CHSUCB CS285CS285

Designing Viae Globi

(Roads on a Sphere)

Carlo H. Séquin

University of California, Berkeley

Inspired by

Brent Collins

Gower, Missouri

CHSUCB ““Hyperbolic Hexagon” by B. CollinsHyperbolic 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 ?

CHSUCB Sculpture Generator, GUI Sculpture Generator, GUI

CHSUCB ““Hyperbolic Hexagon II” (wood)Hyperbolic Hexagon II” (wood)

Brent Collins

CHSUCB Family of Symmetrical TrefoilsFamily of Symmetrical Trefoils

W=2

W=1

B=1 B=2 B=3 B=4

CHSUCB 9-story Intertwined Double Toroid9-story Intertwined Double Toroid

Bronzeinvestment casting from wax original made on 3D Systems’“Thermojet”

CHSUCB Stepwise Expansion of HorizonStepwise 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

CHSUCB Note:Note:

The computer becomesan amplifier / acceleratorfor the creative process.

CHSUCB

Inspiration: Inspiration:

Brent Collins’ Brent Collins’

“Pax Mundi”“Pax Mundi”

CHSUCB Keeping up with Brent ...Keeping up with Brent ...

Sculpture Generator I can only do warped Scherk towers,not able to describe a shape like Pax Mundi.

Need a more general approach ! Use the SLIDE modeling environment

(developed at U.C. Berkeley by J. Smith)to capture the paradigm of such a sculpturein a procedural form. Express it as a computer program

Insert parameters to change salient aspects / features of the sculpture

First: Need to understand what is going on

CHSUCB Sculptures by Naum GaboSculptures by Naum Gabo

Pathway on a sphere:

Edge of surface is like seam of tennis ball;

2-period Gabo curve.

CHSUCB 2-period Gabo curve2-period Gabo curve

Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used.

CHSUCB 4-period Gabo curve4-period Gabo curve

Same construction as for as for 2-period curve

CHSUCB ““Pax Mundi” RevisitedPax Mundi” Revisited

Can be seen as:

Amplitude modulated, 4-period Gabo curve

CHSUCB SLIDESLIDE

SLIDE = Scene Language for Interactive Dynamic Environments

Developed as a modular rendering pipelinefor our introductory graphics course.

Primary Author: Jordan Smith

Based on OpenGL and Tcl/tk.

Good combination of interactive 3D graphicsand parameterizable procedural constructs.

CHSUCB SLIDE Example: Klein BottleSLIDE Example: Klein Bottle

Final Project CS 184, Nerius Landys & Shad Roundy

CHSUCB SLIDE Example Bug’s LifeSLIDE Example Bug’s Life

Final Project CS 184, David Cheng and James Chow

CHSUCB SLIDE as a Design ToolSLIDE as a Design Tool

SLIDE originally a modular rendering tool.

Later enhanced to serve as a CAD tool:

Spline curves and surfaces

Morphing sweeps along such curves

3D warping module (Sederberg, Rockwood)

Many types of subdivision surfaces

These are key elements for a 2nd Generation Sculpture Generator

CHSUCB SLIDE-UI for Knot GenerationSLIDE-UI for Knot Generation

CHSUCB

SLIDE-UI for “Pax Mundi” ShapesSLIDE-UI for “Pax Mundi” Shapes

CHSUCB Via Globi 5 (Gold)Via Globi 5 (Gold)

Wilmin Martono

CHSUCB Via Globi 3 (Stone)Via Globi 3 (Stone)

Wilmin Martono

CHSUCB ““Viae Globi” Family Viae Globi” Family (Roads on a Sphere)(Roads on a Sphere)

L2 L3 L4 L5

CHSUCB Conclusions (1)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.

CHSUCB Conclusions (2)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.

CHSUCB Conclusions (3)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 !

CHSUCB Conclusions (4)Conclusions (4)

Rapid prototyping (layered fabrication)must now be considered a new facetin the spectrum of MM technologies.

It provides tangible (high-quality haptic)output for objects with which usersmay want to interact.

Even for sculptures(intended primarily for visual enjoyment)the physical maquette disclosessubtle geometrical features that arenot visible in the virtual rendering.