3. Logical Models and Query Languages

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3. Logical Models and Query Languages

• 2007-09-20
• Hong-Koo Kang
• Department of Computer Science Engineering
• Konkuk University
• E-mail hkkang_at_db.konkuk.ac.kr
• URL http//db.konkuk.ac.kr

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Introduction

• This chapter
• How the representation and querying of geographic
  objects can be supported by the DBMS
• Abstract Data Type(ADT)
• Combinations of data types and operations
• Ex) type polygon, its operation PolygonArea
• Encapsulation
• ADTs are encapsulated in the sense that they are
  accessible only through the operations defined on
  them
• The DBMS need not have any knowledge on the ADT
  implementation

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3.1 Reference Schemas (1/2)

• Administrative Units (Schema 1)
• A country (ex the United States or Germany)
  consists of states, and a single state, in turn,
  consists of counties
• The diamond shaped symbol(?)
• Between two entity types express an aggregation
  relationship
• Ex) a State consists of Counties
• The solid circle symbol(?)
• Is used to denote a one-to-many relationship

Figure 3.1 Administrative units in the United
States (schema 1)
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3.1 Reference Schemas (2/2)

• Highway Network Among Cities (Schema 2)
• A highway entity consists of sections
• A section may be shared by several highways
• Many-to-many relationship
• The sections of highways connect cities to each
  other
• A section starts in a given city and ends in
  another
• Land Use (Schema 3)
• A particular area in the plane is associated with
  a type of use
• Such as housing, agricultural area, and forest

Figure 3.2 Highway network among cities (schema 2)
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3.2 Reference Queries (1/4)

• Query classification
• Queries with alphanumeric criteria (ALPHA-)
• Queries with a spatial criteria (SPAT-)
• Ex) an operation that applies to the spatial part
  of one or several geographic objects
• Interactive queries (INTER-)
• which require participation from the end user
• Ex) to select a particular area by drawing it on
  a display device using a mouse
• Schema
• Administrative units (ADM)
• Roads (R)
• Land use (LU)
• Ex) ALPHA-ADM2 for the second alphanumeric query
  on administrative units

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3.2 Reference Queries (2/4)

• Queries with alphanumeric criteria are as follows
• ALPHA-ADM1
• Number of inhabitants in the County of San
  Francisco
• ALPHA-ADM2
• List of the counties of the State of California
• ALPHA-ADM3
• Number of inhabitants in the United States
• ALPHA-R1
• Number of lanes in the first section of
  Interstate 99
• ALPHA-R2
• Name of all sections that constitute Interstate
  99

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3.2 Reference Queries (3/4)

• Queries involving spatial criteria are as follows
• SPAT-ADM4
• Counties adjacent to the County of San Francisco
  in the same state
• SPAT-ADM5
• Display of the State of California
• SPAT-ADM6
• Counties larger than the largest county in
  California
• SPAT-R3
• Length of Interstate 99
• SPAT-ADM-R1
• All highways going through the State of
  California
• SPAT-ADM-LU1
• Display of all residential area in the County of
  San Jose
• SPAT-ADM-LU2
• Overlay of the themes of administrative units and
  land use

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3.2 Reference Queries (4/4)

• Interactive queries are as follows
• INTER-ADM7
• Description of the county pointed to on the
  screen
• INTER-ADM8
• Counties that intersect a given rectangle on the
  screen
• INTER-ADM9
• Parts of counties within a given rectangle on the
  screen
• INTER-R5
• Description of the section pointed to on the
  screen
• INTER-R6
• Description of the highway of which a section is
  pointed to on the screen

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3.3 Spatial Abstract Data Types

• Extending Data Models with Spatial ADTs
• Designing Spatial ADTs
• Exploring Relationships Between Spatial Objects
  Topological Predicates

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Extending Data Models with Spatial ADTs (1/6)

• Spatial ADTs Basic Concepts
• The list of operations that one can perform on
  the spatial object
• Independently of its internal representation
• ex) Testing of intersection with other objects,
  area size calculation
• Geographic data models and spatial data models

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Extending Data Models with Spatial ADTs (2/6)

• The abstraction of the region in the geographic
  data model allows for any choice of spatial data
  model
• Ex) spaghetti, network, or topological

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Extending Data Models with Spatial ADTs (3/6)

