CHS UCB CS285 Designing Viae Globi (Roads on a Sphere) Carlo H. Séquin University of California, Berkeley Inspired by Brent Collins Gower, Missouri

CHS UCB “Hyperbolic Hexagon” by B. Collins u 6 saddles in a ring u 6 holes passing through symmetry plane at ±45º u “wound up” 6-story Scherk tower u What would happen, l if we added more stories ? l or introduced a twist before closing the ring ?

CHS UCB Sculpture Generator, GUI

CHS UCB “Hyperbolic Hexagon II” (wood) Brent Collins

CHS UCB Family of Symmetrical Trefoils W=2 W=1 B=1 B=2 B=3 B=4

CHS UCB 9-story Intertwined Double Toroid Bronze investment casting from wax original made on 3D Systems’ “Thermojet”

CHS UCB Stepwise Expansion of Horizon u Playing with many different shapes and u experimenting at the limit of the domain of the sculpture generator, u stimulates new ideas for alternative shapes and generating paradigms. Swiss Mountains

CHS UCB Note: The computer becomes an amplifier / accelerator for the creative process.

CHS UCB Inspiration: Brent Collins’ “Pax Mundi”

CHS UCB Keeping up with Brent... u Sculpture Generator I can only do warped Scherk towers, not able to describe a shape like Pax Mundi. u Need a more general approach ! u Use the SLIDE modeling environment (developed at U.C. Berkeley by J. Smith) to capture the paradigm of such a sculpture in a procedural form. l Express it as a computer program l Insert parameters to change salient aspects / features of the sculpture l First: Need to understand what is going on 

CHS UCB Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis ball;  2-period Gabo curve.

CHS UCB 2-period Gabo curve u Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used.

CHS UCB 4-period Gabo curve Same construction as for as for 2-period curve

CHS UCB “Pax Mundi” Revisited u Can be seen as: Amplitude modulated, 4-period Gabo curve

CHS UCB SLIDE SLIDE = Scene Language for Interactive Dynamic Environments Developed as a modular rendering pipeline for our introductory graphics course. Primary Author: Jordan Smith u Based on OpenGL and Tcl/tk. u Good combination of interactive 3D graphics and parameterizable procedural constructs.

CHS UCB SLIDE Example: Klein Bottle Final Project CS 184, Nerius Landys & Shad Roundy

CHS UCB SLIDE Example Bug’s Life Final Project CS 184, David Cheng and James Chow

CHS UCB SLIDE as a Design Tool u SLIDE originally a modular rendering tool. u Later enhanced to serve as a CAD tool: l Spline curves and surfaces l Morphing sweeps along such curves l 3D warping module (Sederberg, Rockwood) l Many types of subdivision surfaces u These are key elements for a 2 nd Generation Sculpture Generator

CHS UCB SLIDE-UI for Knot Generation

CHS UCB SLIDE-UI for “Pax Mundi” Shapes

CHS UCB Via Globi 5 (Gold) Wilmin Martono

CHS UCB Via Globi 3 (Stone) Wilmin Martono

CHS UCB “Viae Globi” Family (Roads on a Sphere) L2 L3 L4 L5

CHS UCB Conclusions (1)  Procedural thinking about some art object adds a new and promising dimension. It allows the artist to increase the complexity, precision, and optimality of a particular piece of art.  The computer must be seen as yet another “power-tool” at the artist’s disposition, -- supplementing the pneumatic chisel, the airbrush, and the welding machine.

CHS UCB Conclusions (2) u The computer is not only a great visualization and prototyping tool, u it also is a generator for new ideas and u an amplifier for an artist’s inspiration.

CHS UCB Conclusions (3) u What makes a CAD tool productive for this kind of work ? l Not just “virtual clay,” l partly procedural; l fewer parameters that need to be set. l Keep things aligned, joined; l guarantee symmetry, regularity, l watertight surfaces. l Interactivity is crucial !

CHS UCB Conclusions (4) u Rapid prototyping (layered fabrication) must now be considered a new facet in the spectrum of MM technologies. u It provides tangible (high-quality haptic) output for objects with which users may want to interact. u Even for sculptures (intended primarily for visual enjoyment) the physical maquette discloses subtle geometrical features that are not visible in the virtual rendering.