Intrinsic topological representation of real algebraic surfaces

Abstract

Determining the topology of an algebraic surface is not only an interesting mathematical problem, but also a key issue in computer graphics and CAGD. An algorithm is proposed to determine the intrinsic topology of an implicit real algebraic surface f(x,y,z) = 0 in R3, where f(x,y,z) ∈ Q[x,y,z] and Q is the field of rational numbers. There exist algorithms to determine the topology for algebraic surfaces of special type [2, 3, 4, 7]. The CAD method proposed by Collins [1] can divide the space into cylindrical parts. But it does not give the connection information neither the intrinsic representation.