This book is motivated by surface-surface intersection problems (SSI) in R3, self-intersection surfaces problem in R3 and three hypersurfaces intersection problems (SSSI) in R⁴. It presents algorithms for computing all the differential geometry properties of Frenet apparatus (t, n, b,κ,τ) of intersection curves of surfaces in R3 for transversal and tangential intersection. The surfaces may be implicit parameterization or parametric parameterization. It is also presents algorithms for computing all the differential geometry properties of intersection curves of Frenet apparatus...

Ranking queries are widely used in data exploration, data analysis and decision making scenarios. While most of the currently proposed ranking techniques focus on deterministic data, several emerging applications involve data that are imprecise or uncertain. Ranking uncertain data raises new challenges in query semantics and processing, making conventional methods inapplicable. Furthermore, the interplay between ranking and uncertainty models introduces new dimensions for ordering query results that do not exist in the traditional settings. This lecture describes new formulations and...