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 80
Seite 5
... set E of edges 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 ...
... set E of edges 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 ...
Seite 16
... collection of books about geographic information systems , but most of them do ... set S is defined to be the intersection of all convex sets that contain S ... point r lies left or right of the directed line through two points p and q ...
... collection of books about geographic information systems , but most of them do ... set S is defined to be the intersection of all convex sets that contain S ... point r lies left or right of the directed line through two points p and q ...
Seite 17
... point coordinates . 1.5 Verify that the algorithm CONVEXHULL with the indicated modifica- tions correctly computes the convex hull , also of degenerate sets of points . Consider for example such nasty cases as a set of points that all ...
... point coordinates . 1.5 Verify that the algorithm CONVEXHULL with the indicated modifica- tions correctly computes the convex hull , also of degenerate sets of points . Consider for example such nasty cases as a set of points that all ...
Seite 21
... set , and compute all intersections among the segments in that set . This ... point . This brute - force algorithm clearly requires O ( n2 ) time . In a ... set of segments for which we want to compute all intersections . We want to avoid ...
... set , and compute all intersections among the segments in that set . This ... point . This brute - force algorithm clearly requires O ( n2 ) time . In a ... set of segments for which we want to compute all intersections . We want to avoid ...
Seite 22
... set of segments intersecting it . The status changes while the sweep line moves downwards , but not contin- uously . Only at particular points is an update of the status required . We call these points the event points of the plane ...
... set of segments intersecting it . The status changes while the sweep line moves downwards , but not contin- uously . Only at particular points is an update of the status required . We call these points the event points of the plane ...
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