James Hamlin and Carlo H. Séquin University of California, Berkeley Ribbed Surfaces for Art, Architecture, Visualization Computer-Aided Design and Applications Reno, June 11, 2009
Feb 24, 2016
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?