Two-Dimensional Topology Structure between Vector Layers in GIS

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2011, Scienceline Publicatin Jurnal f Civil Engineering and Urbanism Vlume 1, Issue 1: 10-14 (2011) ISSN-2252-0430 Tw-Dimensinal Structure between Vectr Layers in GIS Davd Parvinnezhad Hkmabadi* 1,

1 2011, Scienceline Publicatin Jurnal f Civil Engineering and Urbanism Vlume 1, Issue 1: (2011) ISSN Tw-Dimensinal Structure between Vectr Layers in GIS Davd Parvinnezhad Hkmabadi* 1, Ali Asghar Alesheikh 2, Mhammad Hssein Jahanpeyma 3 and Arash Rahmanizadeh 4 1,4 Marand Faculty f Engineering, University f Tabriz, Tabriz, Iran 2 Department f GIS, Faculty f Gedesy and Gematics Eng. K.N. Tsi University f Technlgy 3 Department f Civil Engineering, University f Maragheh, Maragheh, Iran *Crrespnding authr dparvinnezhad@tabrizu.ac.ir ABSTRACT: Queries in Spatial databases, such as Gegraphic Infrmatin Systems, are ften based upn the relatinships amng spatial bjects. Unfrtunately, currently used GIS sftware d nt supprt cmplete tplgical structures. As such, answering tplgical queries is time cnsuming, if nt impssible. In this paper, the 9-intersectin mdel is implemented using ActiveX and Dynamic Link Library (DLL) Technlgies. The main characteristic f this package is t create cmplete tplgical relatinships between 2D bjects in a GIS envirnment. Results f the test have shwn the superirity f the prpsed structure versus current cmmercial GIS sftware. Keywrds: Tplgical Relatinships, 9-Intersectin Mdel, Lgical Operatins, Tplgical Queries, Spatial Queries INTRODUCTION Queries in Spatial databases, such as Gegraphic Infrmatin Systems, image databases, r CAD/CAM systems, are ften based upn the relatinships amng spatial bjects. Fr example, in gegraphic applicatins typical spatial queries is Retrieve all cities which are within 50 kilmetres f the interstate highway and typical tplgical queries is Find all highways in the prvince adjacent t City X. Spatial relatins are the basis f many queries that Gegraphic Infrmatin Systems (GISs) perfrm, as such the tplgical relatins deserves a fcused attentin frm GIS researchers. Current cmmercial query languages d nt sufficiently supprt such queries, because these languages prvide nly tls t cmpare equality r rder f simple data types, such as integers r strings. The incrpratin f spatial relatinships ver spatial dmains int the syntax f a spatial query language is an essential extensin beynd the pwer f traditinal query languages. There are three aspects fr gemetry f features: Psitin and rientatin can be expressed with respect t a spatial reference r crdinate system. The psitin f each pint will then be represented by a crdinate pair. The rientatin f sides can be expressed by their angles with respect t (ne f) the crdinate axes. The shape and size f gemetric figures can be expressed withut any reference t a crdinate system. These metric aspects can be derived frm the length f the sides f the figures and frm the angles between their sides. This infrmatin is invariant under changes f the reference system, i.e. crdinate transfrmatins. The tplgical relatinships between the bjects can be described withut reference t their psitin, rientatin, shape and size. These are relatinships like: inside, adjacent t, intersect, etc. Tplgical relatinships are invariant under all cntinuus transfrmatins f the crdinate systems and cntinuus defrmatins (Figure 1). Figure 1: Examples f invariant tplgical relatinships. Three classes f spatial relatinships are discriminated which are based upn different spatial 10 T cite this paper: Parvinnezhad Hkmabadi D, Alesheikh A.A, Jahanpeyma MH, Rahmanizadeh A Tw-Dimensinal Structure Between

