ANNALS of Faculty Engineering Hunedoara International Journal of Engineering

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1 ANNALS of Falt Engineering Hnedoara International Jornal of Engineering Tome XIII [15] Fasile 4 [Noember] ISSN: [CD-Rom; online] a free-aess mltidisiplinar pbliation of the Falt of Engineering Hnedoara 1. Ana-Elena IORDAN INTERACTIVE SOFTWARE DESIGNED FOR THE STUDY OF THE PARABOLOID 1. Uniersit Politehnia Timisoara, Falt of Engineering Hnedoara, ROMANIA Abstrat: This artile illstrates the reqired phases for the ahieing of the interatie software sed for the std of the ellipti paraboloid and hperboli paraboloid. The modelling of the interatie software is aomplished b speifi UML diagrams representing the phases of analsis, design and implementation. The analsis phase is harateried b two tpes of UML diagrams: se-ase diagram and atiit diagrams. The design phase is harateried b three tpes of diagrams: lass diagram, state diagrams, and interation diagrams. Implementation phase it orresponds the omponent diagram. B ahieing these tpes of diagrams, the interatie software ths is desribed in an obios and objetie manner, withot ambigit. The implementation of the software was realised throgh the Jaa programming langage. The main options of the software allow drawing a paraboloid, the normal line and tangent plane to a point, well as the appliation of isometr. Kewords: Interatie Software, Jaa, UML, Ellipti Paraboloid, Hperboli Paraboloid 1. INTRODUCTION In mathematis, a paraboloid is a qadri srfae. There are two kinds of paraboloids: ellipti and hperboli. The ellipti paraboloid is shaped like an oal p and an hae a maximm or minimm point. In a sitable oordinate sstem with three axes Ox, O, and O, it an be represented b the eqation [1]: (x x ) ( ) + p ( ) (1) a b where a and b are onstants that ditate the leel of ratre in the xo and O planes respetiel. This is an ellipti paraboloid whih opens pward for p> and downward for p<. The point of oordinates ( x,, ) represents the paraboloid ertex. For p 1 it obtains the following parametri eqations of ellipti paraboloid []: x(, ) x + a os (, ) + b sin ; R +, [,36]. () (, ) + The hperboli paraboloid is a dobl rled srfae shaped like a saddle. In a sitable oordinate sstem, a hperboli paraboloid an be represented b the eqation: (x x ) ( ) p ( ). (3) a b For p>, this is a hperboli paraboloid that opens down along the x-axis and p along the -axis. For p 1/4 it obtains the following parametri eqations of hperboli paraboloid [3]: x (,) (,) (,) x + a + b +. SOFTWARE ANALYSIS From the perspetie of nified modelling langage, interatie software analsis inldes the representation of two tpes of diagrams: the se-ase diagram and atiit diagrams. (4) 63 Fasile 4

2 ISSN: [CD-ROM]; ISSN: [online] The se-ase diagram [4] offers simplified and graphial representation of what the interatie software mst reall do. Use-ase diagram is based pon fntionalit and ths will fos on the "what" offers the interatie software and not the "how" will be realied. The se ase diagram orresponding to this software, presented in figre 1, inldes: an ator, seen se ases that desribe the fntionalit of the software and relationships among them. For eer se-ase of the preios diagram was ahieed an atiit diagram. Eah atiit diagram speifies proesses and algorithms sed to ahiee the prpose speified b the se-ase. In terms of UML, atiit diagrams [5] are meant to model both omptational proesses and those of the organiation. Atiit diagrams show the general flow of ontrol. In figre is rendered the atiit diagram orresponding to the se-ase Drawing of geometri elements speifi to the paraboloid. Figre 1. Use-ase diagram Figre. Atiit diagram 3. SOFTWARE DESIGNING Class diagram [6] represents the main blok of objetoriented modeling. It is sed both for stati oneptal modeling software as well as detailed modeling aimed at translating in programming sore ode. For ahieing the objeties of software were identified reqired lasses and the relationships between them. Figre 3 presents the inheritane, omposition and aggregation relationships sed. It ma be noted that all attribtes and methods of the Element3D lass will appl to the all its deried lasses: Dreapta3D, Plan3D, Pnt3D, and Paraboloid. Similarl, that all attribtes and methods of the Iometrie3D lass will appl to the all its deried lasses: Rotatie3D and Simetrie3D. This Figre 3. Class diagram lass diagram shows ontain speifi lasses to the interatie software as well as existing lasses and interfaes from Jaa. A seqene diagram [7] presents the interations between objets arranged in a temporar seqene. He desribes the objets inoled in interation and the seqene of messages exhanged between the needed objets to ahiee the desired prpose. Seqene diagrams are sall assoiated with a se-ase. The diagram illstrates in figre 4 shows the interations between objets, whih hae as prpose the drawing the tangent plane of a paraboloid. One an notie that there are interations between nine objets, ot of whih the objets of Sprafata3D, Vetor<Element3D> and GraphisD tpe are alread reated, and the other two objets: Parametr, Pnt3D, Plan3D and Paraboloid tpe will be instantiate dring the interations. At first the exetion ontrol is taken b the objet of Sprafta3D tpe. Following an eent that interats with the Sprafta3D objet allows the reation of an instane of Parametr lass. After getting the parameters that haraterie the paraboloid, ontrol is retrned to the Sprafata3D objet. Following is reated an instane of Pnt3D lass. The ontrol will be gien to the objet of Sprafata3D tpe that will destro the objet of Parametr. We an obsere that lifeline of the Parametr objet is interrpt, b marking an X, the message appears bearing the stereotpe <<destro>>. Control is transmitted to the objet of Vetor<Element3D> tpe to obtain the last drawing paraboloid. The ontrol will be gien to the objet of Sprafta3D tpe that will reate the objet of Plan3D tpe. Throgh interation with GraphisD objet will redraw the tangent plane. 64 Fasile 4

