Geoinformation I
description
Transcript of Geoinformation I
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Institut für Kartographie und GeoinformationProf. Dr. Lutz Plümer
Geoinformation IVorlesung 7
WS 2000/2001
Topologische Relationen (Egenhofer)
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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Punktmengentopologie
• Beziehungen zwischen Punktmengen
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Y
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot
X
Y
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not
X
Y
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not
X
Y
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
X
Y
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X disjoint Y
Topologische Relationen
X Y X° Y° X Y° X° Y Operation
not X meets Ynot not X equals Y
X
Y
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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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
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7 Lutz Plümer - Geoinformation - 1./5. Semester - WS 00/01 - Vorlesung 7
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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