Solid Freeform Fabrication of Aesthetic Objects George W. Hart Stony Brook University Dept. Computer...
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Transcript of Solid Freeform Fabrication of Aesthetic Objects George W. Hart Stony Brook University Dept. Computer...
Solid Freeform Fabrication of Aesthetic Objects
George W. Hart
Stony Brook University
Dept. Computer Science
1. Sculpture
2. Mathematical Models:
• Fractals
• Goldberg Polyhedra
• 4D Polytope Projections
3. Historical Leonardo Models
4. Orderly Tangles
5. Puzzles
6. Student Projects
1. Sculpture
72 Pencils
Chronosynclastic Infundibulum
Just Two Cavities
Disk Combobulation
The Plastic Tableware of Damocles
Rainbow Bits
Fire and Ice
I’d like to make one thing perfectly clear
Battered Moonlight
Yin and Yang
Gazmogenesis
Rorschachohedron
Fat and Skinny
Whoville
Whoville -- detail
Roads Untaken
The Susurrus of the Sea
Loopy
Millennium Bookball
Twisted Rivers, Knotted Sea
Twisted Rivers, Knotted Sea
Twisted Rivers -- reconstruction
Twisted Rivers – RP design
Tangled Reindeer
This End Up
Knot Structured
Nessie
Quintessence of Hedgehog
Bouquet
Frabjous
Salamanders
SFF Model (2.5 inch diam.)
Complete!
“People”
Snarl — wood model, 14 inch
Snarl — SFF model, 1 inch
Snarl — SFF model, 2 inch
Star Corona
Compass Points
Compass Points
“Cagework”
Aardvarks
Spaghetti Code
Rendering
Rendering, along 5-fold axis
Solid Freeform Fabrication Model
Spaghetti Code
Deep Structure
Gonads of the Rich and Famous
Gonads of the Rich and Famous-- design --
Gonads of the Rich and Famous-- design --
Untitled
Untitled
Untitled
Untitled
Untitled
2. Mathematical Models
Fractal — Sierpinski Tetrahedron
Connected Structure
Snub Truncated Icosahedron
Zonohedron-61
4D Polytope Projection Models
FDM Machine with 120-Cell Model
120-Cell, before dissolving support
120-Cell
• 120 cells, 720 faces, 1200 edges, 600 vertices.
• Cell-first parallel projection,(shows less than half of the edges.)
Five-Legged-Bee Hive
120-Cell – perspective projection
(smallest ?) 120-Cell
Wax model, made on Sanders machine
120-Cell – perspective projection
Selective laser sintering
Truncated 120-Cell
Truncated 120-Cell - Stereolithography
Zometool Truncated 120-Cell
MathCamp 2000
Ambo 600-Cell
Bridges Conference, 2001
Ambo 120-Cell
Orthogonal projection
Stereolithography
Can do with Zome
48 Truncated Cubes
Poor FDM model
Goldberg Polyhedra(Fullerenes)
“Buckyballs”• C60, form of carbon
• 1985 discovery
• 1996 Nobel Prize in chemistry
• By:– Richard Smalley (Rice Univ.)– Robert Curl (Rice Univ.)– Sir Harold Kroto
Geodesic Dome from Icosahedron
Dual Tessellations
Triangular Subdivisions
Area = x2 + xt + t2
Goldberg Polyhedra
(2,0)
(2,1)
(3,0)
Goldberg(2,2) Goldberg(4,1)
Goldberg (3,3) Goldberg(6,0)
Goldberg (7,3)
Goldberg (7,3)
Ernst Haeckel
Ernst Haeckel
Artificial Radiolarian
Goldberg (2,1)
Goldberg (3,1)
Goldberg (3,1)
Metal Goldberg (8, 3)
Nested Spheres
Nested Balls
Untitled (Abraham Sharp)
Untitled (Abraham Sharp)
3. Historical Models Leonardo / Pacioli
Sphere Model from Euclid
Leonardo Model
Leonardo Model
4. Orderly Tangles
Regular Polylinks
• Symmetric linkages of regular polygons
• Alan Holden built models– Cardboard or dowels
• Holden wrote:– Shapes, Spaces and
Symmetry,1971– “Regular Polylinks”,
1980– Orderly Tangles, 1983
• Table of lengths 4 Triangles
Regular Polylinks
4 Triangles 6 Squares
Left and right hand forms
Regular Polylinks
12 Pentagons
Regular Polylinks
6 Pentagons - size scaled
Derivation from Regular Polyhedron
Rotate faces Slide in or out
Wooden Puzzles
• Taiwan– Teacher Lin– Sculptor Wu
• Square cross sections
• Simple lap joint• No glue• Trial and error to
determine length12 Pentagons
Second Puzzle from Lin and Wu
10 Triangles
Many Analogous Puzzles
Possible• Each regular polylink gives a puzzle• Also can combine several together:
– Different ones interweaved– Same one nested
• Need critical dimensions to cut lengths• No closed-form formulas for lengths• Wrote program to:
– Determine dimensions– Output templates to print, cut, assemble– Output STL files for solid freeform
fabrication
Generates Template to Print and Cut
4 Triangles
Paper or Wood Models
6 Squares
Solid Freeform Fabrication
6 Squares
Square Cross Section
6 Pentagons
Paper or Wood Models
Orderly Tangle Puzzle
aluminum
30 parts
Selective Laser Sintering (SLS)
Selective Laser Sintering
Curved ComponentsCentral Inversion
4 Triangles Inverted
Curved ComponentsCentral Inversion
20 Triangles Inverted
SLS Models — Inverted Tangles
4 triangles 5 tetrahedra
Tangle Software
Available free at
http://www.georgehart.com
5. Puzzles
Sculpture Puzzles
aluminum
12 parts
Sculpture Puzzles
SLS
3 inch
30-Piece Puzzle
6. Student Projects
CSE391 Special TopicsAlgorithms for Solid Modeling
Student Projects