LASER, December 10, 2014 Carlo H. Séquin University of California, Berkeley "Hyperbolic Hexagon" to "Evolving Trefoil“ my 20-year collaboration with Brent Collins
Basel, Switzerland M N G
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
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
More Sculptures by Brent Collins Photos by Phillip Geller
The Math in Collins’ Sculptures u Collins works with rulers and compasses; any math in his early work is intuitive. u He is inspired by nature, e.g. soap films (= minimal area surfaces) (& minimal bending, too). u George Francis analyzed Collins’ sculptures in terms of the knots formed by their rims and the topology of the spanning surfaces. u Let’s look at the local geometry found often in these tunnel & saddle surfaces:
Scherk’s 2 nd Minimal Surface (1834) Normal “biped” saddles “Scherk Tower” 2 planes: bi-ped saddles
“Hyperbolic Hexagon” by Brent Collins u 6 saddles in a ring... u = “wound up” (toroidal) 6-story Scherk tower. u 6 holes passing through symmetry plane at ±45º u Discussion: What if … l we added more stories ? l or introduced a twist before closing the ring ?
Closing the Loop straight or twisted “Scherk Tower”“Scherk-Collins Toroids”
Brent Collins’ Prototyping Process Armature for the "Hyperbolic Heptagon” (7 Scherk stories) Mockup for the "Saddle Trefoil" Time-consuming ! (1-2 weeks) Bees wax
Sculpture Generator 1, GUI
Shapes from Sculpture Generator 1
Brent Collins, 1997 “Hyperbolic Hexagon II”
Collins’ Fabrication Process Example: Vox Solis Layered laminated main shape Wood master pattern for sculpture
u One thick slice thru sculpture, from which Brent can cut boards and assemble a rough shape. u Traces represent: top and bottom, as well as cuts at 1/4, 1/2, 3/4 of one board. Profiled Slice through “Heptoroid”
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 u 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 u branches = 4 u storeys = 11 u height = 1.55 u flange = 1.00 u thickness = 0.06 u rim_bulge = 1.00 u warp = u twist = u azimuth = u mesh_tiles = 0 u textr_tiles = 1 u detail = 8 u bounding box: u xmax= 6.01, u ymax= 1.14, u zmax= 5.55, u xmin= -7.93, u ymin= -1.14, u zmin= -8.41
12 Signs of the Zodiac
David Lynn, Nova Blue Studio Arts u
Master Module for “Millennium Arch”
Fabrication of “Millennium Arch” The mold for the key moduleA 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 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 Milled foam core coated with clay About 20 fiberglass pieces bolted together
Formation of a Main Sculpture Module
Sealed-off Mold (Catalyzed Matrix Inside)
Fabricate 6 Identical Pieces u 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