James Hamlin and Carlo H. SéquinUniversity of California, Berkeley

Ribbed Surfaces for Art, Architecture, Visualization

Computer-Aided Design and ApplicationsReno, June 11, 2009

Overview

Charles O. Perry's Solstice Reverse engineering Solstice Ribbed Surface Paradigm Solstice Program Visualization of complex surfaces Ribbed surfaces in architecture

Motivation

Inspired byCharles O. Perry'sribbed sculptures.

Emulate and generalize by abstraction.

Parameterization of Solstice

(3, 2) torus knot

Curved “ribs” in nearlytriangular configuration

Parameterization of Solstice

(3, 2) torus knot

Curved “ribs” in nearlytriangular configuration

Parameterization of Solstice

Staggering of ribs:rib offset along

guide rail

Rib shapes:concave “hyperbolic”

triangles

Guide rail:(3, 2) torus knot

Ribbed Surfaces

Guide rail(s) very application specific.

Ribs swept along rail(s) shapes determined procedurally, e.g., in terms of guide rail derivative information

(Frenet frame).

Reduces the number of input parameters (e.g., compared to sweep surfaces).

Sweep Surfaces A

One or two path or rail curves

One or two more profile curves

Maya: Extrusions (A), Lofts (B), Bi-Rails (C).(A)

(C)(B)

Sweeping Ribs

Single rail[0, 0.5) → [0.5, 1.0)

Two rails[0, 0.5] → [0.0, 1.0]

Guide Rails: Solstice

Guide rails are application-specific

For Solstice: ( p, q ) torus knots

( 3, 2 )

( 4, 3 )

( 2, 3 )

Sweeping Ribs: Solstice

0°

303°

83°

360°

RibOffsets:

Rib Parameterization

Cubic Hermite Tangent directions and

magnitudes at both ends

Circular Arcs Embedding plane Turning angle

θRails Rails

Cubic Hermite Ribs

End tangents specified in terms of Frenet frames of guide rails.

V t

nb

Symmetric, Planar Cubic Hermite Ribs

Constrain ribs to be symmetric, planar.

Select a plane through chord with an angle against rail tangent.

Rib tangent angles are offset from chord;or a curve offset dfrom chord is set.

3D Cubic Hermite Ribs

A combination of the previous two approaches.

Uses: rail tangent,chord direction, and their cross product.

Rib Shapes in Solstice

Rib Shapes in Solstice

Solstice emulation uses circular arc ribs.

Plane determined by cross product of rib chord direction and normal of plane of minor circle.

Rib Shapes in Solstice

Solstice emulation uses circular arc ribs.

Plane determined by cross product of rib chord direction and normal of plane of minor circle.

Rib Shapes in Solstice

Solstice emulation uses circular arc ribs.

Plane determined by cross product of rib chord direction and normal of plane of minor circle.

Rib Shapes in Solstice

Solstice and Variations

Modified ( 2, 3 ) knotSolstice ( 3, 2 ) knot

Solstice and Variations

Modified ( 4, 3 ) knotSolstice ( 3, 2 ) knot

Solstice and Variations

Modified ( 4, 5 ) knotSolstice_2 ( 3, 2 ) knot(with denser ribs)

Early Mace (Atlanta, GA)

Emulation

Variation with straight ribs Variation with convex ribs

Harmony (Hartford, CT)

Two semi-circular guide rails. Four ribbed surfaces. Ribs take off in direction of curve normal.

Ribbed Surfaces in Visualization

Mathematician’s Models and Sculptures

HyperboloidBoy’s Surface String art by

Ray Schechter

Ribbed Surfaces in Visualization

Our Own Visualization Models

Non-orientable, single-sided building blocks for the construction of abstract 4D polyhedra

such as the 11-Cell and the 57-Cell.

Python Module

Python module for rapid development of design programs.

Quick and dirty creation of GUIthrough GLUI.

Supports output to RenderMan RIB format for high-quality rendering.

ConclusionsRibbed surfaces are a concise representation of a broad range of sculptural forms:

Reduced weight and construction costs. “Airy” realization, less shadows.

Ribbed “transparency” ideal for visualization of self-intersecting surfaces.

Naturally describes objects in architecture or in other design domains:

Balcony railings, furniture.

QUESTIONS?