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 32
Seite ix
... Convex Hulls Degeneracies and Robustness Application Domains Notes and Comments Exercises 1 20035 8 10 13 15 2.2 2 ... Polygon Triangulation 45 Guarding an Art Gallery 3.1 Guarding and Triangulations 46 3.2 Partitioning a Polygon into ...
... Convex Hulls Degeneracies and Robustness Application Domains Notes and Comments Exercises 1 20035 8 10 13 15 2.2 2 ... Polygon Triangulation 45 Guarding an Art Gallery 3.1 Guarding and Triangulations 46 3.2 Partitioning a Polygon into ...
Seite 4
... convex hull of P. This leads to an alternative 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 ...
... convex hull of P. This leads to an alternative 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 ...
Seite 7
... convex hull vertices were also ordered from left to right as they occur along the boundary . But this is not the ... polygon in clockwise order , we make a turn at every vertex . For an arbitrary polygon this can be both a right turn and ...
... convex hull vertices were also ordered from left to right as they occur along the boundary . But this is not the ... polygon in clockwise order , we make a turn at every vertex . For an arbitrary polygon this can be both a right turn and ...
Seite 8
... convex hull , so collinear points must be treated as if they make a left ... polygon , and any three consecutive points form a right turn or , because of ... polygon . A way out of this is to make sure that points in the input that are ...
... convex hull , so collinear points must be treated as if they make a left ... polygon , and any three consecutive points form a right turn or , because of ... polygon . A way out of this is to make sure that points in the input that are ...
Seite 11
... convex polygon but we know that the structure of the output is correct and that the output polygon is very close to the convex hull . Finally , it is possible to predict , based on the input , the precision in the number representation ...
... convex polygon but we know that the structure of the output is correct and that the output polygon is very close to the convex hull . Finally , it is possible to predict , based on the input , the precision in the number representation ...
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