Computational geometry emerged as a discipline in the seventies and has had considerable
success in improving the asymptotic complexity of the solutions to basic geometric problems …

1 Introduction A geometric algorithm usually takes decisions based on some basic
geometric questions called predicates. Numerical inaccuracy in the evaluation of geometric …

The Minkowski sum of two sets A, B∈ IR d, denoted A⊕ B, is defined as
\left{a+b~|~a∈A,b∈B\right\}. We describe an efficient and robust implementation for the …

We present the first release of the Exacus C++ libraries. We aim for systematic support of
non-linear geometry in software libraries. Our goals are efficiency, correctness …

We present a generic C++ design to perform exact geometric computations efficiently using
lazy evaluations. Exact geometric computations are critical for the robustness of geometric …

The Minkowski sum of two sets A, B∈ R2, denoted A⊕ B, is defined as {a+ b∣ a∈ A, b∈
B}. We describe an efficient and robust implementation of the construction of the Minkowski …

Arrangements of planar curves are fundamental structures in computational geometry.
Recently, the arrangement package of Cgal, the Computational Geometry Algorithms …

Our work goes towards answering the growing need for the robust and efficient manipulation
of curved objects in numerous applications. The kernel of the CGAL library provides several …

Adding motion to geometric data structures creates a host of new computational issues. This
thesis explores the issues encountered when using two different motion models–smooth …

Lower envelopes are fundamental structures in computational geometry, which have many
applications, such as computing general Voronoi diagrams and performing hidden surface …