Topological Data Models and 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) Spaghetti Model (x 1,y 1 ) (x 2,y 2 ) (x 3,y 3 ) (x 4,y 4 ) (x 5,y 5 ) (x 6,y 6 ) (x 7,y 7 ) (X 8,y 8 ) (x 9,y 9 ) (x 10,y 10 ) (x 11,y 11 ) (x 12,y 12 ) (x 13,y 13 ) (x 14,y 14 ) StringCoordinate List S1(x 1,y 1 ), (x 2,y 2 ), (x 3,y 3 ), (x 4,y 4 ), (x 5,y 5 ), (x 6,y 6 ), (x 7,y 7 ), (x 8,y 8 ), (x 9,y 9 ), (x 10,y 10 ), (x 11,y 11 ), (x 12,y 12 ) S2 (x 3,y 3 ), (x 13,y 13 ), (x 14,y 14 ) (x 5,y 5 ), (x 14,y 14 ), (x 9,y 9 ) S3 P1 P2 P3 (x 1,y 1 )

Polygon Model Path Topological Models (2) (x 1,y 1 ) (x 2,y 2 ) (x 3,y 3 ) (x 4,y 4 ) (x 5,y 5 ) (x 6,y 6 ) (x 7,y 7 ) (X 8,y 8 ) (x 9,y 9 ) (x 10,y 10 ) (x 11,y 11 ) (x 12,y 12 ) (x 13,y 13 ) (x 14,y 14 ) P1 P2 P3 PolygonCoordinate List P1 (x 1,y 1 ), (x 2,y 2 ), (x 3,y 3 ), (x 13,y 13 ), (x 14, y 14 ), (x 9, y 9 ), (x 10,y 10 ), (x 11,y 11 ), (x 12,y 12 ), (x 1,y 1 ) P2(x 3,y 3 ), (x 4,y 4 ), (x 5,y 5 ), (x 14,y 14 ), (x 13,y 13 ), (x 3,y 3 ) P3 (x 5,y 5 ), (x 6,y 6 ), (x 7,y 7 ), (x 8,y 8 ), (x 9,y 9 ), (x 14,y 14 ), (x 5,y 5 )

The Slivering Problem Polygon A Polygon B

Path Topological Models (3) Ppoint Dictionary Model (x 1,y 1 ) (x 2,y 2 ) (x 3,y 3 ) (x 4,y 4 ) (x 5,y 5 ) (x 6,y 6 ) (x 7,y 7 ) (X 8,y 8 ) (x 9,y 9 ) (x 10,y 10 ) (x 11,y 11 ) (x 12,y 12 ) (x 13,y 13 ) (x 14,y 14 ) P1 P2 P3 PolygonPoint 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 PointCoordinate p1(x 1,y 1 ) p2 p14 (x 2,y 2 ) (x 14,y 14 )...

Path Topological Models (4) CChain/Point Dictionary Model P1 P2 P3 PolygonChain List P1 P2 P3 C1 C2 C3 C4 C5 C6 C1, C2, C3 C4, C5, C2 C6, C3, C5 ChainPoint List C1 p9, p10, p11, p12, p1, p2, p3 C2p3, p13, p14 ··· C6 p5, p6, p7, p8, p9 Point file necessary

Graph Topological models DIME (Dual Independent Map Encoding) File and a DIME segment p1p2 Tract 101 Tract 102 From Endpoint p1 To Endpoint p2 Left Tract 101 Right Tract 102

DIME Model of a Map P1 P2 P3 L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 Line Segment From Point To Point Left Polygon Right Polygon L1p9p10 P4 P1 L2p10p11P4P1 ··· L7p3p4P4P2 L8p4p5P4P2 L9p5p6P4P3 L10p6p7P4P3 L11p9p8P3P4 ··· L16p13p3P1P2 Point file necessary

Retrieval from DIME Structure (1) P1 P2 P3 L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 P4 Stage 1 – Retrieve all segments belonging to P3 L9 Seg. No.FromToLeftRight L10 L11 L12 L13 L14 p5p6P4P3 p6p7P4P3 p9p8P3P4 p8p7P3P4 p9p14P1P3 p14p5P2P3 Point file necessary

Retrieval from DIME Structure (2-3) P1 P2 P3 L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 P4 Stage 2 – Reorder the segments for path topology L9 Seg. No.FromToLeftRight L10 L11 L12 L13 L14 p5p6P4P3 p6p7P4P3 p9p8P3P4 p8p7P3P4 p9p14P1P3 p14p5P2P3 Point file necessary

POLYVRT System P1 P2 P3 P4 C1 C2 C3 C4 C5 C6 Chain From Node To Node Left Polygon Right Polygon C1N1N2P4P1 C2N2N4P2P1 C3N2N3P4P2 C4N3N1P4P3 C5N1N4P1P3 C6N4N3P2P3 Point list for each chain necessary, a polygon file (circular list of chains) recorded N1 N2 N3 N4

Node Model P1 P2 P3 P4 C1 C2 C3 C4 C5 C6 N1 N2 N3 N4 Node Cobounding Chains Right-hand Polygons Adjoining Nodes N1 N2 N3 N4 C4 C5 C1P4 P3 P1N3 N4 N2 C2 C3 C1P1 P2 P4N4 N3 N1 C6 C4 C3P2 P3 P4N4 N1 N2 C6 C2 C5P3 P2 P1N3 N2 N1 PolygonNode P1N1 P2N2 P3N3 Chain file containing its list of points necessary

Four Corner Situation UTCO AZNM N UT CO NM AZ N N’N’

Extended Chain Model P1 P2 P3 P4 C1 C2 C3 C4 C5 C6 N1 N2 N3 N4 Chain From Node To Node Left Polygon Right Polygon Left Chain Right Chain C1N1N2P4P1C4C2 N2N4P2P1C3C5 C3N2N3P4P2C1C6 C4N3N1P4P3C3C5 N1N4P1P3C1C6 N4N3P2P3C2C4 A polygon file containing the ID of one chain on its boundary and a chain file containing its list of points are recorded

PAN Graphs P AN P AN ( a )( b )

Questions 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.