Spatial Data Types

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• Spatial Data Types
• and their
• Embedding in Query Languages

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In-Class Presentation
Padmavati Sridhar

• As Partial Course Requirement for
• Spatial Databases as a Foundation of
• Geographical Information Systems
• (CIS 6930,Fall 2004)
• Instructor Dr. Markus Schneider

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Objective

• To provide a detailed overview of the
• Modeling
• Design and
• Implementation
• approaches of Spatial data types and operations
• Emphasis Understanding the basic concepts

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Outline

• Introduction to Spatial Databases
• Spatial Modeling
• Data Models
• Modeling of Spatial Data Types (SDTs)
• Modeling of Spatial Operations
• Design
• Formal Definition Methods
• Implementation

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Outline

• Introduction to Spatial Databases
• Spatial Concepts and Data Models
• Spatial Data Types
• Modeling
• Design
• Implementation
• Spatial Operations

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Introduction to Spatial Databases (1)

• What Is Spatial Data ?
• Eg Satellite Images, Weather and Climate Data
• To extract information, data has to be processed
  with respect to a Spatial frame of Reference (Eg
  Latitude/Longitude )
• Spatial Queries
• Queries posed on Spatial Data
• Eg 1.1 What are the names of libraries within 10
  miles of GNV?
• Non-Spatial Queries
• Eg 1.2 What are the names of libraries which
  possessgt10K titles ?

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Introduction to Spatial Databases (2)

• Why is a traditional DBMS incapable of managing
  Spatial Data ?
• Simple Data Numbers, Names, Descriptions etc
• Database efficiently organized to answer limited
  set of Queries
• Why does problem arise with a Spatial Query?
• Problems involved in processing Query Eg 1.1

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Introduction to Spatial Databases (3)

• Whos interested in Spatial Data?
• User Classes
• Scientific Community (Spatial Data Analysts )
• (Environmental Studies, Natural Resources,
  Geography)
• Business Professionals
• (Marketing Campaigns, Retail Locations)
• Common Man
• (Eg Direction Maps, Spatially sensitive Search
  Engines over the internet)
• Sample Map Application on the Net

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Introduction to Spatial Databases (4)

• Spatial DataBase Management System (SDBMS)
• A Software module that
• can work with an underlying DBMS
• supports Spatial Data Models, Spatial Abstract
  Data Types (ADTs) and a query language
• supports Spatial Indexing, efficient Algorithms
  for processing spatial operations, and domain
  specific rules for query optimization
• Example Oracle Spatial data cartridge, ESRI SDE
• can work with Oracle 8i DBMS
• Has spatial data types (e.g. polygon), operations
  (e.g. overlap) callable from SQL3 query language
• Has spatial indices, e.g. R-trees
• Oracle Spatial Oracle Locator

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Fundamental Issue in SDBMS

• Definition and Implementation of
• SPATIAL DATA TYPES (SDTs)
• SDTs provide the fundamental abstraction for
  modeling the geometric structure of
  spatially-referenced objects, and their spatial
  Relationships, Properties and Operations

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Three Layer Architecture of SDBMS
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Outline

• Introduction to Spatial Databases
• Spatial Modeling
• Data Models
• Modeling of Spatial Data Types (SDTs)
• Modeling of Spatial Operations
• Design
• Formal Definition Methods
• Implementation

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Spatial Data Models

• Models of Spatial Information
• Field Based
• Object Based

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Field /Space Based Model

• Each point in space is associated with one or
  several attribute values, defined as continuous
  functions in x and y
• f(x,y)

Wheat, 0ltxlt4 2ltylt4
Rice, 0ltxlt2 0ltylt2
Maize, 2ltxlt4 0ltylt2
x
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Field Based Model Concepts

• Spatial Framework is a partitioning of space
• e.g., Grid imposed by Latitude and Longitude
• Field Functions
• f Spatial Framework ? Attribute Domain
• Field Operations
• Eg addition() and composition(o)

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Field Operations

• Local
• value of the new field at a given location in the
  spatial frame-work depends only on the value of
  the input field at that location
• Eg Thresholding
• Focal
• value of the resulting field at a given location
  depends on the values that the input field
  assumes in a small neighborhood of the location
• Eg Gradient
• Zonal
• Zonal operations are naturally associated with
  aggregate operators or the integration function
• Eg The Average Height of Trees for each species
  in a Forest

