Definitions
angle-monotone motion
:a motion in which each vertex
angle is a monotone function in time.
configuration:
a polygon with the same counterclockwise set of edge lengths as another.
convexify :
to reconfigure a polygon into a convex one.
convex
configuration:
a convex configuration of edge lengths L
1 , L
2 , ..., L
n is a convex polygon with edge
lengths in that counterclockwise order.
distance-monotone motion
: a motion between two convex polygons
in which every distance between a pair of vertices varies monotically with
time.
hyperplane-flip:
similar to a pivot, a hyperplane-flip of a polygon P consists of
the reflection of a polygonal chain of P across a hyperplane H supporting
the convex hull of P and containing at least two vertices of P.
inscribed configuration:
a configuration in which each of the vertices of a polygon are co-circular.
linkage: a closed set
of hinges and rigid bars; the hinges can be seen as "linking" the bars
together, and allowing the bars motion limited only by their dinmensional
space and their attachment to another link.
motion
: see reconfiguration
pivot: a pivot on line segment
Vi V
j is a motion whereby the section
of the polygon between V i
and V j
is rotated about the diagonal V i
Vj
polygon:
here polygon P is characterized by
- its vertices, denoted V
1, V
2, ..., V
n in counterclockwise order.
- its edges E
i, where E
i = (V
i, V
i+1)
- its edge lengths l = |
E i| = |
V i -
V i+1|
All operations carried out
on polygons of n vertices will be done modulo n.
reconfiguration: a continuous function
of time from the unit interval [0,1] to a configuration.
universality: the proving of a number
of variations of a result by numerous independent sources, leading to the
acceptance that result is generalizable to many cases (or universal).
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