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On Local Transformations of Simple Polygons

Michael E. Houle

Department of Computer Science,
The University of Newcastle,
Callaghan, Newcastle, NSW 2308, Australia.

mike@cs.newcastle.edu.au

#### Abstract

This paper investigates the following fundamental problems from computational
geometry:
Given an integer $k$, a set of points $S$, and a non-convex simple
polygon $P$, is it always possible to transform $P$ into a new polygon $P'$
on $S$ by the modification of at most $k$ edges?

Given two polygons $P$ and $P'$ on a common vertex set $S$, is it
always possible to transform $P$ into $P'$ via a finite sequence of
modifications (called $k$-flips) of this type?

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