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. |
Im Buch
Ergebnisse 1-5 von 84
Seite 13
... points . For other positions we have to obtain the heights by interpolating between nearby sample points . But which sample points should we choose ? Chapter 9 deals with this problem . The combination of ... stored characters to find the.
... points . For other positions we have to obtain the heights by interpolating between nearby sample points . But which sample points should we choose ? Chapter 9 deals with this problem . The combination of ... stored characters to find the.
Seite 14
... stored characters to find the one that best fits it . This leads to a ... points in a higher - dimensional space , and we will present a geometric ... points in the plane . This is a classic topic in computational geometry and the amount ...
... stored characters to find the one that best fits it . This leads to a ... points in a higher - dimensional space , and we will present a geometric ... points in the plane . This is a classic topic in computational geometry and the amount ...
Seite 20
... stored in a layer can be very different : the layer for a road map could store the roads as collections of line segments ( or curves , perhaps ) , the layer for cities could contain points labeled with city names , and the layer for ...
... stored in a layer can be very different : the layer for a road map could store the roads as collections of line segments ( or curves , perhaps ) , the layer for cities could contain points labeled with city names , and the layer for ...
Seite 24
... point - we have computed all intersection points . This is guar- anteed by the following invariant , which holds at any time during the plane sweep : all intersection points above the sweep line have been computed cor- rectly . After ...
... point - we have computed all intersection points . This is guar- anteed by the following invariant , which holds at any time during the plane sweep : all intersection points above the sweep line have been computed cor- rectly . After ...
Seite 25
... point p which lies on the sweep line . At each internal node v we simply test whether p lies left or right of the segment stored at v . Depending on the outcome we descend to the left or right subtree of v , eventually ending up in a ...
... point p which lies on the sweep line . At each internal node v we simply test whether p lies left or right of the segment stored at v . Depending on the outcome we descend to the left or right subtree of v , eventually ending up in a ...
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 |
Andere Ausgaben - Alle anzeigen
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