Week2: 03 - Spatial Relations: matrix/overlayed

Question 1

How can spatial objects (in a vector based representation) be characterised?

Answer 1

In terms of their spatial relations

Question 2

Two regions are said to be adjacent if …

Answer 2

if they share part of a boundary but do not share any points in their interior

Question 3

What are the pros and cons of the 4-intersection matrix?

Answer 3

Pros:
1) simple model
2) well accepted
Cons:
1) Does not distinguish between conceptually different situations

Question 4

What is a possible extension of the 4-intersection matrix?

Answer 4

Use different values for matrix entries:

1) number of connected components
2) adding the dimension of each component

Question 5

Non-overlayed approach

Answer 5

We can consider generic sets of entities (any topological relations allowed) or sets with specific properties/structures

Question 6

Overlayed approach

Answer 6

We do not allow for proper intersections among entities i.e. intersections between the interior of entities
This approach is useful to define data structures for storing vector spatial data

Question 7

Properties of generic sets of entities

Answer 7

1) all relations are possible between pairs of entities
2) No specific structure characterises these sets of entities
3) Inefficient to maintain topology
4) Layered model
5) Each layer (usually kept separately) is an overlayed set but different layers can intersect each other

e.g. intersection point (bridge) is not recorded in the dataset

Question 8

Properties of overlayed sets

Answer 8

1) If the same dataset is stored as an overlayed set, all interactions are calculated and stored in the dataset
e. g. intersection point (bridge) is explicitly recorded in dataset
2) With overlayed sets of entities, only disjoint and meet relations are possible between two polygons/lines
3) Overlayed sets of entities correspond to plane graphs in which we consider nodes, edges & faces (polygons) bounded by closed cycles of edges