TopologiTopological Data Models cal Data Models and Structuresand Structures

A major distinction among different vector data models is between those that have used a path topological approach versus those that have used a graph topological approach.

Today most vector models are a hybrid of both as path topological models became a subcomponent of the other.

Path Topological Models (1)Path Topological Models (1)

• Spaghetti Model(x1,y1)

(x2,y2)

(x3,y3)

(x4,y4)

(x5,y5)

(x6,y6)

(x7,y7)

(X8,y8)

(x9,y9)

(x10,y10)

(x11,y11)

(x12,y12)

(x13,y13)

(x14,y14)

String Coordinate List

S1 (x1,y1), (x2,y2), (x3,y3), (x4,y4),

(x5,y5), (x6,y6), (x7,y7), (x8,y8),

(x9,y9), (x10,y10), (x11,y11), (x12,y12)

S2 (x3,y3), (x13,y13), (x14,y14)

(x5,y5), (x14,y14), (x9,y9)S3

P1

P2

P3

(x1,y1)

• Polygon Model

Path Topological Models (2)Path Topological Models (2)(x1,y1)

(x2,y2)

(x3,y3)

(x4,y4)

(x5,y5)

(x6,y6)

(x7,y7)

(X8,y8)

(x9,y9)

(x10,y10)

(x11,y11)

(x12,y12)

(x13,y13)

(x14,y14)

P1

P2

P3

Polygon Coordinate List

P1(x1,y1), (x2,y2), (x3,y3), (x13,y13),

(x14, y14), (x9, y9), (x10,y10), (x11,y11),

(x12,y12), (x1,y1)

P2 (x3,y3), (x4,y4), (x5,y5), (x14,y14),

(x13,y13), (x3,y3)

P3 (x5,y5), (x6,y6), (x7,y7), (x8,y8),

(x9,y9), (x14,y14), (x5,y5)

The Slivering ProblemThe Slivering Problem

Polygon A

Polygon B

Path Topological Models (3)Path Topological Models (3)• Ppoint Dictionary Model

(x1,y1)(x2,y2)

(x3,y3)

(x4,y4)

(x5,y5)

(x6,y6)

(x7,y7)

(X8,y8)

(x9,y9)

(x10,y10)

(x11,y11)

(x12,y12)

(x13,y13)

(x14,y14)

P1

P2

P3

Polygon Point List

P1

P2

P3

p1, p2, p3, p13, p14, p9, p10,

p11, p12, p1

p3, p4, p5, p14, p13, p3

p5, p6, p7, p8, p9, p14, p5

Point Coordinate

p1 (x1,y1)

p2

p14

(x2,y2)

(x14,y14)

..

....

Path Topological Models (4)Path Topological Models (4)• CChain/Point Dictionary Model

P1P2

P3

Polygon Chain List

P1

P2

P3

C1C2

C3

C4

C5

C6

C1, C2, C3

C4, C5, C2

C6, C3, C5

Chain Point List

C1 p9, p10, p11, p12, p1, p2, p3

C2 p3, p13, p14

···

···

C6 p5, p6, p7, p8, p9

Point file necessary

Graph Topological modelsGraph Topological models• DIME (Dual Independent Map Encoding)

File and a DIME segment

p1 p2

Tract 101

Tract 102

From Endpoint p1

To Endpoint p2

Left Tract 101

Right Tract 102

DIME Model of a MapDIME Model of a Map

P1P2

P3

L1

L2

L3

L4L5

L6

L7

L8

L9

L10L11

L12

L13

L14

L15

L16

Line

Segment

From

Point

To

Point

Left

Polygon

Right

Polygon

L1 p9 p10

P4

P4 P1

L2 p10 p11 P4 P1

···

···

··· ···

···

L7 p3 p4 P4 P2

L8 p4 p5 P4 P2

L9 p5 p6 P4 P3

L10 p6 p7 P4 P3

L11 p9 p8 P3 P4

···

···

···

···

···

L16 p13 p3 P1 P2

Point file necessary

Retrieval from DIME Structure Retrieval from DIME Structure (1)(1)

P1P2

P3

L1

L2

L3

L4L5

L6

L7

L8

L9

L10L11

L12

L13

L14

L15

L16

P4Stage 1 – Retrieve all segments belonging to P3

L9

Seg. No.

From To Left Right

L10

L11

L12

L13

L14

p5 p6 P4 P3

p6 p7 P4 P3

p9 p8 P3 P4

p8 p7 P3 P4

p9 p14 P1 P3

p14 p5 P2 P3

Point file necessary

Retrieval from DIME Structure Retrieval from DIME Structure (2-3)(2-3)

P1P2

P3

L1

L2

L3

L4L5

L6

L7

L8

L9

L10L11

L12

L13

L14

L15

L16

P4Stage 2 – Reorder the segments for path topology

L9

Seg. No.

From To Left Right

L10

L11

L12

L13

L14

p5 p6 P4 P3

p6 p7 P4 P3

p9p8 P3P4

p8p7 P3P4

p9 p14 P1 P3

p14 p5 P2 P3

Point file necessary

POLYVRT SystemPOLYVRT System

P1P2

P3

P4

C1

C2C3

C4

C5C6

ChainFromNode

ToNode

LeftPolygon

RightPolygon

C1 N1 N2 P4 P1

C2 N2 N4 P2 P1

C3 N2 N3 P4 P2

C4 N3 N1 P4 P3

C5 N1 N4 P1 P3

C6 N4 N3 P2 P3

Point list for each chain necessary, a polygon file (circular list of chains) recorded

N1

N2

N3

N4

Node ModelNode Model

P1P2

P3

P4C1

C2C3

C4

C5

C6

N1

N2

N3

N4

NodeCobounding

Chains

Right-hand

Polygons

Adjoining Nodes

N1

N2

N3

N4

C4 C5 C1 P4 P3 P1 N3 N4 N2

C2 C3 C1 P1 P2 P4 N4 N3 N1

C6 C4 C3 P2 P3 P4 N4 N1 N2

C6 C2 C5 P3 P2 P1 N3 N2 N1

Polygon Node

P1 N1

P2 N2

P3 N3 Chain file containing its list of points necessary

Four Corner SituationFour Corner Situation

UT CO

AZ NM

N

UT CO

NMAZ

N

N’

Extended Chain ModelExtended Chain Model

P1P2

P3

P4C1

C2

C3

C4

C5C6

N1

N2

N3

N4

ChainFrom Node

To Node

Left Polygon

Right Polygon

Left Chain

Right Chain

C1 N1 N2 P4 P1 C4 C2

C2 N2 N4 P2 P1 C3 C5

C3 N2 N3 P4 P2 C1 C6

C4 N3 N1 P4 P3 C3 C5

C5 N1 N4 P1 P3 C1 C6

C6 N4 N3 P2 P3 C2 C4

A polygon file containing the ID of one chain on its boundary and a chain file containing its list of points are recorded

PAN GraphsPAN Graphs

P

A N

P

A N

( a ) ( b )

Questions for ReviewQuestions for Review• Please understand the spaghetti model,

polygon model, point dictionary model and chain/point dictionary model of the data structures and their respective advantages and disadvantages.

• Compare the DIME and POLYVRT file structures and their advantages and disadvantages.

• Describe the process of the retrieval of the outlines of polygons using the node model and the extended chain model.