• Choosing Appropriate Types
• A set of possible choices for geometric types

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Extending Data Models with Spatial ADTs (4/6)

• Simple choices in representing spatial objects
• Type point (zero-dimensional)
• A point is an instance of this type
• Type polyline, line in short (one-dimensional)
• A list of pairwise connected segments
• An endpoint can be shared by, at most, two
  segments
• Type region ?? (two-dimensional)
• Any set of nonoverlapping polygons
• We do not consider polygons with holes

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Extending Data Models with Spatial ADTs (5/6)

• Defining Spatial ADT Operations
• The result of the operation must be either any
  atomic type provided by the DBMS or one of the
  three abstract types

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Extending Data Models with Spatial ADTs (6/6)

• Region ADT operations
• PointInRegion region?point -gt bool
• Overlaps region?region -gt bool
• OverlapsRect region?rectangle -gt bool
• Clipping region?rectangle -gt region
• Intersection region?region -gt region
• Meets region?region -gt bool
• Area region -gt real
• RegionUnion region -gt region
• Line ADT operations
• PointInline line?point -gt bool
• Length line -gt real
• OverlapsLR line?region -gt bool
• Point ADT operations
• Distance region?point -gt real

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Designing Spatial ADTs (1/5)

• The spatial operation classification
• Unary operations with Boolean result
• Test a spatial object for a given property
• Ex) convex, connected
• Unary operations with scalar result
• Computing the length, area size, and perimeter of
  a spatial object
• Unary operations with spatial result
• Topological transforms
• Rotation, translation, scale change, symmetry
• Boundary
• Mapping a d-dimensional object into a
  (d-1)-dimensional one (d gt 0)
• Object extraction
• minimal bounding rectangle, region centroid

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Designing Spatial ADTs (2/5)

• N-ary operations with spatial result
• Voronoi diagram construction of a set of points
• and convex hull
• Binary operations with spatial result
• Ex) intersection, union, difference
• Binary operations with Boolean result (spatial
  predicates)
• Topological predicates
• Ex) intersects, contains, adjacent
• Direction predicates
• Ex) above, North of
• Metric predicates
• Whether the distance between two objects is less
  than a given number of units
• Binary operations with scalar result
• Ex) Distance

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Designing Spatial ADTs (3/5)

• Semantics of Operations
• An operation may have different meanings
  depending on the dimension considered
• For example, intersection operation
• Two convex polygons
• Always a single convex polygon
• Two nonconvex polygons
• May generate many polygons
• A line and a polygon
• The part of the line inside the polygon
• The intersection points between the line and the
  boundary of the polygon
• Two lines
• A segment
• The set of segments common to the two lines given
  as argument
• The set of points of intersection between the two
  lines
• Two adjacent polygons or regions
• Regularized intersection the returned value is
  empty
• Geometric intersection the returned value is
  their common boundary

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Designing Spatial ADTs (4/5)
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Designing Spatial ADTs (5/5)

• The result of spatial operations should satisfy
  one of the existing types
• The limits of simple type system
• The intersection of a line and a region returns
  many points
• The union of two (poly)lines is not a (poly)line
• The difference of two polygons (without holes)
  may be a polygon with a hole
• Weak typing
• Chooses a type large enough to remain closed
  under a set of common operations
• Ex) geometry a set of either points or polygons
• Strong typing
• Control on the operations
• Ex) Modeling a line by as set of segments enables
  us to perform a union of lines

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Exploring Relationships Between Spatial Objects
Topological Predicates (1/5)

• Focus on topological relationship between two
  objects
• Definitions for the relations
• Function point(x)
• The set of points that belongs to a spatial
  region x
• Set operations
• , ?, ?, n
• Definition of following relations
• x y corresponds to point(x) point(y)
• x ? y corresponds to point(x) ? point(y)
• x inside y corresponds to point(x) ? point(y)
• x outside y corresponds to point(x) n point(y)
  Ø
• x intersects y corresponds to point(x) n point(y)
  ? Ø

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Exploring Relationships Between Spatial Objects
Topological Predicates (2/5)

• 4-intersection schema
• With the notion of boundary and interior
• Overlap and meets can be distinguished
• By comparing whether or not boundaries and
  interiors of two spatial regions intersect
• ??
• A non-empty set of points
• A0 interior of A
• dA boundary of A

