mycaule / hinge-patterns

Hinge Patterns

Compare ASCII encoding and Hinge encoding.

$ sbt run

A: ArraySeq(65)
   ArraySeq(List(1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 3, 0, 0, 4, 0, 2))
B: ArraySeq(66)
   ArraySeq(List(1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 3, 0, 1, 0, 2, 0, 0))
C: ArraySeq(67)
   ArraySeq(List(0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0))
Hello: ArraySeq(72, 101, 108, 108, 111)
   ArraySeq(List(1, 0, 0, 0, 3, 0, 1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 2), List(0, 0, 2, 0, 1, 0, 0, 3, 0, 1, 0, 2, 0, 0), List(0, 0, 0, 0, 0, 4, 3, 0, 0), List(0, 0, 0, 0, 0, 4, 3, 0, 0), List(0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2))
1: ArraySeq(49)
   ArraySeq(List(0, 5, 0, 0, 0, 0, 5, 2))
2: ArraySeq(50)
   ArraySeq(List(0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0))
3: ArraySeq(51)
   ArraySeq(List(0, 0, 2, 0, 1, 0, 0, 3, 0, 1, 0, 2, 0, 0))
42: ArraySeq(52, 50)
   ArraySeq(List(1, 0, 2, 0, 2, 0, 0, 3, 0, 1, 0, 2, 0, 0, 3, 0, 0, 0, 2), List(0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0))

For example,

// letter 1 needs 8 folds using 0, 2, 5
Seq(0, 5, 0, 0, 0, 0, 5, 2)

// letter X needs 22 folds using 0, 1, 2, 3.
Seq(1, 1, 1, 0, 2, 2, 0, 3, 1, 1, 1, 2, 2, 2, 0, 3, 1, 1, 0, 2, 2, 2)

References

• Nadia Benbernou et al. - Universal Hinge Patterns for Folding Strips Efficiently into Any Grid Polyhedron
• Erik Demaine - Strip Folding Font
• Roger Mansuy's tweet
• Similar to the mower problem in mycaule/bb-assessment