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Object Based Model

• A Set of Points is identified as an Entity or
  Object
• An Object has an explicit Identity assigned to
  it.
• Geographic Object
• Identity Description Spatial
  Component(Spatial Object)

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Object Based Model Concepts

• Objects distinct identifiable things relevant to
  an application
• Objects have attributes and operations
• Attribute a simple (e.g. numeric, string)
  property of an object
• Operations function maps object attributes to
  other objects
• Illustration from the UF Campus Map
• Objects roads, landmarks, ...
• Attributes of Objects
• Spatial location, e.g. polygon boundary of
  land-parcel
• Non-Spatial name (e.g. Museum Road), type (e.g.
  interstate, residential street), number of lanes,
  speed limit,
• Operations on road objects determine center
  line, determine length, determine intersection
  with other roads, ...

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Spatial objects Classification

• Spatial Object Types
• Zero dimensional POINT
• One dimensional LINE
• Two - dimensional REGION

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Zero dimensional POINT

• Basic Geometry Type POINT
• Use
• To represent the location of entities
• Whose shape is not considered useful
• Whose Area is quite small with respect to the
  Embedding Space
• Eg Cities, Churches Spatial extent might be
  reduced to a point on a large-scale map

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One dimensional LINE

• Basic Geometry Type POLYLINE
• Definition
• A finite set of Line Segments or Edges, such that
  each segment end point (Vertex), is shared by
  exactly 2 segments, except for 2 endpoints
  (Extreme points), which belong to only 1 segment
• Use
• To represent Networks Roads, Hydrographs etc
• Types of Polyline
• Closed Extreme points are identical
• Simple No pairs non-consecutive edges intersect
  at any place
• Monotone A polyline is monotone with respect to
  a line L, if every line L orthogonal to L meets
  the polyline at one point at most.

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Example 1-D Objects

• Line Segment
• Polyline
• Simple Closed Polyline
• Non-Simple Polyline
• Monotone Polyline

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TwoDimensional REGION

• Basic Geometry Type POLYGON
• Definition Region of the plane bounded by a
  Closed Polyline, called its Boundary
• Use
• To represent entities with large areas
• Types of Polygons
• Simple Boundary is a Simple Polyline
• Convex For any pair of points A and B in
  Polygon P, the segment AB is fully included in P
• Monotone A Simple Polygon such that its
  boundary can be split into exactly two monotone
  polylines MC1 and MC2

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Example 2-D Objects

• Simple
• Convex
• Polygon with Hole

• Non Simple
• Monotone

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Object based Model

• Note
• Choice of Geometric Types is arbitrary depends
  on future use of the Entity collection
• Factors Scale of Interest
• Eg Airport -gt Point, for Air Links Region, for
  Detailed View
• Linear Approximation of Entities (1-D and 2-D)
• Simplifies Database design
• Leads to Efficient modeling and Querying Spatial
  Information
• Could be precisely represented with higher-order
  polynomials in x and y

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Operations on spatial objects Illustration

• Set Oriented Museum Road intersects Newell Dr
• Topological Operations Boundary of USA touches
  boundary of Canada
• Directional Florida is to the south of Georgia
• Metric Chicago is about 700 miles from New York
  city

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Spatial Operations Classification

• Topological relationships
• e.g., equal, unequal, disjoint, adjacent
  (neighboring), intersect (overlap), meet,
  (touch), inside (in), outside, covered_by,
  contains
• Spatial operations returning numbers
• e.g., area, perimeter, length, diameter, dist,
  mindist, maxdist, direction, components
  (cardinality)
• Metric relationships
• e.g., in_circle, in_window
• Spatial order and strict order relationships
• e.g., behind / in_front_of, above / below, over /
  under, inside / contains
• Directional relationships
• e.g., north / south, left / right

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Spatial Operations Classification

• Spatial operations returning new spatial objects
• - object construction operations
• e.g., union, intersection, difference, center,
  boundary (border), box
• - object transformation operations
• e.g., extend, rotate, translate
• Spatial operations on sets of spatially related
  objects
• - General
• e.g., closest, compose, decompose
• - operations for partitions
• e.g., overlay, superimposition, fusion, cover,
  windowing, clipping
• - operations for networks
• e.g., shortest_path

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Topological Relationships

• Invariant under elastic deformation (without
  tear, merge)
• - Eg Two countries which touch each other in a
  planar paper map
• will continue to do so in
  spherical globe maps.

