Post on 02-Jan-2016
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CS 285, Fall 2007CS 285, Fall 2007
Analogies from 2D to 3D
Carlo H. Séquin
University of California, Berkeley
Exercises to Stimulate Creative Thinking
Do this in 3D !
3D Yin-Yang Solutions:3D Yin-Yang Solutions:Two congruent partsTwo congruent parts(Fall 1997)(Fall 1997)
A. Hsu: Clay Model R. Hillaire: R. Hillaire: Acrylite Model
J. Smith: Computer Model
3D Yin-Yang (Robert Hillaire)3D Yin-Yang (Robert Hillaire)
Max Bill’s SolutionMax Bill’s Solution
Many Solutions for 3D Yin-YangMany Solutions for 3D Yin-Yang
Most popular: -- Max Bill solution
Unexpected: -- Splitting sphere in 3 parts
Hoped for: -- Semi-circle sweep solutions
Machinable: -- Torus solution
Perfection ? -- Cyclide solution
Yin-Yang VariantsYin-Yang Variants
http//korea.insights.co.kr/symbol/sym_1.html
Yin-Yang VariantsYin-Yang Variants
http//korea.insights.co.kr/symbol/sym_1.html
The three-part t'aeguk symbolizes heaven, earth, and humanity. Each part is separate but the three parts exist in unity and are equal in value. As the yin and yang of the Supreme Ultimate merge and make a perfect circle, so do heaven, earth and humanity create the universe. Therefore the Supreme Ultimate and the three-part t'aeguk both symbolize the universe.
Yin-Yang SymmetriesYin-Yang Symmetries
From the constraint that the two halves should be either identical or mirror images of one another, follow constraints for allowable dividing-surface symmetries.
C2 S2Mz
My Preferred 3D Yin-YangMy Preferred 3D Yin-Yang
The Cyclide Solution:
Yin-Yang is built from cyclides only !
What are cyclides ?
Spheres, Cylinders, Cones, andall kinds of Tori (Horn tori, spindel tory).
Principal lines of curvature are circles.
Minumum curvature variation property !
3D Yin-Yang 3D Yin-Yang :: Two mirror partsTwo mirror parts
Stereolithography models (Séquin 1999)
The 2D Hilbert Curve (1891)The 2D Hilbert Curve (1891)A plane-filling Peano curve
Do This In 3 D !
Construction of 3D Hilbert CurveConstruction of 3D Hilbert Curve
Construction of 3D Hilbert CurveConstruction of 3D Hilbert Curve
Use this element with proper orientation, mirroring.
Typical Early Student SolutionTypical Early Student Solution
Design Flaws:
2 collinear segments
less than maximal symmetry
4 coplanar segments
D. Garcia, and T. Eladi (1994)
Jane Yen: “Jane Yen: “Hilbert Radiator PipeHilbert Radiator Pipe” ” (2000)(2000)
Flaws( from a sculptor’s . point of view ):
4 coplanar segments
Not a closed loop
Broken symmetry
Design Choices: 3D Hilbert CurveDesign Choices: 3D Hilbert Curve
What are the things one might optimize ?
Maximal symmetry
Overall closed loop
No consecutive collinear segments
No (3 or 4 ?) coplanar segment sequence
others ... ?
More than one acceptable solution !
Basic Element, Lowest LevelBasic Element, Lowest Level
not this – but this
avoid 4 coplanar segments !
Plastic Model (from FDM) (1998)Plastic Model (from FDM) (1998)
Support removal can be tedious, difficult !
The Next Level of RecursionThe Next Level of Recursion
Presented a challenge to remove supports.
Resulted in a flimsy, spongy model.
Would like to have a more durable model in metal.
2006: Metal Sculpture in Exhibit2006: Metal Sculpture in Exhibit
Design:Design: closed loopclosed loop maximal symmetrymaximal symmetry at most 3 coplanar segmentsat most 3 coplanar segments
CREATIVITYCREATIVITY
PLAY