Spatial Databases - Representation Spring, 2017 Ki-Joune Li

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

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

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

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

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

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

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

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

Linear Quadtree N-order Peano Key Bit Interleaving Method 11 1. Binary representation of coordinates (10,01) 10 2. Bit-Interleaving x = 1 0 y = 0 1 01 Peano key = 1 0 0 1 00 = 9 00 01 10 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

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

Example: OGC Simple Feature Geometry

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

Winged Edge Representation Example

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 #

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