### Table 2. Properties of spatial relation-based representation systems Representation

1994

"... In PAGE 4: ... Further extensions are possible for applications that require higher direction and topological resolution. Table2 summarises the properties of several relation-based systems. The first two columns refer to the representation systems and the type of spatial relations that they have been used to represent.... ..."

Cited by 68

### Table 2. Properties of spatial relation-based representation systems Representation

1994

"... In PAGE 27: ... Further extensions are possible for applications that require higher direction and topological resolution. Table2 summarises the properties of several relation-based systems. The first two columns refer to the representation systems and the type of spatial relations that they have been used to represent.... ..."

Cited by 68

### Table 3. Spatial autocorrelation results for the topological case

2004

"... In PAGE 7: ...able 2. Time periods for data collection...................................65 Table3 .... In PAGE 79: ...5.1 Topological The p-values are high for the Blaster worm ( Table3 ). Thus, the topographical case does not show an autocorrelation between the incidents of the Blaster epidemic in the LAN.... ..."

Cited by 1

### Table 3: Typical Spatial Queries from GIS

1999

"... In PAGE 6: ... (b) Corresponding query tree. Other example GIS queries which can be implemented using OGIS operations are provided in Table3 . The OGIS speci cation is con ned to topological and metric operations on vector data types.... In PAGE 7: ...pace (points, lines, areas). The spaghetti-ring and DCEL focus on the topological concepts. The representation of the eld data model includes a regular tessellation (triangular, square, hexagonal grid), as well as triangular irregular networks (TIN). The spatial queries[7] shown in Table3 are often processed using lter and re ne techniques. Approximate geometry such as the minimal orthogonal bounding rectangle of an extended spatial object is rst used to lter out many irrelevant objects quickly.... ..."

Cited by 17

### Table 3: Typical Spatial Queries from GIS

1999

"... In PAGE 6: ... (b) Corresponding query tree. Other example GIS queries which can be implemented using OGIS operations are provided in Table3 . The OGIS speci cation is con ned to topological and metric operations on vector data types.... In PAGE 7: ...pace (points, lines, areas). The spaghetti-ring and DCEL focus on the topological concepts. The representation of the eld data model includes a regular tessellation (triangular, square, hexagonal grid), as well as triangular irregular networks (TIN). The spatial queries[7] shown in Table3 are often processed using lter and re ne techniques. Approximate geometry such as the minimal orthogonal bounding rectangle of an extended spatial object is rst used to lter out many irrelevant objects quickly.... ..."

Cited by 17

### Table 3: Typical Spatial Queries from GIS

1999

"... In PAGE 6: ... (b) Corresponding query tree. Other example GIS queries which can be implemented using OGIS operations are provided in Table3 . The OGIS speci cation is con ned to topological and metric operations on vector data types.... In PAGE 7: ...pace (points, lines, areas). The spaghetti-ring and DCEL focus on the topological concepts. The representation of the eld data model includes a regular tessellation (triangular, square, hexagonal grid), as well as triangular irregular networks (TIN). The spatial queries[7] shown in Table3 are often processed using lter and re ne techniques. Approximate geometry such as the minimal orthogonal bounding rectangle of an extended spatial object is rst used to lter out many irrelevant objects quickly.... ..."

Cited by 17

### Table 3: Numbers of topological predicates between two simple spatial objects.

1999

"... In PAGE 5: ...Table 3: Numbers of topological predicates between two simple spatial objects. Table3 also indicates that the numbers of topological predicates can already become quite large for topological predicates between simple spatial objects so that the predicates are difficult to handle by the user. A further increase of the number of predicates has even to be expected for complex spatial objects.... In PAGE 31: ...uch more complex internal structure than simple objects (Section 2.1). We have seen that topological predicates operating on complex spatial objects comprise, generalize, and extend the predicates found so far for simple object structures (see Section 2.2 and Table3 ). Table 12 summarizes the number of predicates obtained for each type combination.... In PAGE 32: ... 7.1 The Quantity Problem Compared to Table3 , unsurprisingly the number of topological predicates has increased for each com- bination of complex data types. Already for topological predicates on simple spatial objects, the large numbers of predicates have been considered a problem since they make it difficult for users to distin- guish, remember, and handle them [7].... ..."

Cited by 1

### Table 2: Summary of Spatial Layout Data Characteristics

1993

"... In PAGE 80: ...2.2 Data characteristics Table2 summarizes characteristics of the collected data according to the uniform position-extent-type representation. The characteristics of the data for the organizing tasks varied considerably.... ..."

### Table 1: Number of identified vague topological predicates on the basis of complex spatial data types.

"... In PAGE 6: ... The program is successful in invalidating all neces- sary 4-tuples and resulting in the complete set of vague topo- logical predicates. The number of predicates for each vague data type combination of v(point), v(line) and v(region) is rather large (as seen in Table1 ). Thus the clustering mecha- nism from (Pauly amp; Schneider 2005b) still proves useful in generating an accessible set of predicates for the user.... ..."

### Table 1: Numbers of topological predicates between two simple spatial objects (top) and between two complex spatial objects (bottom).

"... In PAGE 2: ... The work in [7] does the same for all com- binations of complex spatial data types. Table1 shows the number of predicates for each type combination. Note that all topologi- cal predicates for simple types are contained in those for complex types.... ..."