Boundary representation of 3D objects

Boundary representation (B-rep) describes a 3D solid by its surface: the set of faces, edges and vertices that separate the interior of the object from the outside. The most common form is the polygon mesh, where each face is a planar polygon.

The data are held in tables:

• Vertex table: coordinates of every vertex.
• Edge table: each edge as a pair of vertices.
• Surface table: each face as a list of edges.

Example: a pyramid with square base V1 V2 V3 V4 and apex V5

 Top view (apex V5 is above the centre of the base)
   V4 -------- V3
   |  \      /  |
   |    \  /    |
   |     V5     |
   |    /  \    |
   |  /      \  |
   V1 -------- V2

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

Features:

• Easy to render, since most graphics hardware works on polygons.
• Curved surfaces are approximated by many small polygons or by spline patches.
• A valid solid must be closed: each edge is shared by exactly two faces.
• Only the surface is stored, so volume properties (mass, interior) are not directly available, unlike in CSG or octree representations.