Institut für Kartographie und GeoinformationProf. Dr. Lutz Plümer
Geoinformation IVorlesung 7
WS 2000/2001
Topologische Relationen (Egenhofer)
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
2 2
Punktmengentopologie
• Beziehungen zwischen Punktmengen
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
3 3
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
4 4
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
5 5
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
6 6
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
7 7
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
8 8
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
9 9
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
10 10
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
11 11
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
12 12
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Y
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
13 13
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
14 14
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
15 15
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
16 16
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
17 17
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
18 18
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
19 19
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
20 20
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
21 21
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
22 22
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
23 23
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
24 24
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
25 25
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
26 26
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
27 27
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside X
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
28 28
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
29 29
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
30 30
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
31 31
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
32 32
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Y
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
33 33
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
34 34
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
35 35
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
36 36
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
37 37
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not not Y covers X
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
38 38
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not not Y covers Xnot
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
39 39
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not not Y covers Xnot not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
40 40
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not not Y covers Xnot not not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
41 41
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not not Y covers Xnot not not not
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
42 42
X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
not not X inside Y
not not Y inside Xnot not not X covers Ynot not not Y covers Xnot not not not X overlaps Y
X
Y
Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
43 43
X disjunkt Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X trifft Y
not not X gleicht Y
not not X innerhalb Y
not not not Y überdeckt X
not not Y innerhalb X
not not not X überdeckt Y
not not not not X überlappt Y
X
Y
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