Ribbed Surfaces for Art, Architecture, Visualization

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Ribbed Surfaces for Art, Architecture,
Visualization
James Hamlin and Carlo H. Séquin University of
California, Berkeley
Computer-Aided Design and Applications Reno, June
11, 2009
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Overview

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

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Motivation

• Inspired byCharles O. Perry'sribbed
  sculptures.
• Emulate and generalize by abstraction.

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Parameterization of Solstice

• (3, 2) torus knot
• Curved ribs in nearly
• triangular configuration

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Parameterization of Solstice

• (3, 2) torus knot
• Curved ribs in nearly
• triangular configuration

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Parameterization of Solstice
Staggering of ribsrib offset alongguide rail
Rib shapes concave hyperbolic triangles
Guide rail (3, 2) torus knot
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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).

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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)
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Sweeping Ribs
Single rail 0, 0.5) ? 0.5, 1.0)
Two rails 0, 0.5 ? 0.0, 1.0
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Guide Rails Solstice
Guide rails are application-specific For
Solstice ( p, q ) torus knots
( 4, 3 )
( 3, 2 )
( 2, 3 )
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Sweeping Ribs Solstice
Rib Offsets
0
83
303
360
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Rib Parameterization

• Cubic Hermite
• Tangent directions and magnitudes at both ends

• Circular Arcs
• Embedding plane
• Turning angle

Rails
Rails
?
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Cubic Hermite Ribs

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

n
b
t
V
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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 chordor a
  curve offset dfrom chord is set.

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3D Cubic Hermite Ribs

• A combination of the previous two approaches.
• Uses rail tangent,chord direction, and their
  cross product.

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Rib Shapes in Solstice
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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.

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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.

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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.

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Rib Shapes in Solstice
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Solstice and Variations
Modified ( 2, 3 ) knot
Solstice ( 3, 2 ) knot
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Solstice and Variations
Modified ( 4, 3 ) knot
Solstice ( 3, 2 ) knot
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Solstice and Variations
Modified ( 4, 5 ) knot
Solstice_2 ( 3, 2 ) knot (with denser ribs)
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Early Mace (Atlanta, GA)
Emulation
Variation with straight ribs
Variation with convex ribs
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Harmony (Hartford, CT)

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

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Ribbed Surfaces in Visualization
Mathematicians Models and Sculptures
Hyperboloid
Boys Surface
String art by
Ray Schechter
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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.
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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.

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Conclusions

• Ribbed 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.

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QUESTIONS?