Conceptual modeling of line oriented objects

• Lines in fact represent an infinite number of points

• how can we represent them

• use vector modeling– use of extensional rules– may be explicit– may be implied

• in Arc/Info for example all are implied

Basic idea of representation

• selection of privileged points (data)• several ways to select privileged points

– different representations possible

• given different ways we need to define rules– generating

• mechanisms such as equations through which privileged points can be ‘extended’ to the full set of points

– membership• rules to test to determine if a particular point meets

specifications of object

Ideal and practical schema

• Different rules for selection of privileged points will lead to different representations

Storing line segments

Store “rule” x = xa + t(xb - xa) y = ya +t(yb - ya) o <= t <= 1

Relational representationSEGMENT(Segment-ID, Point1-ID, Point2-ID)POINT(Point-ID, X, Y)+RULE: point-in-segment rule

Polylines

POLYLINE0 (Polyline-ID,Closure-flag)POLYLINE1 (Polyline-ID, Segement-IDSEGMENT( Segment-ID, Point1-ID, Point2-ID)POINT (Point-ID, X , Y)RULE: point-in-polyline by iteration of point-in-segment rule

If represented by set of sorted points then:POLYLINE2(Polyline-ID, Closure-flag)POLYLINE3 (Polyline-ID, Point-ID, Order-of-point)POINT(Point-ID, X, Y)RULE: point-in-polyline by iteration of point-in-segment rule

POLYLINE (Polyline-ID, (Point-ID)*)

Mixit- or mixed form-lines

Spline curve based line structure

Simple polygon structure

POLYGON(Polygon-ID, Point-ID, Order-of-point)POINT(Point-ID, X, Y)RULE: point-in-polygon

Complex isolated polygons

POLYGON(Polygon-ID, Segment-ID)SEGMENT (Segment-ID, Point1-ID, Point2-ID)POINT( Point-ID, X, Y)RULE: point-in-polygon

Irregular tessellation

Polygons delimited by polylines

Tessellations delimited by mixtilines

Oriented polygons

ORIENTED_POLYGON(Polygon-ID, Segment-ID, Orientation)SEGMENT(Segment-ID, Point1-ID, Point2-ID, Left-Polygon-ID, Right-polygon-ID)POINT(Point-ID, X, Y)RULE: point-in-polygon

Hierarchical territories

Graph modeling

EXTREMITY(Edge-ID, Node1-ID, Node2-ID)NODE (Node-ID, Edge-ID)LINKS (Edge-ID, Neighbor-edge-ID) EXTREMITY(Arc-ID, To-node-ID, From-node-ID)

TO-ARC (Node-ID, To-arc-ID)FROM-ARC(Node-ID, From-arc-ID)TO-ARC-LINK(Arc-ID, To-arc-ID)FROM-ARC-LINKS(Arc-ID, From-arc-ID)

City blocks and land parcels

Land parcels and blocks together

Street and city blocks

Conceptual model of a river

Model for pipes

• Road structures

Conceptual model for road structure