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Exploring Relationships Between Spatial Objects
Topological Predicates (3/5)
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Exploring Relationships Between Spatial Objects
Topological Predicates (4/5)
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Exploring Relationships Between Spatial Objects
Topological Predicates (5/5)
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3.4 Relational Models Extended with ADT

• Representation of reference schemas
• Reference Queries

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Representation of reference schemas (1/3)

• Administrative units (schema 1)

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Representation of reference schemas (2/3)

• Highway network and cities (schema 2)

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Representation of reference schemas (3/3)

• Land Use (schema 3)

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Reference Queries (1/9)

• ALPHA-ADM1
• Number of inhabitants in the County of San
  Francisco
• ALPHA-ADM2
• List of the names of the counties in the State of
  California

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Reference Queries (2/9)

• ALPHA-ADM3
• Number of inhabitants of the United States of
  America
• ALPHA-R1
• Number of lanes in the first section of
  Interstate 99

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Reference Queries (3/9)

• ALPHA-R2
• Names of sections that constitute Interstate 99

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Reference Queries (4/9)

• SPAT-ADM4
• Counties adjacent to the County of San Francisco
  in the same state
• SPAT-ADM5
• Display of the State of California

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Reference Queries (5/9)

• SPAT-ADM6
• Counties larger than the largest county in
  California
• SPAT-R3
• Length of Interstate 99

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Reference Queries (6/9)

• SPAT-ADMR1
• All highways going through the State of
  California
• SPAT-ADM-LU1
• Display of all residential areas in the County of
  San Jose

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Reference Queries (7/9)

• SPAT-ADM-LU2
• Overlay of the themes of administrative units and
  land use

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Reference Queries (8/9)

• INTER-ADM7
• Description of the county pointed to on the
  screen
• INTER-ADM8
• Counties that intersect a given rectangle on the
  screen
• INTER-ADM9
• Parts of counties within a given rectangle on the
  screen

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Reference Queries (9/9)

• INTER-R5
• Description of the section pointed to on the
  screen
• INTER-R6
• Description of the highway of which a section is
  pointed to on the screen

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3.5 Object-Oriented Models

• A Brief Overview of Object-Oriented DBMS
• Representation of Reference Schemas
• Spatial Classes
• Reference Queries

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A Brief Overview of Object-Oriented DBMS

• Database systems object-oriented programming
  languages
• Object Identity
• Using an identifier or oid (object identifier)
• Types, Classes, and Methods
• Type corresponds to its structure and to the
  operations
• Class objects with same type are grouped into
  classes
• Method express behavior of objects
• Encapsulation
• One accesses objects only via the methods defined
  on the class they belong to
• Without any knowledge of their detail of
  implementation
• Inheritance
• To define a (sub)class from an existing
  (super)class with a refinement of its structure
• Ex) Person -gt Student

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Representation of Reference Schemas (1/3)

• Each theme and each spatial ADT is materialized
  by a class
• Administrative Units (Schema 1)

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Representation of Reference Schemas (2/3)

• Highway Network (Schema 2)

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Representation of Reference Schemas (3/3)

• Land Use (Schema 3)

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Spatial Classes (1/2)
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Spatial Classes (2/2)

• Methods in class Region
• method pointInRegion (p Point) in class Region
  boolean
• method overlaps (r Region) in class Region
  boolean
• method overlapsRect (r Rectangle) in class
  Region boolean
• method clipping (r Rectangle) in class Region
  Region
• method intersection (r Region) in class Region
  Region
• method meets (r Region) in class Region boolean
• method area in class Region real
• Methods in class Line
• method pointInLine (p Point) in class Line
  boolean
• method length in class Line real
• method overlapsLR (r Region) in class Line
  boolean
• Methods in class Point
• method distance (r Region) in class Point real

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Reference Queries (1/2)

• OQL
• Similar to SQL
• Proposed by the Object Database Management
  Group(ODMG)
• To access complex structures, to run methods, and
  to return a result that may be structured in a
  complex way
• Queries with Alphanumeric Criteria
• ALPHA-ADM1
• Number of inhabitants in the County of San
  Francisco

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Reference Queries (2/2)

• Queries Involving Spatial Criteria
• SPAT-R3
• Length of Interstate 99