Determining the topology of real algebraic surfaces

An algorithm is proposed to determine the topology of an implicit real algebraic surface in R3. The algorithm consists of four steps: surface pro-jection, projection curve topology determination, space curve segmenta-tion and surface patch composition, combination of surface patches and surface topology representation. The topology is represented by a set of surface patches, and each surface patch is presented by an ordered list of space curve segments. The relationship between the surface patches can be found by their space curve segments. Some examples show that our algorithm is effective