Efficient Boundary Extraction from Orthogonal Pseudo-Polytopes: An Approach Based on the 𝑛D-EVM

Table 5

Identifying faces, of the 3D-OPP from Figure 5, through backward differences and Algorithm 4 (see text for details. Faces’ vertices are listed in the order they are discovered).

	Backward difference	Connected components labeling	Discovered vertices and faces
			𝑣21,𝑣22,𝑣23,𝑣24; 𝑉(𝑝)={𝑣1,𝑣2,𝑣3,𝑣4,𝑣5,𝑣6,𝑣7,𝑣8,𝑣9,; 𝑣10,𝑣11,𝑣12,𝑣13,𝑣14,𝑣15,𝑣16,; 𝑣17,𝑣18,𝑣19,𝑣20,𝑣21,𝑣22,𝑣23,𝑣24}; 𝐹(𝑝)={{𝑣1,𝑣2,𝑣3,𝑣4},{𝑣5,𝑣6,𝑣7,𝑣8},; {𝑣9,𝑣10,𝑣11,𝑣12},{𝑣13,𝑣14,𝑣15,𝑣16},; {𝑣17,𝑣18,𝑣19,𝑣20},{𝑣21,𝑣22,𝑣23,𝑣24}}
			𝑣2,𝑣25,𝑣26,𝑣27; (Vertex 𝑣2 was discovered; when processing FD^11(𝑝)); 𝑉(𝑝)={𝑣1,𝑣2,𝑣3,𝑣4,𝑣5,𝑣6,𝑣7,𝑣8,𝑣9,; 𝑣10,𝑣11,𝑣12,𝑣13,𝑣14,𝑣15,𝑣16,; 𝑣17,𝑣18,𝑣19,𝑣20,𝑣21,𝑣22,𝑣23,𝑣24,; 𝑣25,𝑣26,𝑣27}; 𝐹(𝑝)={{𝑣1,𝑣2,𝑣3,𝑣4},{𝑣5,𝑣6,𝑣7,𝑣8},; {𝑣9,𝑣10,𝑣11,𝑣12},{𝑣13,𝑣14,𝑣15,𝑣16},; {𝑣17,𝑣18,𝑣19,𝑣20},{𝑣21,𝑣22,𝑣23,𝑣24},; {𝑣2,𝑣25,𝑣26,𝑣27}}
			𝑣1,𝑣2,𝑣28,𝑣29; (Vertices 𝑣1 and 𝑣2 were; discovered when processing FD^11(𝑝)); 𝑉(𝑝)={𝑣1,𝑣2,𝑣3,𝑣4,𝑣5,𝑣6,𝑣7,𝑣8,𝑣9,; 𝑣10,𝑣11,𝑣12,𝑣13,𝑣14,𝑣15,𝑣16,𝑣17,; 𝑣18,𝑣19,𝑣20,𝑣21,𝑣22,𝑣23,𝑣24,𝑣25,; 𝑣26,𝑣27,𝑣28,𝑣29}; 𝐹(𝑝)={{𝑣1,𝑣2,𝑣3,𝑣4},{𝑣5,𝑣6,𝑣7,𝑣8},; {𝑣9,𝑣10,𝑣11,𝑣12},{𝑣13,𝑣14,𝑣15,𝑣16},; {𝑣17,𝑣18,𝑣19,𝑣20},{𝑣21,𝑣22,𝑣23,𝑣24},; {𝑣2,𝑣25,𝑣26,𝑣27},{𝑣1,𝑣2,𝑣28,𝑣29}}