VISUAL SELECTION OF SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES

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1 UbCC 2011, Volume 6, x manuscrpts OPEN ACCES UbCC Journal ISSN VISUAL SELECTION OF SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES Mohammed Al-Matah Computer scence department, Ryadh communty college, Kng Saud Unversty, Saud Araba ABSTRACT For vsual pctoral presentaton of three-dmensonal geometrc objects wth the help of modern computer engneerng t s necessary to have effectve program realzaton of programmatc selecton of specfc ponts and also feature lnes of the surfaces represented wth the help of functon of two varables. Ths artcle gves techncal approach from the poston of the surface type allowng to undertake vsual selecton of the surface features durng ther geometrc smulaton wth the help of computer technologes. Keywords: three-dmensonal geometrc smulaton, surface feature. 1 INTRODUCTION One of the dynamcally growng n software development today s development of new nformaton technologes and methods of vsualzaton of the program performance results [1, 2], that s such a presentaton of them whch s perceved by a person n the most adequate way. The theme of the work s actual as vsualzaton s one of new nstruments for gettng new knowledge about the object under consderaton whle desgnng complcated engneerng constructons. The followng terms, determnng basc types of the surface, are used n the work. Hll cone-shaped elevaton on the surface. It has a characterstc pont peak. Peak - the pont of the surface of the maxmum heght. Slope - sde surface Rdge - elevaton on the surface, gong down n one drecton and havng two steep slopes. Depresson - deepenng n the surface n the form of a bowl. The lowest pont of the depresson s the pont of the surface of the mnmum heght. Ravne- prolate deepenng n the surface, gong down n one drecton. Saddle - the lowered part of the surface between two peaks. Surface shape can be descrbed as ts feature that has sx basc vsualzatons: peak, rdge, slope, ravne, saddle, depresson [3]. The generally accepted three-level herarchy of the presentaton of the surface geometrc model n three-dmensonal space served as analogue whle determnng levels of the model of the characterstc forms. The surface model can be determned by three basc levels. At the lowest level the model s lmted to pont presentaton (by the set of coordnates of ponts x, y, z). The second level ncludes the frst one wth the addtonal descrpton of the topology of connectons between ponts (wre-frame model). On the thrd level connectons unte n closed boundares (facet model). Descrpton of the surface model from the poston of form has a smlar structure (table 1) UbCC Journal, Volume 6: Issue 1 736

2 Level number Table 1:Surface model accordng to shape Geometrc model Model of characterstc shapes 0 level Pont Hll, saddle, depresson 1 level Edge Rdge, ravne 2 level Bound (facet) Slope These vsualzatons make set V. In scheme the un ambguty of characterstc shapes s acheved by analyss of four of the condtonal snk, as shown n fg.1. peak rdges Thus, the peak n the ndcated scheme s determned by four zero, and the depresson - by four unt. For determnaton of the schemes of the rest of the forms t s necessary to set to tracng of the four of the condtonal snk. Let s set to clockwse drecton. The begnnng of the tracng wll be the drecton upwards. As a result we have a four-bt set, determnng n ts dfferent combnatons the decmal values from 0 to 15 (set V). Hence, the area of the form s characterzed by the followng classfcaton (table 2). Table 2: Classfcaton of surface types A O V E V peak rdge 1 depresso slopes rdge saddles ravnes rdge rdge Fgure 1: Man vsualzaton of typcal shape slope slope 6 2 TECHNICAL APPROACH TO VISUAL SELECTION OF THE SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES FROM THE POSITION OF SHAPE. By condtonal snk we ll mean the drecton from a hgher pont to a lower one. The drecton of the condtonal snk s shown wth an arrow n the scheme. Template encodng stpulates the followng. If the drecton comes from the central pont, we wll consder t as zero. Otherwse, when the drecton comes n central pont, we wll defne t as unt slope slope ravne ravne ravne 13 UbCC Journal, Volume 6: Issue 1 737

