Computational Geometry: Algorithms and ApplicationsSpringer Science & Business Media, 17.04.2013 - 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 playafundamental 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. |
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Seite 3
... defined as the systematic study of algorithms and data structures for geometric objects , with a focus on exact algorithms that are asymptotically fast . Many researchers were attracted by the challenges posed by the geometric problems ...
... defined as the systematic study of algorithms and data structures for geometric objects , with a focus on exact algorithms that are asymptotically fast . Many researchers were attracted by the challenges posed by the geometric problems ...
Seite 4
... definition of the convex hull of a finite set P of points in the plane : it is the unique convex polygon whose vertices are points from P and that contains all points of P. Of course we should prove rigorously that this is well defined ...
... definition of the convex hull of a finite set P of points in the plane : it is the unique convex polygon whose vertices are points from P and that contains all points of P. Of course we should prove rigorously that this is well defined ...
Seite 8
... defined . Fortunately , this turns out not to be a serious problem . We only have to generalize the ordering in a suitable way : rather than using only the x - coordinate of the points to define the order , we use the lexicographic ...
... defined . Fortunately , this turns out not to be a serious problem . We only have to generalize the ordering in a suitable way : rather than using only the x - coordinate of the points to define the order , we use the lexicographic ...
Seite 15
... defined in any dimension . Convex hulls in 3- dimensional space can still be computed in O ( nlogn ) time , as we will see in Chapter 11. For dimensions higher than 3 , however , the complexity of the convex hull is no longer linear in ...
... defined in any dimension . Convex hulls in 3- dimensional space can still be computed in O ( nlogn ) time , as we will see in Chapter 11. For dimensions higher than 3 , however , the complexity of the convex hull is no longer linear in ...
Seite 16
... defined to be the intersection of all convex sets that contain S. For the convex hull of a set of points it was indicated that the convex hull is the convex set with smallest perimeter . We want to show that these are equivalent ...
... defined to be the intersection of all convex sets that contain S. For the convex hull of a set of points it was indicated that the convex hull is the convex set with smallest perimeter . We want to show that these are equivalent ...
Inhalt
5 | |
17 | |
30 | |
5 | 40 |
4 | 57 |
2 | 66 |
Orthogonal Range Searching | 80 |
4 | 109 |
5 | 178 |
3 | 191 |
9 | 200 |
7 | 207 |
Convex Hulls | 236 |
Binary Space Partitions | 251 |
Robot Motion Planning | 267 |
2 A Point Robot | 270 |
8 | 117 |
3 | 129 |
6 | 144 |
3 | 154 |
4 | 162 |
2 | 169 |
Quadtrees | 291 |
Visibility Graphs | 307 |
Simplex Range Searching | 319 |
64 | 341 |
Index | 359 |
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Häufige Begriffe und Wortgruppen
2-dimensional associated structure beach line bound boundary BSP tree canonical subsets Chapter compute configuration space construct contains convex hull convex polygon corresponding data structure defined Delaunay triangulation denote disc doubly-connected edge list dual endpoint face facets Figure free space geometric half-edge half-plane Hence input inside interior intersection point interval tree kd-tree leaf Lemma lies line segments linear program mesh Minkowski sum motion planning number of edges number of reported O(n² O(nlogn objects obstacles P₁ partition tree pixel planar point location point q point stored pointers problem Proof prove Pstart quadtree query algorithm query point query range range queries range searching range tree recursive region robot search path search structure Section segment tree set of points shortest path simple polygon square subdivision subtree sweep line Theorem total number trapezoidal map triangles vertex vertical line visibility graph Vor(P Voronoi diagram xmid y-coordinate