Recent Sculptures Graphics Lunch, Feb. 1, 2013 Carlo H. Séquin ISAMA 2004 Graphics Lunch, Feb. 1, 2013 Recent Sculptures Carlo H. Séquin EECS Computer Science Division University of California, Berkeley

Brent Collins with Hyperbolic Hexagon II ISAMA 2004 Brent Collins with Hyperbolic Hexagon II An amazing variety of different shapes can result ! Here is Brent Collins holding Hyperbolic Hexagon II, the first collaborative piece, designed by Carlo Sequin and then carved by Brent Collins from 15 detailed layer plans cutting through the sculpture 7/8 of an inch apart. It features six 3-rd-order “monkey”-saddles in a loop without any twist.

Inauguration Sutardja Dai Hall 2/27/09 Granada 2003 Inauguration Sutardja Dai Hall 2/27/09 And here is a bronze cast of that same piece -- displayed in the 3rd floor lobby of Sutardja Dai hall – the CITRIS building. Now I want to tell you how we got from that first telephone conversation to this real physical object.

Snowsculpting Championships 2003 ISAMA 2004 Snowsculpting Championships 2003 Sculpture Generator I also created this shape, which was carved (with hand tools only) in a span of four days by this team headed by Stan Wagon, a professor of Mathematics and Computer Science at Macalester College in St. Paul, Minnesota, USA. The team named their creation the “Whirled White Web” and they received the silver medal for it. Unfortunately the sculpture collapsed only 45 minutes after judging had ended. The Team: “Whirled White Web” (C. Séquin, S. Wagon, D. Schwalbe, B. Collins, S. Reinmuth)

12:40 pm -- 42° F

12:41 pm -- 42° F

12:40:01 Photo: StRomain

“WWW” Wins Silver Medal

Eurographics Award Trophy ISAMA 2004 This is the story behind the Eurographics Award Trophy

Brent Collins’ “Pax Mundi” 1997: wood, 30”diam. Granada 2003 Brent Collins’ “Pax Mundi” 1997: wood, 30”diam. 2006: Commission from H&R Block, Kansas City to make a 70”diameter version in bronze. My task: to define the master geometry. This issue came up in 2006, when Brent got a commission from H&R Block in Kansas City to build 6 foot diameter bronze sculpture similar to his 1997 “Pax Mundi” wood sculpture shown here. Brent immediately called me, because he knew that I had already captured this geometry in another parameterized computer program. He asked: Carlo can you scale this up for me? So here is a case where there was this real physical model – which I had already captured in a VR representation – and which we now needed to export again to the real world as a large bronze sculpture.

Steve Reinmuth Bronze Studio, Eugene Granada 2003 Steve Reinmuth Bronze Studio, Eugene Three pieces are put together – forming the larger horse-shoe part made on the NC machine. -- This would not have fit into Steve’s kiln!

Granada 2003 Patina is applied with the help of some spray flask containing some chemicals and with a flame torch. Applying Patina

People like it a lot; -- and this led to other commissions! Granada 2003 Here we had to do just ONE sculpture. And even though it took much longer to fabricate than anticipated, it turned out beautifully. Here it is a few months later – without the scaffolding. People like it a lot; -- and this led to other commissions!

MWSU, Saint Joseph, MO

Scherk Tower

6-inch mode on FDM machine ISAMA 2004 6-inch mode on FDM machine

Yet Another Medium: Stone Granada 2003 Yet Another Medium: Stone And I am also getting experience with outputting a virtual design into yet another medium: Stone ! That is what the sculpture looked a few days ago before it was packaged up and put on a ship from China to Oakland. “The Three Pillars of Engineering” Math – Materials – Physics(Science) Sponsored by Paul Suciu (EECS alum)

Spring, 2012

ISAMA 2004 Contents of the crate

Installation, May 31, 2012

3D Yin-Yang : Two mirror parts Granada 2003 Mathematical Visualization Models 3D Yin-Yang : Two mirror parts But I like even better this solution with two parts that are mirror images of one another. Stereolithography model (Séquin 1999)

A plane-filling Peano curve Granada 2003 The 2D Hilbert Curve (1891) A plane-filling Peano curve Another example to exercise this analogy from 2D to 3D Do This In 3 D !

Construction of 3D Hilbert Curve

Granada 2003 Hilbert-Cube-512 (2006) Can I do the next generation 4096 “ells” on the new FDM machine we have in the basement of SD hall ?

A Gridded Model of Trefoil Knottle ISAMA 2004 A Gridded Model of Trefoil Knottle And here is a physical model of the central picture; -- made on a FDM machine.

2 Möbius Bands Make a Klein Bottle ISAMA 2004 2 Möbius Bands Make a Klein Bottle This is a very important insight; and it is shown here explicitly: On the left: Classical Klein bottle. The lower yellow half is a right-twisted Moebius band. The upper blue half – here shown flipped open to the right -- is a left-twisted Moebius band. The two are mirror images of one another. KOJ = MR + ML

Make Klein Bottle from 2 Boy-Caps ISAMA 2004 Make Klein Bottle from 2 Boy-Caps Here we have used a left-handed and a right-handed Boy cap to make a Klein bottle of type KOJ – the classical inverted sock Klein bottle. The result is a Klein Bottle with mirror symmetry and with 3-fold rotational symmetry. Actually with C3h symmetry overall. More than one way to do this . . . -- there is more than one type of Klein bottle

Klein Bottle with S6 Symmetry ISAMA 2004 Klein Bottle with S6 Symmetry This is still just a Klein bottle. We can make higher-genus non-orientable surfaces!

4 Boy Caps Make Genus-4 N.O. Surface

125 Tetras in 25 Projected 5-Cells