3 V ravne saddle saddle depres son 15 After generalzaton the table looks as follows (Table 3). Table 3: Unambguous shape presentaton A O V e V All Peak 0 from the One drecton to the Rdge 1 Two on one lne to the Two perpendcu lar Three All saddle 3 Slope 5 ravne 7 depress on Generc varable V for the concrete varable s determned wth the help of abstractve 9 functon e 1 : V V [4]. Ths functon must be somorphc as to orderng to V. Thus, functon e, accordng scheme (see fg.1), can be defned as functon of transton from the decmal presentaton of the nteger bnary Eq. (1). e 1 k k (2) where k 0,1,3,5,7,9., (1) The set of decmal values of shape vsualzaton s mutually unambguous reflecton of the set V and makes the set V. Set V conssts of sx subsets V, where =1,6. Set V contans sxteen dfferent elements whch as a result of mutual unambguous reflecton passes elements of subsets V of set V. Accordng decmal value of each of sx concrete forms the domnant drecton of the condtonal snk s determned. 3 VISUALIZATION OF GEOMETRIC FEATURES OF THE SURFACE, DETERMINED THROUGH FUNCTION OF TWO VARIABLES Let s consder functon of two varables F(x,y). To determne the decmal value of the surface form vsualzaton of the gven functon F(x,y), t s necessary to consder the drecton of the condtonal snk. Let s desgnate: - Meanng Functon (),[=0,3]- as meanng of functon F(x,y) n four of the condtonal snk; - Meanng Functon _Center - meanng of functon F(x,y) n the central pont of the template; - Sgneq. (2) - decmal value of the surface form vsualzaton of the consdered template. The successve comparng of values of Meanng_Functon() wth the value Meanng_Functon_Center gves an opportunty to defne the decmal value of the form vsualzaton. Sgn Sgn( ), (2) f 3 0 UbCC Journal, Volume 6: Issue 1 738

4 Sgn( ) 2, Meanng _ Functon Meanng _ Functon _ Center; Sgn( ) 0. It s conceptually suggested that a many-sded pyramd wth the regular base fgure and amount of faces multple to four should be consdered an element of the form. Let s consder an example wth a pyramd wth regular base. Applcaton of an n - angle wth the regular base and amount of sdes multple to four enables to use n /4 templates, outgong from the vertces of the n - angle. As a result we get n/4 schemes as auxlary templates (fg.2). oppostely drected as other of the condtonal snk of the analyzed area. Thus, the decmal value for rdge s determned as check for equalty of the derved decmal value combnaton of values 2, where s an amount of of the condtonal snk. Smlarly to that for ravne the decmal value of the form of the area s compared combnaton of values n , where s the amount of the of the condtonal snk. The other varety of combnatons s not unambguous and s elmnated from consderaton. By fllng of the convex areas (hll, rdge) wth green color and concave areas (depresson, ravne,) wth dark blue colour, we get an mage consstng of the specal ponts and lnes of the studed surface. In the test example (fg. 3.) wth the use of octahedron as an element of the shape on the rectangular area, t s shown the result of the performance of the method of vsual selecton of specal ponts and characterstc lnes on the surface fractures. Fgure 2: Placng of templates orentaton for an otagon The task conssts n vsual selectng of pont and lnear forms of the studed surface by means of teraton clarfcaton of the form vsualzaton of the examned area The prncple of vsual selecton of forms conssts n researchng of the drecton of the condtonal snk by means of determnaton of decmal value of form vsualzaton. As every turn of the template ncreases the amount of combnatons of form vsualzaton, t s suggested that only some unambguously determned ones should be selected. The followng four man types should be consdered unambguously determned ones: hll, depresson, rdge and ravne As hll and depresson presuppose the sngle drecton of the condtonal snk ether central pont of the studed area or from t, the decmal value for hll s determned as equal to zero, and for n1 depresson as 2, where n s the amount of the 0 studed of the condtonal snk on the area beng analysed Rdge and ravne come to lght as exstence of the unque drecton of the condtonal snk whch s Fgure 3 a: surface descrbed by the functon x y z 100cos (Math CAD) Fgure 3 b: Vsualzatons of specfc ponts and characterstc fractures. UbCC Journal, Volume 6: Issue 1 739

5 4 CONCLUSIONS: 1. In ths work t s suggested a method of the data ware of the condtonal snk for the selecton of the specfc ponts and characterstc lnes of the surface fractures of the shape, durng ther geometrc smulaton wth the help of computer technologes, whch allows to mprove qualty of the graphc mage of the object beng desgned. 2. The suggested method of the data ware of the condtonal snk allows to provde good and valdated graphc presentaton of geometrc shapes whch s especally mportant whle desgnng complcated engneerng constructons. 5 REFERENCES [1 ] W. Bruckschen Ralph., Kuester Falko, Hamann Bernd, I Joy Kenneth: Real-Tme Out-of-Core Vsualzaton of Partcle Traces., IEEE, 2001 Symposum on Parallel and Large-Data Vsualzaton and Graphcs PVG, pp (2001). [2] T.J.Jankun Kelly, Ma Kwan-Lu, Gertz Mchael: A Model for the Vsualzaton Exploraton Process., Proc. of IEEE Vsualzaton. pp (2002). [3] N.A.Korneev: Grapho-analtcal desgn style of vertcal shapng. M.:Stroyzdat,pp. 131 (1983). [4] J. Klr George Systemology: Automaton of Systems problem solvng.: transl. from Englsh: Archtecture of Systems problem. M. Rado and communcaton,. p 540 (1990). UbCC Journal, Volume 6: Issue 1 740