1. Spatial Databases - Representation
Spring, 2017
Ki-Joune Li

2. Spatial Databases Entity-Based Databases vs. Field-Based Databases
Set of Spatial Objects
Non-Spatial Attributes for each object
Field-Based Databases
No clear boundary of an object
No non-spatial attributes

3. Entity-Based Spatial Databases
Feature: Meaningful Spatial Entity
Example
Building: a meaningful entity
Edge: a spatial piece
Each feature has
Geometry
OID
Non-spatial Attributes
Spatial Database
Set of Features
Set of Relationships between Features
Representation of Geometry
Raster Model
Vector Model
Constrained Representation

4. Representation of Geometry: Raster Model
A geometric object: set of pixels or tessels (mosaics)
A value is assigned to each pixel
Example
Pros and Cons
Pollution Area
Non-Pollution Area
Pros
Cons
1. Simple
2. Easy to Collect
Example: Satellite Image
1. Huge
2. Difficult to manipulate Example: Rotation, Zooming

5. Irregular Tessellation
Regular Raster Model
Huge Size of Data
To reduce the size, Irregular Tessellation
Irregular Tessellation
Irregular Size
Irregular Shape
K-D tree
Quadtree
Region Quadtree
Point Quadtree

6. K-D tree Partitioning of a space bipartition
X-axis and Y-axis alternatively x1
<
> y1
x12
y12
x11
x12 y1
y12
x11 x1

7. Quadtree Extension of KD-tree: KD-tree: binary split
Quadtree 4-way equi-split instead
Quadrant

8. Point Quadtree A variation of quadtree Analysis by quadtree
Center of division is given by (x,y)
More flexible than region quadtree
Analysis by quadtree
Area computation
Difference p1 p2 p1 p3 p2 p3

9. Linear Quadtree Linearization of Quadtree
Transformation of 2-D space to 1-D space
By Space Filling Curve
Peano key is assigned to each quadrant 11 6 13
N-order
Hilbert
Column-wise

10. Linear Quadtree N-order Peano Key Bit Interleaving Method 11
1. Binary representation of coordinates (10,01) 10
2. Bit-Interleaving x = y = 01
Peano key = 00
= 9 00 01 10 11

11. Linear Quadtree Each Quadrant
Represented by (kpeano, size)
Size:
Object is represented by a set of pairs (k,s)
Size 2
2n split
Size 1
Size 0

12. Vector Model Geometric object is represented by its Geometric type
Coordinates (x,y), or (x,y,z)
Geometric type
Point (x,y)
Line (x1,y1,x2,y2) or (p1, p2)
Polyline (x,y)* or p*
Polygon: Closed polyline

13. Example: OGC Simple Feature Geometry

14. Database Schema for Vector Model
By Relational Data Model
Point and Line: No problem
Polyline, Polygon
1st Normal Form of relational model
Atomic type only
Set type is not allowed
Polyline: ordered set of points
Geo-relational model: Based on Winged-Edge Topology
By Object-Oriented Data Model or OR Model
Provide Set type
Provide Polygon, Polyline Type

15. Winged Edge Representation
Example

16. Winged Edge Representation: Topology
Point Topology
Face Topology
Point #
Start Line #
Face #
Start Line #
Left Line
End Point
Start Point
Right Line
Line Topology
Line #
Starting Point #
Ending Point #
Left Line #
Right Line #
Left Face #
Right Face #

17. Winged Edge Representation: Geometry
Why Line-Oriented Representation ?
Line Geometry Table
Line #
Starting Point
Intermediate Points
Ending Point