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.