Unfolding H-convex Manhattan towers (Q2084660)

A \textit{Manhattan tower} is a set of cubes defined by a rectangular 2D matrix \(M\) (Manhattan matrix), containing only positive or null integer values. A value \(M(i, j) = k\) in \(M\) represents a tower, a stack of \(k\) cubes of coordinates between \((i, j, 0)\) to \((i, j, k-1)\) and such that the cubes of all the towers form a polycube. An \textit{\(H\)-convex} (horizontal-convex) Manhattan tower is a Manhattan tower such that each \(x\)-row of the corresponding Manhattan matrix is formed of a unique contiguous sequence of strictly positive integer values (there can be zeroes at the beginning or end of the row but not in between non null values). An \textit{up-and-down orthoterrain} is defined by a rectangular matrix where all the values are formed of a pair of integers \((m_{i, j} , M_{i, j})\), such that \(m_{i, j} < M_{i, j}\). Each pair represents a set of cubes of coordinates \((i, j, z)\in {\mathbb Z}^3\) with \(m_{i, j}\leq z < M_{i, j}\). The aim of this paper is to present a new algorithm of grid edge-unfolding without refinement for Manhattan towers with a H-convex base, an algorithm that can be extended to up-and-down orthoterrains.