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恳请大家将这个理论翻译一下,谢谢!
Define a simply connected tree T with leaf nodes Pi
,
i = 1, 2,…N. Define by l
ij
the dis-tance between nodes
Piand P
j
as measured along the edges of the tree; that
is, l
ij
is the sum of the lengths of all the edges between
nodes P
iand P
j. For each leaf node P
i
, define a leaf
vertex ui
in the unit square u
i,x∈[0,1], u
i,y∈[0,1]. Then
a crease pattern exists that transforms the unit square
into a uniaxial base whose projection is T if
(a) |ui
–uj
| ≥ l
ij
for every i,j;
(b) every leaf vertex belongs to a polygon whose
boundary is composed of segments, each of
which is either on the convex hull of the leaf
vertices or is a line along which |ui
–uj
| = l
ij
;
(c) the projection of a path around each polygon
follows a simple path around some subset of
the tree that does not cross any edge of the tree
more than twice.
Furthermore, in such a base, Pi
is the projection of ui
for all i.
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