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 22
... line & downwards over the plane , starting from a position above all segments . While we sweep the imaginary line , we keep track of all segments intersecting it — the details of this will be explained later — so that we can find the ...
... line & downwards over the plane , starting from a position above all segments . While we sweep the imaginary line , we keep track of all segments intersecting it — the details of this will be explained later — so that we can find the ...
Seite 23
... sweep line reaches the endpoint . So the only question is whether intersections between the interiors of segments are always detected . Lemma 2.1 Let si and Sj be two non - horizontal segments whose interiors in- tersect in a single ...
... sweep line reaches the endpoint . So the only question is whether intersections between the interiors of segments are always detected . Lemma 2.1 Let si and Sj be two non - horizontal segments whose interiors in- tersect in a single ...
Seite 24
... sweep line , then their intersection point is an event point . ( Again , this event could have been detected already . ) Assume three segments Sk , $ 1 , and sm appear in this order on the sweep line when the lower endpoint of s is ...
... sweep line , then their intersection point is an event point . ( Again , this event could have been detected already . ) Assume three segments Sk , $ 1 , and sm appear in this order on the sweep line when the lower endpoint of s is ...
Seite 25
... sweep line . The status structure , denoted by T , is used to access the neighbors of a given segments , so that they can be tested for intersection with s . The status structure must be dynamic : as segments start or stop to intersect ...
... sweep line . The status structure , denoted by T , is used to access the neighbors of a given segments , so that they can be tested for intersection with s . The status structure must be dynamic : as segments start or stop to intersect ...
Seite 26
... sweep line just below p . If there is a horizontal segment , it comes last among all segments containing p . ( * Deleting and re - inserting the segments of C ( p ) reverses their order . * ) if U ( p ) UC ( p ) = 0 then Let s and s ...
... sweep line just below p . If there is a horizontal segment , it comes last among all segments containing p . ( * Deleting and re - inserting the segments of C ( p ) reverses their order . * ) if U ( p ) UC ( p ) = 0 then Let s and s ...
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