martono
85
Figure-8 Knot with C-Section
86
Conclusions (1)
  • Interactive computer graphics is a novel (to
    artists) medium that can play an important role
    -- even for traditional artists.
  • Virtual Prototyping can save time and can tackle
    sculptures of a complexitythat manual techniques
    could not conquer.

87
Conclusions (2)
  • The computer is not only a great visualization
    and prototyping tool,
  • It also is a generator for new ideas and
  • an amplifier for an artists inspiration.

88
Questions ?
THE END
89
SPARE

90
Conclusions (3)
  • What makes a CAD tool productive for this kind
    of work ?
  • Not just virtual clay,
  • partly procedural
  • fewer parameters that need to be set.
  • Keep things aligned, joined
  • guarantee symmetry, regularity,
  • watertight surfaces.
  • Interactivity is crucial !

91
Some of the Parameters in SC1
92
AAAS 2001, San Francisco
  • Procedurally Defined Geometrical Sculptures
  • Carlo H. Séquin
  • University of California, Berkeley
  • Brent Collins
  • Gower, Missouri
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