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 5
... O ( n2 ) time . This can easily be improved to O ( nlogn ) , but the time required for the rest of the algorithm dominates the total running time anyway . Analyzing the time complexity of SLOWCONVEXHULL is easy . We check n2 - n ... n - 2 ...
... O ( n2 ) time . This can easily be improved to O ( nlogn ) , but the time required for the rest of the algorithm dominates the total running time anyway . Analyzing the time complexity of SLOWCONVEXHULL is easy . We check n2 - n ... n - 2 ...
Seite 9
... n points in the plane can be computed in O ( nlogn ) time . Proof . We will prove the correctness of the computation of the upper hull ; the lower hull computation can be proved correct using similar arguments . The proof is by induction on ...
... n points in the plane can be computed in O ( nlogn ) time . Proof . We will prove the correctness of the computation of the upper hull ; the lower hull computation can be proved correct using similar arguments . The proof is by induction on ...
Seite 14
... on the records can be answered efficiently . We hope that the above collection of geometric ... O ( logn ) time per insertion [ 287 ] . Overmars and van Leeuwen gen ... n ) time where h is the complexity of the convex hull . 13 Chapter 1 ...
... on the records can be answered efficiently . We hope that the above collection of geometric ... O ( logn ) time per insertion [ 287 ] . Overmars and van Leeuwen gen ... n ) time where h is the complexity of the convex hull . 13 Chapter 1 ...
Seite 15
... O ( nlogn ) time , as we will see in Chapter 11. For dimensions higher than 3 , however , the complexity of the ... on computer graphics.
... O ( nlogn ) time , as we will see in Chapter 11. For dimensions higher than 3 , however , the complexity of the ... on computer graphics.
Seite 16
... on computer graphics . The book by Foley et al . [ 151 ] is very extensive and generally considered one of the best ... n segments that are the edges of a convex polygon . Describe an O ( nlogn ) algorithm that computes from E a list ...
... on computer graphics . The book by Foley et al . [ 151 ] is very extensive and generally considered one of the best ... n segments that are the edges of a convex polygon . Describe an O ( nlogn ) algorithm that computes from E a list ...
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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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