In the context of a diploma thesis at the university of Bonn we present an implementation of the deterministic algorithm for constructing a single face in an arrangement of line segments using CGAL´s arrangement package and its sweep line framework. The algorithm is developed and presented in the book “Davenport-Schinzel sequences

and their geometric applications” by Micha Sharir and Pankaj K. Agarwal, Cambridge University Press, 1995.

While the complexity of a full arrangement of line segments is in *O(n ^{2})*, Sharir and Agarwal show that any single face in such arrangement has a maximum complexity of O(α(

*n*)*

*n*) where α(

*n*) denotes the extremely slow-growing inverse Ackermann function which can be regarded as constant for any conceivable real-world input. Any single face can be constructed in time O(α(

*n*)*

*n**log

^{2}n) using a deterministic divide and conquer algorithm including – in the words of Sharir and Agarwal – a “sophisticated sweep-line technique” in the merge step (“red blue merge”).