Moldable and Castable Polygons

This paper introduces the concepts of Moldability and Castability of simple polygons and relates Moldability to Monotonicity. We detail a (n) algorithm for determining all n forward maximal monotone chains of a simple polygon and apply this algorithm to the problems of determining 2-Moldability, 2-Castability and the minimum monotone decomposition of a simple polygon 9]. Our results include a simple optimal algorithm solving the minimum monotone decomposition problem, an optimal algorithm to determine 2-Moldability and an O(n log n) algorithm to determine 2-Castability.