Czech Technical University in Prague Faculty of Transportation

Czech Technical University in Prague Faculty of Transportation Sciences Department Transport Telematics Geographical Information Systems Doc. Ing. Pavel Hrubeš, Ph. D.

Rehearsal precision in graphics traditional cartography data volume topology computation update continuous space integration discontinuous raster vector x x v v v v x x x x v Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

§ Vector data models § § § Spaghetti model Topological model (most common) Triangulated irregular network (TIN) Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Spaghetti data model Polygon Coordinates A (1, 4), (1, 6), (6, 4), (4, 4), (1, 4) B (1, 4), (4, 1), (1, 4) C (4, 4), (6, 1), (4, 4) § 6 A 5 4 § 3 B 2 C 1 § 1 2 3 4 5 6 The spaghetti model is the most simple vector data model The model is a direct representation of a graphical image NO explicit topological information Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Spaghetti data model § § § Description: direct line for line translation of the paper map (often viewed as raw digital data) Easy to implement, good for fast drawing Storage and searches are sequential, storage of attribute data Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Topology § Branch of mathematics dealing with geometric properties § Topology of objects remain invariant under transformations § Neighborhood relationships remain the same § Topology is the distinguishing basis for more complicated vector models Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Topological Vector Model Topological data models are provided with information that can help us in obtaining solutions to common operations in advanced GIS analytical techniques. § This is done by explicitly recording adjacency information into the data structure, eliminating the need to determine it for multiple operations. § Each line segment, the basic logical entity in topological data structures, begins and ends when it either contacts or intersects another line, or when there is a change in direction of the line. § Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Topological Vector Model § Each line has two sets of numbers, a pair of coordinates and an associated node number. § Each line segment has its identification number that is used as a pointer to indicate which set of nodes represent its beginning and ending. Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Topological Vector Model Polygons also have identification codes that relate back to the link numbers. Each link in the polygon now is capable of looking left and right at the polygon numbers to see which two polygons are also stored explicitly, so that even this tedious step is eliminated. § The Topological data model more closely approximates how we as map readers identify the spatial relationships contained in an analog map document. § Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Topological vector model Vector Model: Topological Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Topological model for 3 D § 3 D entities § nodes, § edges, § faces, § volumes § a support entities : § rings -, list of edges round the face § shells -, list of faces round the volume § Pfund, M. , 2001, Topologic data structure for a 3 D GIS, . Proceedings of ISPRS, Vol. 34, Part 2 W 2, 23 -25 May, . Bangkok, Thailand, pp. 233 -237 Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Node Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Node § Unique coordinates X, Y a Z. § It is not possible that two points overlays. § In 2 D space should be Z coordinate different. Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Edge Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Edge § It is collection two or more vertexes, orientation is done by its order. § Edge cant cross another edge. Node has to divide both edges. § Edges are connected only in nodes. Faces or rings have to contain it complete. Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Face Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Face § Geometrie of face is defined: § Collection of on ore more edges which form the face, § Collection of non or more interior points which form the face, § Collection of non or more interior nodes which are identical to nodes of appropriate edges. Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Rings Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Ring § Rings are collection of edges which form a face. Each ring is connected to the specified are, one edge should be contained by more rings. § Edge, which is inside the face and is connected to the border of face is also contained by the ring. Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Shell Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Shells § Shell is collection of two or more faces § Face, which is a border between two volumes is contained by both shells. § Shell should contain one face twice, for both orientations of the face. § Each face within volume, connected to the border of volume, is contained by shell. Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Volume Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Volume § Volume is 3 D object collected from faces. § Volume cant cross or overlay another volume. § Should have inside a empty space, which is defined by inside faces. Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Topological links § Link Node - Edge § Link Node - Face § Link Node - Volume § Link Edge – Face § Link Edge - Volume § Link Face - Volume § „Floating“ Node and Edge Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Link Node - Edge Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Link Node - Face Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Link Node - Volume Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Link Edge – Face Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Link Edge - Volume Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Link Face - Volume Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

„Floating“ Node and Edge Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics

Database implemetation of 3 D data model Czech Technical University in Prague - Faculty of Transportation Sciences Department Transport Telematics