Geometric tables for 3D object

Geometric tables are the data tables that describe the shape of a polygon-mesh object: a vertex table (coordinates), an edge table (end vertices of each edge) and a polygon/surface table (edges of each face). A 3D object is the collection of its surfaces, so the three tables together define the whole object; extra tables store attributes (colour, transparency).

Example: a square pyramid has 5 vertices, 8 edges and 5 faces.

Vertex table        Edge table          Surface table
V1 (0,0,0)          E1: V1 V2           S1: E1 E2 E3 E4 (base)
V2 (2,0,0)          E2: V2 V3           S2: E1 E6 E5
V3 (2,2,0)          E3: V3 V4           S3: E2 E7 E6
V4 (0,2,0)          E4: V4 V1           S4: E3 E8 E7
V5 (1,1,2)          E5: V1 V5           S5: E4 E5 E8
                    E6: V2 V5
                    E7: V3 V5
                    E8: V4 V5

For fast processing, the edge table may also hold the faces that share each edge (E1: S1, S2), and the vertex table the edges meeting at each vertex.

Conditions for an error-free table

1. Every vertex belongs to at least two edges.
2. Every edge belongs to at least one polygon (exactly two in a closed solid).
3. Every polygon is a closed loop of edges.
4. Every polygon shares at least one edge with another polygon.
5. Pointers are consistent: if a polygon lists an edge, that edge points back to the polygon.
6. Polygons are planar and listed in a consistent (counter-clockwise) vertex order.