Computing the Discrete Compactness of Orthogonal Pseudo-Polytopes via Their 𝑛D-EVM Representation

Algorithm 4

Computing the number of ($n$-1)D adjacencies between the hypervoxels that originally defined an $n$D-OPP p.

Input:   An $n$D-EVM $p$ and the number $n$ of dimensions.

Output:  The number of internal contacts, perpendicular to the X_A-axis, between

     the hypervoxels that originally composed p.

Procedure  InternalContacts(EVM p, int n)

      EVM hvl// Current couplet of p.

      EVM ${\text{S}}_{\text{i}}$, ${\text{S}}_{\text{j}}$// Previous and next sections about hvl.

      EVM ${\text{S}}_{\mathrm{int}\hspace{0.17em}}$// The result of intersecting the projections of S_i and S_j.

      int c₁// Common X_A-coordinate of couplet hvl.

      int c₂// Common X_A-coordinate of couplet next to hvl.

      int nCoords// Number of integer coordinates between c₁ and c₂.

      int L = 0// Number of internal contacts ((n-1)D adjacencies).

      S_i = InitEVM( )

      c₁ = GetCoordNextHvl(p)

      hvl = ReadHvl(p)

      while (Not(EndEVM(p)))

     S_j = GetSection(S_i, hvl)

     c₂ = GetCoordNextHvl(p)

     nCoords = ${\text{c}}_2-{\text{c}}_1-1$

     L = L + nCoords * Content(S_j, n $-$ 1)

     S_int = BooleanOperation(${\text{S}}_{\text{i}}$, ${\text{S}}_{\text{j}}$, Intersection, n $-$ 1)

     L = L + Content(${\text{S}}_{\mathrm{int}\hspace{0.17em}}$, n $-$ 1)

     S_i = S_j

     c₁ = c₂

     hvl = ReadHvl(p)// Read next couplet.

     end-of-while

     return L

end-of-procedure