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Directional Relationships

• Types
• Absolute
• Defined in context to a Global Reference System
• North/South, East/West
• Object Relative
• Defined using the orientation of a given object
• Left, Right, Front, Behind, Above, Below
• Viewer based
• Defined with respect to a specifically designated
  Reference Object called Viewer

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Dynamic Spatial Operations

• Dynamic Spatial Operations alter the objects upon
  which the operations act
• Create
• Reproduce(X) Produces an exact replica of X
• Split(X) - Creates Objects whose
  aggregation is X
• Destroy
• Update
• Translate Shifts Object position
• Rotation - Changes Orientation
• Scale - Changes Shape

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Object Model vs Field Model

• Similar to the object model in computer software
• Programming languages like Java, C, Visual
  basic support Object-Oriented modeling
• Post-relational databases, e.g. OODBMS, ORDBMS
  support Object-Oriented modeling
• OGIS standard set of spatial data types and
  operations exists
• Entity-Relationship Model (Conceptual Design) is
  designed with an implicit assumption of an
  Object-based model

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Three-Step Database Application Design

• STEP 1
• Conceptual Model (Users Model)
• User Requirements
• Highly Expressive, versatile, well-defined and
  consistent data types and operations
• Simplicity for understanding
• Entity-Relationship (ER) Model
• Actual Implementation details are not included
• Focus Datatypes, relationships and constraints

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Conceptual Model Illustration

• ER Model
• 3 Entities Country, City, River
• 2 Relationships capital-of, originates-in

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Three-Step Database Application Design

• STEP 2
• Logical Model (Designers Model)
• Actual implementation of a conceptual model in a
  commercial DBMS
• Eg Hierarchical, Network, Relational
• Relational Most widely implemented
• Tightly coupled with formal Query language
  Relational Algebra(RA)
• RA consists of simple operations that allow
  querying of data organized as Relations

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• Logical Model
• 3 Relations
• Country(Name, Cont, Pop, GDP, Life-Exp, Shape)
• City(Name, Country, Pop,Capital, Shape)
• River(Name, Origin, Length, Shape)
• Keys
• Primary Country.Name, City.Name, River.Name
• Foreign River.Origin, City.Country

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Sample Data
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Three-Step Database Application Design

• Logical Model (Designers Model)
• Issues
• Visibility
• Designer decides whether the internal structure
  of spatial objects is made visible at the users
  level(Query language) or only to domain-specific
  operations
• Formal Definition
• To guarantee Clarity and Consistency at both the
  Users and Implementation levels
• Fundamental Datatypes
• Numerical, String, Boolean Inadequate for
  Spatial Applications
• Requires collection of Spatial Data Types (ADT)
• Fixed, Standard set universal to all Geo-Apps
  Completeness ?
• A Kernel-set of App-independent SDTs
  Extensibility ?
• Contradicting concepts of Minimality and
  Convenience

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Three-Step Database Application Design

• STEP 3
• Implementation Model (Users Model)
• Implementation strategies
• Data Structures Representation of Spatial
  Objects
• Algorithms Operations on Spatial Objects
• Issues
• Storage (Physical File structures)
• Indexing
• Memory Management

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Extending SQL for Spatial Data

• Motivation
• SQL has simple atomic data-types, like integer,
  dates and string
• Not convenient for spatial data and queries
• Spatial data (e.g. polygons) is complex
• Spatial operations topological, euclidean,
  directional, metric
• SQL 3 allows user defined data types and
  operations
• Spatial data types and operations can be added to
  SQL3
• Open Geodata Interchange Standard (OGIS)
• Half a dozen spatial data types
• Several spatial operations
• Supported by major vendors, e.g. ESRI,
  Intergraph, Oracle, IBM,...

