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

Algorithm 2

Computing the content of $n$D space enclosed by an OPP.

Input: An $n$D-EVM p.

     The number n of dimensions.

Output: The content of nD space enclosed by p.

Procedure Content(EVM p, int n)

       real cont = 0.0// The content of nD space enclosed by p.

       EVM hvl1, hvl2// Consecutive couplets perpendicular to X_A-axis.

       EVM s// Current section of p.

       if (n = 1) then return Length(p) // Base case: p is a 1D-OPP.

       else

          s = InitEVM( )

          hvl1 = ReadHvl(p)

          while (Not(EndEVM(p)))

                   hvl2 = ReadHvl(p)

                    s = GetSection(s, hvl1)

                    cont = cont + Content(s, n-1) * dist(hvl1, hvl2)

                    hvl1 = hvl2

          end-of-while

          return cont

       end-of-else

end-of-procedure