Computational Geometry: Algorithms and ApplicationsSpringer Science & Business Media, 09.03.2013 - 367 Seiten Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field 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 in formation 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 difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem 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. |
Inhalt
5 | |
9 | |
11 | |
Line Segment Intersection | 21 |
3 | 30 |
5 | 40 |
4 | 59 |
2 | 66 |
4 | 160 |
2 | 167 |
5 | 177 |
More Geometric Data Structures | 209 |
Convex Hulls 233 | 232 |
63 | 246 |
Binary Space Partitions | 249 |
Robot Motion Planning | 265 |
Orthogonal Range Searching | 93 |
4 | 107 |
7 | 115 |
3 | 127 |
5 | 138 |
Voronoi Diagrams | 145 |
3 | 152 |
2 A Point Robot | 268 |
Quadtrees | 289 |
Visibility Graphs | 305 |
Simplex Range Searching | 317 |
339 | |
357 | |
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Computational Geometry: Algorithms and Applications Mark de Berg,Otfried Cheong,Marc van Kreveld,Mark Overmars Eingeschränkte Leseprobe - 2008 |
Häufige Begriffe und Wortgruppen
2-dimensional associated structure beach line binary search tree boundary BSP tree canonical subsets Chapter circle event configuration space construction contains convex hull convex polygon coordinate corresponding data structure defined Delaunay triangulation denote diagonal doubly-connected edge list dual event point face facets Figure geometric graph half-edge half-plane Hence Input interior intersection point kd-tree leaf Lemma lies line segments linear program mesh Minkowski sum motion planning number of reported O(n² O(nlogn objects ORTHOGONAL RANGE SEARCHING P₁ partition tree pixel planar plane sweep point location point q point stored pointer problem prove Pstart quadtree query algorithm query point query range range queries range searching range tree recursive region robot search path search structure Section SEGMENT INTERSECTION segment tree set of points shortest path simple polygon subdivision subtree sweep line Theorem total number trapezoidal map triangles vertex vertical line Vor(P Voronoi diagram y-coordinate