Compactness and Efficiency:

A good representation must be compact enough for saving space and permit for efficient algorithms to find out desired physical characteristics.

These issues might be contradictory with each other. For efficiency cause, a curvilinear solid might be approximated by a polyhedron. There are many efficient and robust algorithms for handling polyhedra; though, accuracy might not be maintained in the process of approximation. For instance, given two curvilinear solids that are tangent to each other, this tangency might disappear after converting to a polyhedron.

Problems take place even for the polyhedra world. Several graphics APIs such as PHIGS PLUS and OpenGL have built-in data structures for representing polyhedra; but, these representations can generate invalid solids. There are representations that might always represent valid solids; but, these representations are generally more complex than those available in graphics APIs.