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Presentation on theme: "Waterloo, March 2017"— Presentation transcript:
Waterloo, March 2017
EECS Computer Sciences University of California, Berkeley
M N G
Jakob Bernoulli (1654‒1705)
Leonhard Euler (1707‒1783)
“Re-creations” of Inspiring Art
Alexander Calder: Mobiles
C. H. Séquin, circa 1957
Naum Gabo String Sculptures
H. Séquin, circa 1977
“Glowing TetraTangle”C. H. Séquin (1983)
Chinese Button Knot
. H. Séquin (1994)
FDM Models by C. H. Séquin (2000)
Brent Collins: Pax Mundi (1994)
Collins (1993) Hyperbolic Hexagon
Brent Collins (1997)
Hyperbolic Hexagon II
Brent Collins: Stacked Saddles
All 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).Prof. George Francis:“Connection to math. Minimal Surfaces!”
Scherk’s 2nd Minimal Surface (1834)
The central part of this is a “Scherk Tower.”
Generalizing the “Scherk
higher-order saddles(“Monkey saddle”)
Closing the Loop
Brent Collins: Hyperbolic Hexagon(1993)
Six balanced saddles
in a circular ring.
Inspired by the shape
of a soap film
suspended in a wire frame.
(with 6 stories).
Brent Collins’ Prototyping Process
Armature for the "Hyperbolic Heptagon"
Mockup for the
Time-consuming ! (1-3 weeks)
Sculpture Generator 1
Some of the Parameters in “SC1”
Generated Scherk-Collins Shapes
Base Geometry: One “Scherk Story”
, hugging a
-- then warped into toroid
Shapes from Sculpture Generator 1
Collins’ Fabrication Process
Example: “Vox Solis”
Layered laminated main shape
Wood master pattern
Slices through “Minimal Trefoil”
One thick slicethru 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, 3/4of one board.
Profiled Slice through
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).
Inauguration Sutardja Dai Hall 2/27/09
“Scherk-Collins” Sculptures (FDM)
SIGGRAPH’2003 Art Gallery
Hypersculpture: Family of 12 Trefoils
B=1 B=2 B=3 B=4
Going more than once around the loop
… results in an interwoven structure.
11 Stories, Monkey-Saddles, W=2:
cross–eye stereo picture
9-story Intertwined Double Toroid
Bronzeinvestment casting from wax original made on 3D Systems’“Thermojet”
Extension of Concept
Allow different kinds of “stretching” …
Extending the Paradigm: Totem 3
Bronze Investment Cast
Stepwise Expansion of Horizon
Playing with many different shapes andexperimenting at the limit of the domain of the sculpture generator,stimulates new ideas for alternative shapes and generating paradigms.
Sculpture Generator 1as a Playground
The computer becomes
an amplifier / accelerator
for the creative process.
Yet Another Medium: Stone
Progress picture from Dingli Stone Carving Art Co., SE China
The Viae Globi Series
Another example how one special piece of artled to a computer program, which then allowed me to make a whole series of sculpture designs that all seem to belong to the same family.
(Roads on a Sphere)
Brent Collins’ Pax Mundi1997: Wood, 30”diam.
2006: Commission from
H&R Block, Kansas City
to make a 70”diameter
version in bronze.
Define the master geometry.
CAD tools play important role!
How to Model Pax Mundi ...
Already addressed that issue in 1998:
be done with
Sculpture Generator I
Needed a more general program !
Used the “Berkeley SLIDE” environment.
Needed to find the basic paradigm
Sculptures by Naum Gabo
Pathway on a sphere:Edge of surface is like seam of tennis- or base-ball; “2-period Gabo curve.”
2-period “Gabo Curve”
Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used (symmetry!).
4-period “Gabo Curve”
Same construction as for as for 2-period curve
Pax Mundi Revisited
Can be seen as: “Amplitude modulated, 4-period Gabo curve”
Sculpture is not just a mathematical curve.
There is some substance; it has volume.
Define shape by sweeping a cross section
along a given 3D space curve.
SLIDE-GUI for “Pax Mundi” Shapes
Good combination of interactive 3D graphics
and parameterizable procedural constructs.
Modularity of Gabo Sweep Generator
Sweep Curve Generator:Gabo Curves as B-splines:Cross Section Fine Tuner:Paramererized shapes:Sweep / Twist Controller:How is cross section applied?
Intrinsic Sweep Mode
Keep cross section perpendicular to tangent
cross section into the
Keep orientation / rotation as it was
in the defining
Add any additional azimuth angle
as a rotation around the
Intrinsic Sweep Mode
Problems at inflection points (in plane): Pinched-off “hour-glass” shapes.
“Natural” orientationwith Frenet frame
Minimum-Torsion (-Rotation) Sweep
Project orientation of cross section forward,from one vertex of the sweep polyline to the next.Neutralize rotation of Frenet frame