Results 1 
4 of
4
Computing Signed Permutations of Polygons
, 2002
"... Given a planar polygon (or chain) with a list of edges fe 1 ; e 2 ; e 3 ; : : : ; e n 1 ; e n g, we examine the effect of several operations that permute this edge list, resulting in the formation of a new polygon. The main operations that we consider are: reversals which involve inverting the order ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
Given a planar polygon (or chain) with a list of edges fe 1 ; e 2 ; e 3 ; : : : ; e n 1 ; e n g, we examine the effect of several operations that permute this edge list, resulting in the formation of a new polygon. The main operations that we consider are: reversals which involve inverting the order of a sublist, transpositions which involve interchanging subchains (sublists), and edgeswaps which are a special case and involve interchanging two consecutive edges. Using these permuting operations, we explore the complexity of performing certain actions, such as convexifying a given polygon or obtaining its mirror image. When each edge of the given polygon has also been assigned a parity we say that the polygon is signed. In this case any edge involved in a reversal changes parity. The complexity of some problems varies depending on whether a polygon is signed or unsigned. An additional restriction in many cases is that polygons remain simple after every permutation.
Band Unfoldings and Prismatoids: A Counterexample
, 2008
"... This note shows that the hope expressed in [ADL + 07]—that the new algorithm for edgeunfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap—cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band, ..."
Abstract
 Add to MetaCart
This note shows that the hope expressed in [ADL + 07]—that the new algorithm for edgeunfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap—cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band, with the property that every placement of the prismatoid top face overlaps with the band unfolding. 1
Band Unfoldings and Prismatoids: A Counterexample
, 2008
"... This note shows that the hope expressed in [ADL + 07]—that the new algorithm for edgeunfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap—cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band, ..."
Abstract
 Add to MetaCart
This note shows that the hope expressed in [ADL + 07]—that the new algorithm for edgeunfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap—cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band, with the property that every placement of the prismatoid top face overlaps with the band unfolding. 1
Unfolding FaceNeighborhood Convex Patches: Counterexamples and Positive Results
"... We address unsolved problems of unfolding polyhedra in a new context, focusing on special convex patches—disklike polyhedral subsets of the surface of a convex polyhedron. One longunsolved problem is edgeunfolding prismatoids. We show that several natural strategies for unfolding a prismatoid can ..."
Abstract
 Add to MetaCart
We address unsolved problems of unfolding polyhedra in a new context, focusing on special convex patches—disklike polyhedral subsets of the surface of a convex polyhedron. One longunsolved problem is edgeunfolding prismatoids. We show that several natural strategies for unfolding a prismatoid can fail, but obtain a positive result for “petal unfolding ” topless prismatoids, which can be viewed as particular convex patches. We also show that the natural extension of an earlier result on faceneighborhood convex patches fails, but we obtain a positive result for nonobtusely triangulated faceneighborhoods. 1