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

Table 4

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

	Forward difference	Connected components labeling	Discovered vertices and faces
			𝑣1,𝑣2,𝑣3,𝑣4
			(Vertex 𝑣1 was not in EVM3(𝑝)).; 𝑉(𝑝)={𝑣1,𝑣2,𝑣3,𝑣4}; 𝐹(𝑝)={{𝑣1,𝑣2,𝑣3,𝑣4}}
			𝑣5,𝑣6,𝑣7,𝑣8; 𝑉(𝑝)={𝑣1,𝑣2,𝑣3,𝑣4,𝑣5,𝑣6,𝑣7,𝑣8}; 𝐹(𝑝)={{𝑣1,𝑣2,𝑣3,𝑣4},{𝑣5,𝑣6,𝑣7,𝑣8}}
			𝑣9,𝑣10,𝑣11,𝑣12; 𝑉(𝑝)={𝑣1,𝑣2,𝑣3,𝑣4,𝑣5,𝑣6,𝑣7,𝑣8,𝑣9,𝑣10,; 𝑣11,𝑣12}; 𝐹(𝑝)={{𝑣1,𝑣2,𝑣3,𝑣4},{𝑣5,𝑣6,𝑣7,𝑣8},; {𝑣9,𝑣10,𝑣11,𝑣12}}
			𝑣13,𝑣14,𝑣15,𝑣16; 𝑉(𝑝)={𝑣1,𝑣2,𝑣3,𝑣4,𝑣5,𝑣6,𝑣7,𝑣8,𝑣9,𝑣10,; 𝑣11,𝑣12,𝑣13,𝑣14,𝑣15,𝑣16}; 𝐹(𝑝)={{𝑣1,𝑣2,𝑣3,𝑣4},; {𝑣5,𝑣6,𝑣7,𝑣8},{𝑣9,𝑣10,𝑣11,𝑣12},; {𝑣13,𝑣14,𝑣15,𝑣16}}
			𝑣17,𝑣18,𝑣19,𝑣20; 𝑉(𝑝)={𝑣1,𝑣2,𝑣3,𝑣4,𝑣5,𝑣6,𝑣7,𝑣8,𝑣9,𝑣10,; 𝑣11,𝑣12,𝑣13,𝑣14,𝑣15,𝑣16,𝑣17,𝑣18,; 𝑣19,𝑣20}; 𝐹(𝑝)={{𝑣1,𝑣2,𝑣3,𝑣4},{𝑣5,𝑣6,𝑣7,𝑣8},; {𝑣9,𝑣10,𝑣11,𝑣12},{𝑣13,𝑣14,𝑣15,𝑣16},; {𝑣17,𝑣18,𝑣19,𝑣20}}