We discuss a shape representation based on a set of disconnected (planar) polygons. The polygons are computed by creating a BSP that contains approximately linear surface patches in each cell. This is achieved by employing two heuristics for finding appropriate split planes in each cell. Leaf nodes in the BSP tree represent either polygonal surface approximations or empty (clip) cells rather than split planes. We show that the resulting set of disconnected primitives typically leads to a better two-sided Hausdorff error for a given number of primitives than meshes. The BSP cells can be coded with few bits and, consequently, the tree is a compact shape representation. The special properties of BSPs are very useful in applications that need to perform spatial queries on the primitives, such as for occlusion and view frustum culling, and proximity or collision tests