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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Ergebnisse 1-5 von 62
Seite xi
... Planar Point Sets 185 9.2 The Delaunay Triangulation 188 9.3 Computing the Delaunay Triangulation 191 9.4 The Analysis 197 9.5 * A Framework for Randomized Algorithms 200 9.6 Notes and Comments 206 9.7 Exercises 207 10 More Geometric ...
... Planar Point Sets 185 9.2 The Delaunay Triangulation 188 9.3 Computing the Delaunay Triangulation 191 9.4 The Analysis 197 9.5 * A Framework for Randomized Algorithms 200 9.6 Notes and Comments 206 9.7 Exercises 207 10 More Geometric ...
Seite 3
... planar convex hulls . We'll skip the motivation for this problem here ; if you are interested you can read the introduction to Chapter 11 , where we study convex hulls in 3 - dimensional space . A subset S of the plane is called convex ...
... planar convex hulls . We'll skip the motivation for this problem here ; if you are interested you can read the introduction to Chapter 11 , where we study convex hulls in 3 - dimensional space . A subset S of the plane is called convex ...
Seite 28
... planar graph embedded in the plane . ( If you are not familiar with planar graph terminology , you should read the first paragraphs of Section 2.2 first . ) Its vertices are the endpoints of segments and intersection points of segments ...
... planar graph embedded in the plane . ( If you are not familiar with planar graph terminology , you should read the first paragraphs of Section 2.2 first . ) Its vertices are the endpoints of segments and intersection points of segments ...
Seite 29
... planar graph is bounded by at least three edges - provided that there are at least three segments — and an edge can bound at most two different faces . Therefore the number of faces , is at most 2ne / 3 . We now use Euler's nf , formula ...
... planar graph is bounded by at least three edges - provided that there are at least three segments — and an edge can bound at most two different faces . Therefore the number of faces , is at most 2ne / 3 . We now use Euler's nf , formula ...
Seite 30
... planar subdivisions induced by planar embeddings of graphs . Such a subdivision is connected if the underlying graph is con- nected . The embedding of a node of the graph is called a vertex , and the em- bedding of an arc is called an ...
... planar subdivisions induced by planar embeddings of graphs . Such a subdivision is connected if the underlying graph is con- nected . The embedding of a node of the graph is called a vertex , and the em- bedding of an arc is called an ...
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