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CS 284. Sculpture Generator I Carlo H. Séquin University of California, Berkeley In Collaboration with B rent Collins Gower, Missouri. Brent Collins. “Genesis” – Brent Collins at BRIDGES 2000. Brent Collins: Early Sculptures. All photos by Phillip Geller. Collins’ Abstract Geometric Art.
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CS 284 Sculpture Generator I Carlo H. Séquin University of California, Berkeley In Collaboration with Brent Collins Gower, Missouri
Brent Collins “Genesis” – Brent Collins at BRIDGES 2000
Brent Collins: Early Sculptures All photos by Phillip Geller
Collins’ Abstract Geometric Art • Beautiful symmetries • Graceful balance of the saddle surfaces • Superb craftsmanship • Intriguing run of the edges • What type of knot is formed ? • Mystery: one-sided or two-sided ?
Leonardo -- Special Issue On Knot-Spanning Surfaces: An Illustrated Essay on Topological Art George K. Francis with Brent Collins
Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles(monkey saddle) “Scherk Tower”
“Hyperbolic Hexagon” by B. Collins • 6 saddles in a ring • = “wound up” 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 Mockup for the Saddle Trefoil Armature for the Hyperbolic Heptagon Time-consuming ! (1-3 weeks)
Base Geometry: One Scherk Story • Hyperbolic Slices ==> Triangle Strips • Pre-computed -- then warped into toroid
The Basic Element Scherk’s 2ndminimal surface 3-story tower,trimmed, thickened 180 degreesof twist added
Toroidal Warp into Collins Ring 8-story tower warped into a ring 360º twist added
Edge Treatment square, flat cut semi-circular bulging out
Embellishment of Basic Shape color texture background
A Simple Scherk-Collins Toroid Parameters:(genome) • branches = 2 • stories = 1 • height = 5.00 • flange = 1.00 • thickness = 0.10 • rim_bulge = 1.00 • warp = 360.00 • twist = 90 • azimuth = 90 • textr_tiles = 3 • detail = 8
Also a Scherk-Collins Toroid • branches = 1 • stories = 5 • height = 1.00 • flange = 1.00 • thickness = 0.04 • rim_bulge = 1.01 • warp = 360 • twist = 900 • azimuth = 90 • textr_tiles = 1 • detail = 20
A Scherk Tower (on its side) • branches = 7 • stories = 3 • height = 0.2 • flange = 1.00 • thickness = 0.04 • rim_bulge = 0 • warp = 0 • twist = 0 • azimuth = 0 • textr_tiles = 2 • detail = 6
V-art VirtualGlassScherkTowerwith MonkeySaddles(Radiance 40 hours) Jane Yen
How to Obtain a Real Sculpture ? • Prepare a set of cross-sectional blue printsat equally spaced height intervals,corresponding to the board thicknessthat Brent is using for the construction.
Collins’ Fabrication Process Wood master patternfor sculpture Layered laminated main shape Example: Vox Solis
Our First “Joint” Sculpture Six monkey saddles in a ring with no twist (like Hyperbolic Hexagon) azimuth = –30°, flange 1.5 (aesthetics) size, thickness (fabrication consideration)
Brent Collins “Hyperbolic Hexagon II”
Slices through “Minimal Trefoil” 50% 30% 23% 10% 45% 27% 20% 5% 35% 25% 15% 2%
Profiled Slice through “Heptoroid” • 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.
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).
Extending the Paradigm: “Totem 3” Bronze Investment Cast
“Cohesion” SIGGRAPH’2003 Art Gallery
Sculpture Design • 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
Fabrication of “Millennium Arch” The mold for the key module A polyester segment cast