Transcript LASER, December 10, 2014 "Hyperbolic Hexagon" to "Evolving Trefoil“ my 20-year collaboration with Brent Collins Carlo H.

LASER, December 10, 2014
"Hyperbolic Hexagon" to "Evolving Trefoil“
my 20-year collaboration with Brent Collins
Carlo H. Séquin
University of California, Berkeley
Basel, Switzerland
MNG
Jakob Bernoulli (1654‒1705)
Logarithmic Spiral
Leonhard Euler (1707‒1783)
Imaginary Numbers
Geometry in every assignment . . .
CCD TV Camera (1973)
Soda Hall (1992)
RISC 1 MicroChip (1982)
Octa-Gear (2000)
Recent Designs and Models
On Knot-Spanning Surfaces: An
Illustrated Essay on Topological Art
With an Artist’s Statement by Brent Collins
George K. Francis
with Brent Collins
Leonardo -- Special Issue
More Sculptures by Brent Collins
Photos by Phillip Geller
The Math in Collins’ Sculptures
 Collins
works with rulers and compasses;
any math in his early work is intuitive.
 He
is inspired by nature,
e.g. soap films
(= minimal area surfaces)
(& minimal bending, too).
 George
Francis analyzed Collins’ sculptures
in terms of the knots formed by their rims
and the topology of the spanning surfaces.
 Let’s
look at the local geometry found often
in these tunnel & saddle surfaces:

Scherk’s 2nd Minimal Surface (1834)
Normal
“biped”
saddles
2 planes:
 bi-ped saddles
“Scherk Tower”
“Hyperbolic Hexagon” by Brent Collins

6 saddles in a ring . . .

= “wound up” (toroidal)
6-story Scherk tower.

6 holes passing through
symmetry plane at ±45º
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Discussion: What if …
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we added more stories ?
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or introduced a twist
before closing the ring ?
Closing the Loop
straight
or
twisted
“Scherk Tower”
“Scherk-Collins Toroids”
Brent Collins’ Prototyping Process
Bees wax
Armature for the
"Hyperbolic Heptagon”
(7 Scherk stories)
Mockup for the
"Saddle Trefoil"
Time-consuming ! (1-2 weeks)
Sculpture Generator 1, GUI
Shapes from Sculpture Generator 1
Brent Collins, 1997
“Hyperbolic Hexagon II”
Collins’ Fabrication Process
Layered laminated main shape
Wood master pattern
for sculpture
Example: Vox Solis
Profiled Slice through “Heptoroid”

One thick slice
thru sculpture,
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.
Emergence of the Heptoroid (1)
Assembly of the precut boards
Emergence of the Heptoroid (2)
Forming a continuous smooth edge
Emergence of the Heptoroid (3)
Smoothing the whole surface
The Finished
Heptoroid
 at
Fermi Lab
Art Gallery (1998).
2003: “Whirled White Web”
12:40 pm -- 42° F
12:41 pm -- 42° F
“WWW” Wins Silver Medal
12-Story Scherk-Collins Toroid
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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
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bounding box:
xmax= 6.01,
ymax= 1.14,
zmax= 5.55,
xmin= -7.93,
ymin= -1.14,
zmin= -8.41
12 Signs of the Zodiac
David Lynn, Nova Blue Studio Arts

http://sites.google.com/site/novabluestudioarts/
Master Module for “Millennium Arch”
Fabrication of “Millennium Arch”
The mold for the key module
A polyester segment cast
Two Times Three Modules
Merging the Two Half-Circles
Brent Collins and David Lynn
“Millennium Arch” by Night
Millennium Man
Vitruvian Man
by Leonardo
Concept of “Evolving Trefoil”
New: Let a hole-saddle chain follow an arbitrary space curve!
Sculpture Generator #2
An Evolution of Ideas and Forms
3 of 6 Maquette Modules (FDM)
(after cleaning away support)
Full-Size Master Module and Mold
About 20
fiberglass pieces
bolted together
Milled foam core
coated with clay
Formation of a Main Sculpture Module
Sealed-off Mold (Catalyzed Matrix Inside)
Fabricate 6 Identical Pieces
6
identical pieces had to be fabricated
in this labor-intensive way!
Three Units at Nova Blue Studio Arts
Installation at MWSU, Feb. 2013
V-art
(1999)
Virtual
Glass
Scherk
Tower
with
Monkey
Saddles
(Radiance
40 hours)
Jane Yen
Yet Another Medium:
Stone
“The Three Pillars of Engineering”
Math – Materials – Physics(Science)
Sponsored by Paul Suciu (EECS alum)
Spring, 2012
“Pax Mundi” by Brent Collins (1996, 2007)
Team effort: Brent Collins, Steve Reinmuth, Carlo Séquin
SLIDE-GUI for “Pax Mundi” Shapes
Good combination of interactive 3D graphics
and parameterizable procedural constructs.
Assembly of Music of the Spheres
“Music of
the Spheres”
With My Heartfelt Thanks . . .
Steve Reinmuth Brent Collins