1. University of California, Berkeley
Florida 1999
CS285
Sculpture Generator I
Carlo H. Séquin
University of California, Berkeley
In Collaboration with
Brent Collins
Gower, Missouri

2. Brent Collins “Genesis” – Brent Collins at BRIDGES 2000 Florida 1999
Brent Collins is a professional artist living in Gower, MO,
who has been carving abstract geometrical structures from
solid wood blocks or from laminated assemblies. Many of his
sculptures comprise minimal surfaces which form an intricate
composition of tunnels and saddles.
“Genesis” – Brent Collins at BRIDGES 2000

3. Leonardo -- Special Issue
On Knot-Spanning Surfaces: An Illustrated Essay on Topological Art
With an Artist’s Statement by Brent Collins
George K. Francis with Brent Collins

4. Brent Collins: Early Sculptures
All photos by Phillip Geller

5. 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 ?
==> Focus on “Chains of Saddles”

6. Brent Collins: Stacked Saddles

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

8. “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 ?

9. Closing the Loop
straight or
twisted

10. 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.
A key problem is making the sculpture look good from all sides !

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

12. 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 marks and 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 !

13. Collins’ Fabrication Process
Wood master pattern for sculpture
Layered laminated main shape
Example: “Vox Solis”

14. The 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 ?

15. “Sculpture Generator I”
Prototyping tool for Scherk-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.

16. Generated Scherk-Collins Shapes

17. The Basic Element Scherk’s 2nd minimal surface
3-story tower, trimmed, thickened
180 degrees of twist added

18. Toroidal Warp into Collins Ring
8-story tower
warped into a ring
360º twist added

19. A Plethora of Shapes

20. Edge Treatment
square, flat cut
semi-circular
bulging out

21. Embellishment of Basic Shape
color
texture
background

22. Sculpture Generator, GUI

23. Some of the Parameters in “SC1”

24. Main Goal in Sculpture Generator I
Real-time Interactive Speed !
Can’t afford surface optimization to obtain true minimal surfaces;
also, this would be aesthetically too limited.
 Use closed-form hyperbolic approximation.

25. Base Geometry: One Scherk Story
Hyperbolic Slices ==> Triangle Strips
Pre-computed -- then warped into toroid

26. 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 =
twist = 90
azimuth = 90
textr_tiles = 3
detail = 8

27. 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

28. 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

29. 1-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

30. 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

31. How to Obtain a Real 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.

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

33. Profiled Slice through the Sculpture
Florida 1999
Profiled Slice through the Sculpture
One thick slice thru “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, 3/4 of one board.
From these Collins will precut boards
then assemble the complete shape
and fine tune and polish it.

34. 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)

35. “Hyperbolic Hexagon II” (wood)
Florida 1999
“Hyperbolic Hexagon II” (wood)
For whom I designed certain shapes on the computer which he then built oin wood.
Brent Collins

36. Heptoroid ( from Sculpture Generator I )
Cross-eye stereo pair

37. Emergence of the “Heptoroid” (1)
Assembly of the precut boards

38. Emergence of the “Heptoroid” (2)
Forming a continuous smooth edge

39. Emergence of the “Heptoroid” (3)
Smoothing the whole surface

40. “Heptoroid”

41. 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

42. Sculpture Design branches = 4 storeys = 11 height = 1.55 flange = 1.00
thickness = 0.06
rim_bulge = 1.00
warp =
twist =
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

43. FDM Maquette of Solar Arch

44. Breckenridge Competition
2nd place

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

46. Fused Deposition Modeling (FDM)

47. SFF (Solid Free-form Fabrication)
Monkey-
Saddle
Cinquefoil

48. Various “Scherk-Collins” Sculptures

49. Note:
The computer becomes an amplifier / accelerator for the creative process.

50. Questions ?
THE END