2 cncepts (Examples are terms like neighbur and disjint): Spatial rder and strict rder relatinships rely upn the definitin f rder and strict rder, respectively. In general, each rder relatin has a cnverse relatinship. Fr example, behind and its cnverse in-frnt-f. Metric relatinships explit the existence f measurements, such as distances and directins. Tplgical relatinships are invariant under tplgical transfrmatins, such as translatin, scaling, and rtatin. Three different frmal appraches exist fr the definitin f spatial relatinships. The first ne is based upn distance and directin in cmbinatin with the lgical cnnectrs AND, OR, and NOT. This apprach has tw severe deficiencies: (1) It is nt pssible t mdel inclusin r cntainment, unless negative distances are intrduced. (2) The lack f apprpriate cmputer numbering systems fr gemetric applicatins impedes the immediate applicatin f crdinate gemetry and distance-based frmalisms fr spatial relatinships. The secndary apprach is based n the representatin f spatial data in the frm f pint sets. Binary relatinships are described by cmparing the pints f tw bjects with cnventinal set peratrs, such as equal, and less than r equal. A serius deficiency inherent t the pint sets apprach is that nly a subset f tplgical relatinships is cvered with this frmalism. While equality, inclusin, and intersectin can be described, the pint set mdel des nt prvide the necessary pwer t define neighburhd relatinships. The third apprach is based n the intersectin f the bundary, interir, and exterir f tw bjects t be cmpared and distinguishes nly between empty and nn-empty intersectin (The 9-intersectin mdel). This methd is superir t the ther tw frmalisms because it describes tplgical relatins by purely tplgical prperties. The 4-intersectin and 9-intersectin are tw cmprehensive mdels fr binary tplgical spatial relatins and applies t bjects f type regin, line, and pint. The 4-intersectin mdel characterizes the tplgical relatin between tw pint sets, A and B, by the set intersectins f A s interir (A 0 ), and bundary ( A) with the interir, and bundary f B. Hence, the 9-intersectin mdel is better than the 4-intersectin mdel in perfectly expressing the tplgical relatinships between tw bjects. In 9- intersectin mdel with each f these nine intersectins being empty (0) r nn-empty (1), the mdel distinguishes 512 different tplgical relatins between tw pint sets, sme f which cannt be realized, depending n the dimensins f the bjects and the dimensins f their embedding space (fr example r000). The pssible relatins are represented in table 1. Table 1: The pssible relatins between 2D features. Type f intersectin Number f pssible relatins Regin-Regin 10 Regin-Line 19 Regin-Pint 3 Line-Line 33 Line-Pint 3 Pint-Pint 2 Sme f the pssible tplgical relatinships between 2D features are represented in Figure 2. The relatins will be presented by a binary cde which can then be cnverted t a decimal number. T btain the binary cdes a 9-field tuple is defined as fllws: r11 r12 r13 RX(A,B) r21 r22 r23 r11 r22 r21 r12 r33 r13 r23 r31 r32 r 31 r32 r r r11 2 r22 2 r21 2 r32 2 Fr example: r119 : Figure 2: The pssible tplgical relatinships between 2D features is shwn in Figure 2 as A, B, C and D parts The 9-intersectin mdel The 9-intersectin mdel characterizes the tplgical relatin between tw pint sets, A and B, by the set intersectins f A s interir (A 0 ), (, and exterir (A ) bundary A) bundary, and exterir f B (Eq. 1). with the interir, R X (A,B) A A A B B B (1) A B A A B B A B A B A B 11 T cite this paper: Parvinnezhad Hkmabadi D, Alesheikh A.A, Jahanpeyma MH, Rahmanizadeh A Tw-Dimensinal Structure Between

3 Fig.2, A: Tplgical relatinships between tw regin bjects. Fig.2, B: Tplgical relatinships between regin and line bjects. IMPLEMENTATION T use the 9-intersectin mdel in GIS, a sftware package has been designed and implemented. The Fig.2, C: Tplgical relatinships between tw line bjects. Fig.2, D: Tplgical relatinships between (a) regin and pint bjects, (b) line and pint bjects, (c) tw pint bjects. implementatin flwchart and the applied interface fr the sftware are represented in Figures 3, 4, respectively. 12 T cite this paper: Parvinnezhad Hkmabadi D, Alesheikh A.A, Jahanpeyma MH, Rahmanizadeh A Tw-Dimensinal Structure Between

Enter tw vectr layers Layer names are the same? One-layer fr each layer Inter-layer Kind f layer? Create the regin One-layer exists? Create the line What is kind f relatin?

