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