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 xi
... Constructing a BSP Tree 256 12.4 * The Size of BSP Trees in 3 - Space 260 12.5 Notes and Comments 263 12.6 Exercises 264 13 Robot Motion Planning Getting Where You Want to Be 267 13.1 Work Space and Configuration Space 268 xi CONTENTS ...
... Constructing a BSP Tree 256 12.4 * The Size of BSP Trees in 3 - Space 260 12.5 Notes and Comments 263 12.6 Exercises 264 13 Robot Motion Planning Getting Where You Want to Be 267 13.1 Work Space and Configuration Space 268 xi CONTENTS ...
Seite 5
... construct a list of vertices of CH ( P ) , sorted in clockwise order . Two steps in the algorithm are perhaps not entirely clear . The first one is line 5 : how do we test whether a point lies to the left or to the right of a directed ...
... construct a list of vertices of CH ( P ) , sorted in clockwise order . Two steps in the algorithm are perhaps not entirely clear . The first one is line 5 : how do we test whether a point lies to the left or to the right of a directed ...
Seite 6
... construct the sorted list of convex hull vertices in the last step of our algorithm . This step assumes that there is exactly one edge starting in every convex hull vertex , and exactly one edge ending there . Due to the rounding errors ...
... construct the sorted list of convex hull vertices in the last step of our algorithm . This step assumes that there is exactly one edge starting in every convex hull vertex , and exactly one edge ending there . Due to the rounding errors ...
Seite 28
... constructing the event queue on the segment endpoints . Because we implemented the event queue as a balanced binary search tree , this takes O ( nlogn ) time . Initializing the status structure takes constant time . Then the plane sweep ...
... constructing the event queue on the segment endpoints . Because we implemented the event queue as a balanced binary search tree , this takes O ( nlogn ) time . Initializing the status structure takes constant time . Then the plane sweep ...
Seite 36
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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