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Spatial Object Types in OGIS Data Model (1999)
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OGIS Spatial Data Model

• Consists of base-class Geometry and four
  sub-classes
• Point, Curve, Surface and GeometryCollection
• Operations fall into three categories
• Apply to all geometry types
• SpatialReference, Envelope, Export,IsSimple,
  Boundary
• Predicates for Topological relationships
• Equal, Disjoint, Intersect, Touch, Cross, Within,
  Contains
• Spatial Data Analysis
• Distance,Buffer,Union, Intersection, ConvexHull

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Spatial Query Types

• Simple SQL SELECT_FROM_WHERE examples
• Spatial analysis operations
• Unary operator Area
• Binary operator Distance
• Boolean Topological spatial operations - WHERE
  clause
• Touch
• Cross
• Using spatial analysis and topological operations
• Buffer, overlap
• Complex SQL examples
• Using spatial analysis and topological operations
• Aggreagate SQL queries
• Nested queries

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Spatial Query Examples (1)

• Using spatial operation in SELECT clause
• Query List the name, population, and area of
  each country listed in the Country table.
• SELECT C.Name,C.Pop, Area(C.Shape)AS "Area"
• FROM Country C
• Note This query uses spatial operation,
  Area().Note the use of spatial
• operation in place of a column in SELECT clause.

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Spatial Query Examples (2)

• Using Spatial Operation in WHERE clause
• Query Find the names of all countries which are
  neighbors of the United States (USA) in the
  Country table.
• SELECT C1.Name AS "Neighbors of USA"
• FROM Country C1,Country C2
• WHERE Touch(C1.Shape,C2.Shape)1
• AND C2.Name USA
• Note Spatial operator Touch() is used in WHERE
  clause to join Country table with itself. This
  query is an example of spatial self join
  operation

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Spatial Query Examples (3)

• Spatial Query with multiple tables
• Query For all the rivers listed in the River
  table, find the countries through which they
  pass.
• SELECT R.Name, C.Name
• FROM River R, Country C
• WHERE Cross(R.Shape,C.Shape)1
• Note Spatial operation Cross is used to join
  River and Country tables. This query represents a
  spatial join operation

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Spatial Query Examples (4)

• Using spatial operation in an aggregate query
• Query List all countries, ordered by number of
  neighboring countries.
• SELECT Co.Name, Count(Co1.Name)
• FROM Country Co, Country Co1
• WHERE Touch(Co.Shape,Co1.Shape)
• GROUP BY Co.Name
• ORDER BY Count(Co1.Name)

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Outline

• Introduction to Spatial Databases
• Spatial Modeling
• Data Models
• Modeling of Spatial Data Types (SDTs)
• Modeling of Spatial Operations
• Design
• Formal Definition Methods
• Implementation

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Design Criteria for Spatial Data Modeling
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Closure Properties

• Closure
• The domains of SDTs (Point, Line, Regions) should
  be closed under Geometric Union, Intersection and
  difference

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Finite Resolution

• Euclidean Space is continuous
• Basis of Computational Geometry Algorithms
• Compute numbers are finite and discrete
• Leads to Numerical Robustness and Topological
  Correctness problems
• D moved to D due to rounding errors

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Approaches for Topological Correctness

• Simplicial Complexes
• Realms

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Formal Definition Methods

• Need for Formal Definition Methods
• Users level
• Guaranteed clarity and consistency
• Designers level
• Better understanding of the complex semantics of
  spatial objects and operations
• Implementation Level
• formal specification of SDTs for a possible
  realization
• First step towards standardization of Spatial
  Data Types (SDTs)
• Formal definition of SDTs ? Formal definition of
  corresponding
• spatial operations
• consideration of the finiteness of computers and
  the problems of numerical robustness and
  topological correctness

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Formal Definition Methods

• Point Set Theory
• Point Set Topology
• Finite Set Theory
• Other Formal Approaches

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Outline

• Introduction to Spatial Databases
• Spatial Modeling
• Data Models
• Modeling of Spatial Data Types (SDTs)
• Modeling of Spatial Operations
• Design
• Formal Definition Methods
• Implementation

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SDT Implementation

• Goal
• Implementation of a spatial type system (spatial
  algebra) so that it can be integrated into a DBMS
  (query processing, storage management, user
  interface, etc.), fulfilling the design criteria
• Tools
• Data Structures and Algorithms
• Data Structures Representation for the SDTs
• Algorithms Implementation of Atomic SDT
  Operations

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• Discussion

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• Thank You