4 Enter tw vectr layers Layer names are the same? One-layer fr each layer Inter-layer Kind f layer? Create the regin One-layer exists? Create the line What is kind f relatin? Create the pint Inter-layer? (If tw layers exit) END Create the regin-pint Create the line-pint Create the regin-line Create the pint-pint Create the line-line Create the regin-regin Figure 3: The flw-diagram f the written sftware. Figure 4: The interface f the sftware. One layer tplgy Pint tplgy: By running the sftware, three fields are added t an attributes table. These three fields cntain Pinted, X, and Y as crdinates. An instance f the result fr this status has been represented in Figure 5. Figure 5: One-layer tplgy fr pint. Line tplgy: Once the sftware ran, fur fields are added t an attributes table. These fields cntain Lined, Frm nde, Tn de, and Length. The instance f running sftware fr this case has been represented in Figure T cite this paper: Parvinnezhad Hkmabadi D, Alesheikh A.A, Jahanpeyma MH, Rahmanizadeh A Tw-Dimensinal Structure Between

layer tplgy fr line. Regin tplgy: Running the sftware, creates an additinal table i.e. three fields

three fields fr representing tplgical relatins.

8: Inter-layer tplgy fr line-line. 9: Inter-layer tplgy fr line-plygn. 7: One-layer tplgy fr plygn.

pint-plygn, line-line, lineplygn, and plygn-plygn.

5 Figure 6: One-layer tplgy fr line. Regin tplgy: Running the sftware, creates an additinal table i.e. three fields cntain Plygn nd, Perimeter, and Area, are added t an attributes table and ne new table that cntains three fields fr representing tplgical relatins. An instance f running sftware fr this status has been represented in Figure 7. Figure 8: Inter-layer tplgy fr line-line. Figure 9: Inter-layer tplgy fr line-plygn. Figure 7: One-layer tplgy fr plygn. Inter-layers tplgy Inter-layers tplgy is described in 6 statuses as pint-pint, pint-line, pint-plygn, line-line, lineplygn, and plygn-plygn. In all f these cases and using the ne-layer tplgy, ne new table is created. This new table represents tplgy between tw layers. The instances f running sftware fr these statuses have been represented in Figure 8, 9, 10. Figure 10: Inter-layer tplgy fr plygn-plygn. CONCLUSION 14 T cite this paper: Parvinnezhad Hkmabadi D, Alesheikh A.A, Jahanpeyma MH, Rahmanizadeh A Tw-Dimensinal Structure Between

6 Tplgical queries are psed frequently nce a GIS is used. They require the infrmatin abut the relatinships between tw spatial bjects. Currently used sftware lacks the capability f presenting a cmplete tplgical structure. Recgnizing this prblem, the paper aimed at delving n the design and implementatin f a cmplete tplgical structure. A cmprehensive review f the methds that can create such a structure has been presented in this paper. The methds are scientifically assessed. With the use f practical examples, the paper is then revealed the results f running prepared sftware fr creating a cmplete 2D tplgical structure. REFERENCES 1. Egenhfer, M.J A Frmal Definitin f Binary Tplgical Relatinships. Lecture Ntes in Cmputer Science, 367: Egenhfer, M. J A Mdel fr Detailed Binary Tplgical Relatinships. Gematica, 47(3&4): Egenhfer, M.J. and Mark, D. M Mdelling Cnceptual Neighburhds f Tplgical Line- Regin Relatins. Internatinal Jurnal f Gegraphical Infrmatin Systems 9 (5): Egenhfer, M.J. and Shariff, B. M Metric Details fr Natural-Languages Spatial Relatins, ACM Transactins n Infrmatin Systems, 16, (in press). 5. Mlenaar, M An Intrductin t the Thery f Spatial Object Mdelling in GIS, Lndn: Taylr & Francis. 15 T cite this paper: Parvinnezhad Hkmabadi D, Alesheikh A.A, Jahanpeyma MH, Rahmanizadeh A Tw-Dimensinal Structure Between

Deriving the Composition of Binary Topological Relations

Deriving the Composition of Binary Topological Relations Deriving the Cmpsitin f Binary Tplgical Relatins Max J. Egenhfer Natinal Center fr Gegraphic Infrmatin and Analysis and Department f Surveying Engineering Department f Cmputer Science Bardman Hall University