CHS UCB AAAS 2001, San Francisco Procedurally Defined Geometrical Sculptures Carlo H. Séquin University of California, Berkeley Brent Collins Gower, Missouri.
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CHS UCB AAAS 2001, San Francisco Procedurally Defined Geometrical Sculptures Carlo H. Séquin University of California, Berkeley Brent Collins Gower, Missouri CHS UCB My Professional Focus Computer-Aided Design Design useful and beautiful objects with the help of computers. Develop (interactive) computer programs to make these tasks easier. CHS UCB Computer-Aided Design I : Integrated Circuits: “RISC I” chip (1981) CHS UCB Computer-Aided Design II : Mathematical Models “Granny Knot” Lattice Berkeley UniGrafix (1982) CHS UCB Computer-Aided Design III : Buildings Soda Hall, CS Dept. Berkeley (1992) CHS UCB Computer-Aided Design IV : Mechanical Parts Octahedral Gear Design (1985) Realization (FDM) (2000) CHS UCB Computer-Aided Design V : Abstract Sculpture (virtual) (Since 1995) CHS UCB Computer-Aided Design V : Abstract Sculpture (virtual) Scherk-Collins Tower CHS UCB Computer-Aided Design V : Abstract Sculpture (virtual) Doubly-looped Scherk-Collins saddle-chain CHS UCB Computer-Aided Design V : Abstract Sculpture (real) “Bonds of Friendship” (2001) Fabricated by: Fused Deposition Modeling Currently in S.F.: at Gallery 650, Delancy/Brannan CHS UCB Roots of My Passion for Sculpture My love for geometry and abstract sculpture emerged long long before I learned to play with computers. Thanks to: Alexander Calder, Naum Gabo, Max Bill, M.C. Escher, Frank Smullin, ... CHS UCB 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 CHS UCB Brent Collins: Early Sculptures All photos by Phillip Geller CHS UCB My Fascination with... Brent 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 ? ==> Focus on “Chains of Saddles” CHS UCB Brent Collins: Stacked Saddles CHS UCB Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles (monkey saddle) CHS UCB “Hyperbolic Hexagon” by B. Collins 6 saddles in a ring 6 holes passing through symmetry plane at ±45º “wound up” 6-story Scherk tower What would happen, if we added more stories ? or introduced a twist before closing the ring ? CHS UCB Closing the Loop straight or twisted CHS UCB Collins - Séquin Collaboration Discuss ideas on the phone Exchange Vary sketches the topological parameters But how do you know whether it is beautiful ? Need visual feedback. Making models from paper strips is not good enough. CHS UCB Brent Collins’ Prototyping Process Armature for the "Hyperbolic Heptagon" Mockup for the "Saddle Trefoil" Time-consuming ! (1-3 weeks) CHS UCB Collins’ Fabrication Process Building the final sculpture (2-3 months): Take measurements from mock-up model, transfer parallel contours to 1” boards. Roughly precut boards, leaving registration marks and contiguous pillars for gluing boards together. Stack and glue together precut boards, remove auxiliary struts. Fine-tune overall shape, sand and polish the surface. A big investment of effort ! CHS UCB Collins’ Fabrication Process Lamination process to make an overall shape that within contains the final sculpture. Example: “Vox Solis” CHS UCB “Sculpture Generator I” Prototyping & Visualization tool for Scherk-Collins Saddle-Chains. Slider control for this one shape-family, Control of about 12 parameters. Main goal: Speed for interactive editing. Geometry part is about 5,000 lines of C; 10,000 lines for display & user interface. ==> VIDEO CHS UCB === VIDEO === 6 min CHS UCB Base Geometry: One Scherk Story Hyperbolic Slices ==> Triangle Strips precomputed -- then warped into toroid CHS UCB Slices through the Sculpture One thick slice thru “Heptoroid” from which Brent can cut boards and assemble a rough shape. Shown are top and bottom as well as cuts at 1/4, 1/2, 3/4 of one board. CHS UCB 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) CHS UCB “Hyperbolic Hexagon II” (wood) CHS UCB Heptoroid ( from Sculpture Generator I ) Cross-eye stereo pair CHS UCB Emergence of the “Heptoroid” (1) Assembly of the precut boards CHS UCB Emergence of the “Heptoroid” (2) Forming a continuous smooth edge CHS UCB Emergence of the “Heptoroid” (3) Smoothing the whole surface CHS UCB Advantages of CAD of Sculptures Exploration Instant visualization of results Eliminate Create More need for prototyping virtual reality pictures Making Better of a larger domain more complex structures optimization of chosen form precise implementation Rapid prototyping of maquettes CHS UCB 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 CHS UCB Breckenridge Competition CHS UCB FDM Maquette of Solar Arch 2nd place CHS UCB We Can Try Again … in L.A. CHS UCB … or in Washington D.C. CHS UCB V-art Glass Scherk Tower with Monkey Saddles Jane Yen CHS UCB SFF Maquettes of Future Sculptures MonkeySaddle Cinquefoil CHS UCB Various “Scherk-Collins” Sculptures CHS UCB Fused Deposition Modeling (FDM) CHS UCB Looking into the FDM Machine CHS UCB Zooming into the FDM Machine CHS UCB Séquin’s “Minimal Saddle Trefoil” Stereo- lithography master CHS UCB Séquin’s “Minimal Saddle Trefoil” bronze cast, gold plated CHS UCB Minimal Trefoils -- cast and finished by Steve Reinmuth CHS UCB Brent Collins’ Trefoil CHS UCB Family of Symmetrical Trefoils W=2 W=1 B=1 B=2 B=3 B=4 CHS UCB Higher-order Trefoils W=1 (4th order saddles) W=2 CHS UCB Exploring New Ideas Going twice around the loop ... Resulting in an interwoven structure. CHS UCB 9-story Intertwined Double Toroid Bronze investment casting from wax original made on 3D Systems’ “Thermojet” CHS UCB Brent Collins: Pax Mundi CHS UCB Keeping up with Brent ... A bent “Scherk tower” is not able to describe a shape like “Pax Mundi.” Need a broader paradigm ! Use SLIDE modeling environment, it provides a nice combination of procedural modeling and interactivity. CHS UCB SLIDE-UI for “Pax Mundi” Shapes CHS UCB “Viae Globi” Family L2 L3 L4 (Roads on a Sphere) L5 CHS UCB Via Globi 3 (Stone) Wilmin Martono CHS UCB Via Globi 5 (Wood) Wilmin Martono CHS UCB Via Globi 5 (Gold) Wilmin Martono CHS UCB Conclusions (1) Interactive computer graphics is a novel (to artists) medium that can play an important role -- even for traditional artists. Virtual Prototyping can save time and can tackle sculptures of a complexity that manual techniques could not conquer. CHS UCB Conclusions (2) The computer is not only a great visualization and prototyping tool, It also is a generator for new ideas and an amplifier for an artist’s inspiration. CHS UCB Questions ? THE END CHS UCB ========= SPARE ========= ========================= CHS UCB Stepwise Expansion of Horizon Playing with many different shapes and experimenting at the limit of the domain of the sculpture generator, stimulates new ideas for alternative shapes and generating paradigms. Swiss Mountains CHS UCB Figure-8 Knot with C-Section CHS UCB Conclusions (3) What makes a CAD tool productive for this kind of work ? Not just “virtual clay,” partly procedural; fewer parameters that need to be set. Keep things aligned, joined; guarantee symmetry, regularity, watertight surfaces. Interactivity is crucial !