topological relationships between complex spatial objects -- by markus & thomas
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Topological Relationships Between Complex Spatial Objects -- by Markus & Thomas. Presented by: Daniel Hess, Yun Zhang. Outline. • Motivation • Problem statement • Major contributions • Key concepts • Validation methodology • Assumptions • Recommended changes. Motivation. - PowerPoint PPT PresentationTRANSCRIPT
Presented by: Daniel Hess, Yun Zhang
• Motivation• Problem statement• Major contributions• Key concepts• Validation methodology• Assumptions• Recommended changes
• To distinguish simplified spatial objects with complex spatial objects
• To define topological relationships for complex spatial objects
A more complex topological relationship
Input: spatial query (SQL), complex spatial objects
Output: query results Objective: find correct, complete query results Constraints: two spatial objects have only one
topological relationship
• Define complex points, complex lines and complex regions
• Determine topological relationships for all complex spatial data types
• Prove the completeness and mutual exclusion of the topological relationship predicates
• Provide the users concepts of topological cluster predicates and topological predicate groups
• A complex point object may include several points
• A complex line may be a spatially embedded network, possibly consisting of several components
• A complex region may be a multipart region, possibly consisting of multiple faces and holes
(Schneider and Behr, 2006, p. 46)
• Example:-A complex region with two faces in which the
upper face has two holes:
-A complex region with five faces and three holes:(Schneider and Behr, 2006, p. 53)
(Schneider and Behr, 2006, p. 53)
• Derive topological relationships from the 9-Intersection model• Use technique ‘proof-by-constraint-and-drawing’,
determine the complete sets of mutually exclusive topological relationships
• two-step proof technique-Step 1: For each possible data type combination
(e.g. point, line)->collect topological constraint rules
->apply to the topological matrix
-Step 2: Remaining assignments of the topological matrix, indicate possible topological relationships between the data types
• Proof example:
(Schneider and Behr, 2006, p. 68)
(Schneider and Behr, 2006, p. 45) (Schneider and Behr, 2006, p. 74)
(Schneider and Behr, 2006, p. 60)
(Schneider and Behr, 2006, p. 66)
• The proof technique is suitable for validating the approaches used in this paper, as it is generally abstract and precise
• The proof technique may be time consuming and labor intensive
• The authors assume the existence of the Euclidean distance function when making the definition for complex lines:
• The spatial objects are static, and will not change
with time
2 21 1 2 2 1 2 1 2(( , ), ( , )) ( ) ( )d x y x y x x y y
• Keep the key ideas of the approach. We would still apply the 9-intersection model to complex spatial objects
• Keep the clustering of topological predicates in order to reduce the large predicates set and to make the topological relationships more manageable
• Change step 2 of the proof method and apply a math formula to define valid topological relationships between specific data types, in order to improve efficiency
• Extend the spatial data types to three dimensions
The author defines complex point, line, and region in paper MSD 6. Possible trade-off result is large numbers of predicates and the difficulty of handling them. How does this paper solve this problem?
Model answer:The author proposes concepts of topological cluster predicates and topological predicate groups. It reduces the number of predicates to be dealt with in a user-defined and/or application-specific manner.