Mark de Berg - Böcker

Computational geometry is the part of theoretical computerscience that concerns itself with geometrical objects; itaims to define efficient algorithms for problems involvingpoints, lines, polygons, and so on. The field has gainedpopularity very rapidly during the last decade. This ispartly due to the many application areas of computationalgeometry and partly due to the beauty of the field itself. This monograph focuses on three problems that arise inthree-dimensional computational geometry. The first problemis the ray shooting problem: preprocess a set of polyhedrainto a data structure such that the first polyhedron that ishit by a query ray can be determined quickly. The secondproblem is that of computing depth orders: we want to sort aset of polyhedra such thatif one polyhedron is (partially)obscured by another polyhedron then it comes first in theorder. The third problem is the hidden surface removalproblem: given a set of polyhedra and a view point, computewhich parts of the polyhedra are visible from the viewpoint. These three problems involve issues that arefundamental to three-dimensional computational geometry.The book also contains a large introductory part discussingthe techniques used to tackle the problems. This part shouldinterest not only those who need the background for the restof the book but also anyone who wants to know more aboutsome recent techniques in computational geometry.

The success of the ?eld as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains—computer graphics, geographic information systems (GIS), robotics, and others—in which geometric algorithms play a fundamental role.

Computational geometry emerged from the ?eld of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The success of the ?eld as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains—computer graphics, geographic information systems (GIS), robotics, and others—in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or dif?cult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simpli?ed many of the previous approaches. In this textbook we have tried to make these modern algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry,but it can also be used for self-study.

This volume contains the 69 papers presented at the 16th Annual European Symposium on Algorithms (ESA 2010), held in Liverpool during September 6-8, 2010, including three papers by the distinguished invited speakers Artur Czumaj, Herbert Edelsbrunner, and Paolo Ferragina. ESA 2010 was organized as a part of ALGO 2010, which also included the 10th Workshop on Algorithms in Bioinformatics (WABI), the 8th Workshop on Approximation and Online Algorithms (WAOA), and the 10th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS). The European Symposium on Algorithms covers research in the design, use, andanalysisofe?cientalgorithmsanddata structures.As inpreviousyears,the symposium had two tracks: the Design and Analysis Track and the Engineering and Applications Track, each with its own Program Committee. In total 245 papers adhering to the submission guidelines were submitted. Each paper was reviewed by three or four referees.Based on the reviews and the often extensive electronicdiscussionsfollowingthem, thecommittees selected 66papersintotal: 56 (out of 206) to the Design and Analysis Track and 10 (out of 39) to the Engineering andApplicationstrack.We believethat thesepaperstogethermade up a strong and varied program, showing the depth and breadth of current algorithms research.