LASER, December 10, 2014 "Hyperbolic Hexagon" to "Evolving Trefoil“ my 20-year collaboration with Brent Collins Carlo H.
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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
Discussion: What if …
we added more stories ?
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
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
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