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

Algorithm 3

Computing regularized Boolean operations on the EVM.

Input: The nD-OPPs $p$ and $q$ expressed in the $n$D-EVM.

         The number n of dimensions and regularized Boolean operation op.

Output: The output nD-OPP r, such that r = $p$ op*$q$, codified as an $n$D-EVM.

Procedure BooleanOperation(EVM p, EVM q, BooleanOperator op, int n)

       EVM sP, sQ // Current sections of p and q respectively.

       EVM hvl // I/O couplet.

       boolean fromP, fromQ // flags for the source of the couplet hvl.

       CoordType coord // the common coordinate of couplets.

       EVM r, sRprev, sRcurr // nD-OPP r and two of its sections.

       if (n = 1) then // Base case

         return BooleanOperation1D(p, q, op)

       else

         n = n $-$ 1

         sP = InitEVM( )

         sQ = InitEVM( )

         sRcurr = InitEVM( )

         NextObject(p, q, coord, fromP, fromQ)

         while (Not(EndEVM(p)) and Not(EndEVM(q)))

                if (fromP = true) then

                      hvl = ReadHvl(p)

                      sP = GetSection(sP, hvl)

                end-of-if

               if (fromQ = true) then

                      hvl = ReadHvl(q)

                      sQ = GetSection(sQ, hvl)

               end-of-if

               sRprev = sRcurr

               sRcurr = BooleanOperation(sP,sQ,op,n) // Recursive call

               hvl = GetHvl(sRprev, sRcurr)

               SetCoord(hvl, coord)

               PutHvl(hvl, r)

               NextObject(p, q, coord, fromP, fromQ)

         end-of-while

         while (Not(EndEVM(p)))

               hvl = ReadHvl(p)

               PutBool(hvl, r, op)

         end-of-while

         while (Not(EndEVM(q)))

               hvl = ReadHvl(q)

               PutBool(hvl, r, op)

         end-of-while

         return r

       end-of-if

end-of-procedure