1. Art & Science UCB DeCal, September 17, 2013 Carlo H. Séquin University of California, Berkeley

2. SCIENCE ART MATH DESIGN

3. What came first: Art or Mathematics ? u Question posed Nov. 16, 2006 by Dr. Ivan Sutherland “father” of computer graphics (SKETCHPAD, 1963).

4. Early “Free-Form” Art Cave paintings, LascauxVenus von Willendorf

5. Regular, Geometric Art u Early art: Patterns on bones, pots, weavings... u Mathematics (geometry) to help make things fit:

6. Another Question: What came first: Art or Science? What is Art ? -- What do artists do ? What is Science ? -- What do scientists do ?

7. What is the Difference... between Art and Design ?

8. Art? -- or Design? -- or What?

10. Unfinished Construction Site ?

11. Clearly Something Special... Art? or Design?

13. Art or Wallpaper ?

14. Art? -- or Design? -- or What?

15. Another Mysterious Object u Propeller for a submarin ? u Grinder head for tunnel boring ? u Galactic force concentrator ?

16. My Background: Geometry ! u Descriptive Geometry – love since high school

17. Descriptive Geometry

18. 40 Years of Geometry and Design CCD TV Camera Soda Hall RISC 1 Computer Chip Octa-Gear (Cyberbuild)

19. More Recent Creations

20. Aurora Sculptures Inspired by the curtain- or ribbon-like Northern Lights

21. Torus-Knot_5,3 Inspired by a well defined type of mathematical knot Torus-Knot_3,5

22. A Special Result

23. The Process: ( For Scherk-Collins Toroids ) Inspirational Model Generative Paradigm Computer Program Many New Models Insight, Analysis Math, Geometry Selection, Design

24. Scherk-Collins Toroids Collaboration with sculptor Brent Collins:  “Hyperbolic Hexagon” 1994  “Hyperbolic Hexagon II”, 1996  “Heptoroid”, 1998

25. Brent Collins: Hyperbolic Hexagon

26. Scherk’s 2nd Minimal Surface 2 planes the central core 4 planes bi-ped saddles 4-way saddles = “Scherk tower”

27. Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles (monkey saddle) “Scherk Tower”

28. V-art (1999) Virtual Glass Scherk Tower with Monkey Saddles (Radiance 40 hours) Jane Yen

29. Closing the Loop straight or twisted “Scherk Tower”“Scherk-Collins Toroids”

30. Sculpture Generator 1, GUI

31. Shapes from Sculpture Generator 1

32. Inauguration Sutardja Dai Hall 2/27/09

33. The Finished Heptoroid u at Fermi Lab Art Gallery (1998).

34. 2003: “Whirled White Web”

35. 12:40 pm -- 42° F

36. 12:41 pm -- 42° F

37. “WWW” Wins Silver Medal

38. Brent Collins and David Lynn

39. Sculpture Generator #2

40. Tentative Assembly of Three Units

46. Yet Another Medium: Stone “The Three Pillars of Engineering” Math – Materials – Physics(Science) Sponsored by Paul Suciu (EECS alum)

47. Spring, 2012

53. Inauguration Sutardja Dai Hall 2/27/09

54. The Viae Globi Series u Another example how one special piece of art led 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)

55. 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: Define the master geometry. CAD tools play important role!

56. How to Model Pax Mundi... u Already addressed that question in 1998: u Pax Mundi could not be done with Sculpture Generator I u Needed a more general program ! u Used the Berkeley SLIDE environment. u First: Needed to find the basic paradigm   

57. Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis- or base-ball;  “2-period Gabo curve.”

58. 2-period “Gabo Curve” u Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used (symmetry!).

59. 4-period “Gabo Curve” Same construction as for as for 2-period curve

60. Pax Mundi Revisited u Can be seen as: Amplitude modulated, 4-period Gabo curve

61. SLIDE-GUI for “Pax Mundi” Shapes Good combination of interactive 3D graphics and parameterizable procedural constructs.

62. 2-period Gabo Sculpture Tennis ball – or baseball – seam used as sweep curve.

63. Viae Globi Family (Roads on a Sphere) Viae Globi Family (Roads on a Sphere) 2 3 4 5 periods

64. Via Globi 5 (Virtual Wood) Wilmin Martono

65. Modularity of Gabo Sweep Generator u Sweep Curve Generator: l Gabo Curves as B-splines u Cross Section Fine Tuner: l Paramererized shapes u Sweep / Twist Controller

66. Sweep / Twist Control u How do we orient, move, scale, morph... the cross section along the sweep path ? Natural orientation with Frenet frame Torsion Minimization: Azimuth: tangential / normal 900° of twist added.

67. Target Geometry (2007) Constraints: Bronze, 70” diameter Less than 1500 pounds Less than $50’000 Maintain beauty, strength Minimize master geometry

68. Emulation; Define Master Pattern u Use 4 copies. u Master to make a mold from. Alignment tab

69. Joe Valasek’s CNC Milling Machine u Styrofoam milling machine

70. Machined Master Pattern #2

71. (Cut) Master  Silicone Rubber Mold

72. Mold  Several (4) Wax Copies

73. Spruing the Wax Parts for Casting

74. Ceramic Slurry Shell Around Wax Part

75. Taking the Shell out of the Kiln

76. Shell Ready for Casting

77. The Pour

78. Casting with Liquid Bronze

79. Freeing the Bronze Cast

80. Assembling the Segments

81. The “Growing” Ribbon

82. Assembly Completed Assembly Completed

83. Front Door of the... H&R Block Building

84. Steve Reinmuth, Bronze Studio, Eugene OR u http://www.reinmuth.com/ http://www.reinmuth.com/

85. Team effort: Brent Collins, Steve Reinmuth, Carlo Séquin

86. The Process: Example: Pax Mundi Wood Pax Mundi Sweep curve on a sphere Via Globi framework In SLIDE Bronze Pax Mundi Inspirational Model Generative Paradigm Computer Program Many New Models Insight, Analysis Math, Geometry Selection, Design

87. Extension: Free-form Curve on a Sphere Spherical Spline Path Editor (Jane Yen) Smooth interpolating curve through sparse data points

88. Many Different Viae Globi Models

89. Music of the Spheres (Brent Collins) Paradigm Extension: Sweep Path is no longer confined to a sphere!

90. Partitioning; Joint Design 18 pieces: fit in kiln! 1/3 = unique geometry Alignment stubs

91. Some Segments Will Be Cast Hollow This needs a double-walled tube mold!

92. Some of the Hollow Metal Parts

93. Assembly of Music of the Spheres

94. Installation at MWSU, Feb. 2013 Steve Reinmuth Brent Collins

95. Illuminated Music of the Spheres Photo by Phillip Geller

96. Conclusions u Knotted and twisted structures play an important role in many areas of physics and the life sciences. u They also make fascinating art-objects...

97. Is It Math ? Is It Art ? u it is: “KNOT-ART”

98. QUESTIONS ? ?