Local and Global Flat-foldability
Kawasaki's theorem, applied to each of the vertices of an arbitrary crease pattern, determines whether the crease pattern is locally flat-foldable, meaning that the part of the crease pattern near the vertex can be flat-folded. However, there exist crease patterns that are locally flat-foldable but that have no global flat folding that works for the whole crease pattern at once. Tom Hull (1994) conjectured that global flat-foldability could be tested by checking Kawasaki's theorem at each vertex of a crease pattern, and then also testing bipartiteness of an undirected graph associated with the crease pattern, but this conjecture was disproven by Bern & Hayes (1996), who showed that the problem of testing global flat-foldability is NP-complete.
Read more about this topic: Kawasaki's Theorem
Famous quotes containing the words local and/or global:
“There is the falsely mystical view of art that assumes a kind of supernatural inspiration, a possession by universal forces unrelated to questions of power and privilege or the artist’s relation to bread and blood. In this view, the channel of art can only become clogged and misdirected by the artist’s concern with merely temporary and local disturbances. The song is higher than the struggle.”
—Adrienne Rich (b. 1929)
“As the global expansion of Indian and Chinese restaurants suggests, xenophobia is directed against foreign people, not foreign cultural imports.”
—Eric J. Hobsbawm (b. 1917)