Post on 21-Oct-2020
Extruding Towers by Serially Grafting FrustaCHENG HerngYi herngyi@mit.edu
Massachusetts Institute of Technology
mailto:herngyi@mit.edu
IntroductionAutomated origami design: demo
Extrusion Origami
Cheng (2010 – 5OSME)
Cheng (2012)
Ovadya (2009)
Mitani (2009)
Related Work
ORI-REVO,Jun Mitani
Origami Flanged Pots,Robert Lang
Related Work
Mitani Lang Cheng
“flanges”
Grafting
i. Fold an origami (e.g. pattern of scales)
ii. Treat the product as a fresh sheet of paper
iii. Fold another origami (e.g. fish) to combine
Image source: Lang, Koi, opus 425, The Math and Magic of Origami, TED.com (2008)
Grafting
i. Fold an origami
ii. Treat the product as a fresh sheet of paper
iii. Fold another origami to combine
Modularized Design
Break solid into smaller frusta
Frustum(pl. frusta)
Right Frustum
Positive Frustum CP
Special case of biplanar!
Negative Frustum CP
Central Body and Pleats
Grafting Frusta
Modularized Folding: “Hill”
Examples:“Spike”
Examples:Negative Frusta
“Ripple”
“Volcano”
Composing Crease PatternsCPs of each “building block” CP for the combined whole
Pleats Split Creases
Partitioning into Sectors
Can’t unfold pleats one by one
“Cut” the paper into independent sectors then unfold pleats independently
Same as unfolding everything at once
Translating Sectors
Algorithm
Input: Tower of right frusta
Output: CP that folds into the tower
1. Start with a blank CP
2. Use bottommost frustum F for calculations
3. Divide the CP into sectors
4. Translate sectors outward according to F
5. Open up the pleats of F
6. Add the creases of F itself
7. Remove F from the tower
8. Repeat step 2—7 until the whole tower is consumed
Cheng, H. Y. & Cheong, K. H. Designing crease patterns for polyhedra by composing right frusta. Computer-Aided Design 44, 331-342 (2012)
http://www.sciencedirect.com/science/article/pii/S0010448511003058
GeneralizationNo need for n-fold symmetry!
General Frusta
Positive Frusta Negative Frusta
General Frusta
Positive Frusta Negative Frusta
Central Body and Pleats
Modified Sectors
Algorithm
Input: Tower of right frusta
Output: CP that folds into the tower
1. Start with a blank CP
2. Use bottommost frustum F for calculations
3. Divide the CP into sectors
4. Translate sectors outward according to F
5. Open up the pleats of F
6. Add the creases of F itself
7. Remove F from the tower
8. Repeat step 2—7 until the whole tower is consumed
ConclusionJust some final remarks…
Frustum Towers
Future: concave cross-sections? Many towers from one sheet?
Grafting
Modularized design algorithm Decrease-and-conquer origami design
Modularized folding algorithm Collapsing CPs is hard
Thank YouCHENG HerngYi herngyi.com
herngyi@mit.edu
mailto:herngyi@mit.edu