3 ANNALS of Falt Engineering Hnedoara International Jornal of Engineering Collaboration diagrams, on the other side, onentrate on the relationships among the objets [8]. The are er sefl for isaliing the wa seeral objets ollaborate to ahiee the intended prpose and for omparing a dnami model with a stati model (figre 5). Collaboration and seqene diagrams render the same information, and an be transformed into one another withot diffilt. The seletion of the two tpes of diagrams depends pon what the designer wants to make isall apparent. Figre 4. Seqene diagram Figre 5. Collaboration diagram Figre 6. Component diagram 65 Fasile 4

4 ISSN: [CD-ROM]; ISSN: [online] 4. SOFTWARE IMPLEMENTATION The omponent diagram [9] enables the isaliation modles that ompose the software and the dependenies between them. The diagram that is shown in figre 6 desribes the olletion of omponents that all together ensre the fntionalit of the interatie software. Central omponent of the diagram is Sprafata.lass, a omponent obtained b transforming b the Jaa ompiler into exetable ode of the Sprafata.jaa omponent. As an be seen that omponent interats diretl with omponents Sprafata3D.lass. This omponent interats with the next three omponents: Element3D.lass, Iometrie3D. lass and Parametr.lass. 5. GRAPHICAL USER INTERFACE The interatie software is aomplished sing the Jaa objet-oriented programming langage [1, 11]. From the appliation window it an seleted b a main men the following options:» the graphi representation of ellipti paraboloid;» the graphi representation of hperboli paraboloid;» the plan tangent and the normal line to the paraboloid into a point;» the paraboloid obtained b appling an isometr: rotation or smmetr. The eqation of the tangent plane to a qadrati srfaes in a point M(x,, ) is: x x x x For tangent plane determination in the point M(x,, ) at a paraboloid it starts from the parametri eqations of the paraboloid. The eqation of the tangent plane in a point M( x1 (,),1(,),1(,) ) at an ellipti paraboloid is: p x + q + r (p x1 + q 1 + r 1 ), p b p os where q a p sin. (6) r abp The eqation of the tangent plane in a point M( x1 (,),1(,),1(,) ) at an hperboli paraboloid is: p x + q + r (p x + q + r ), b p where a q. (7) a b r 8 In figre 7 it shows the tangent plane harateristi to an ellipti paraboloid, when the tangent point was determined sing an instane of Parametr lass, appling the defalt projetion (α-135, β-3, γ9). If it is desired the iewing sing the projetion angles (α -5, β 45, γ 16), the ellipti paraboloid with the tangent plane will hae representation shown in figre 8. The eqation of the normal line to a qadrati srfaes in a point M(x,, ) is: x x (8) D(, ) D(, x) D( x, ) D(, ) D(, ) D(, ) For normal line determination in the point M(x,, ) at a paraboloid it starts from the parametri eqations of the paraboloid. The eqation of the normal line in a point M( x1 (,),1(,),1(,) ) at an ellipti paraboloid is: x x (9) b os a sin a b The eqation of the normal line in a point M( x1 (,),1(,),1(,) ) at an hperboli paraboloid is: (5) 66 Fasile 4

5 ANNALS of Falt Engineering Hnedoara International Jornal of Engineering x x (9) b a a b 8 In figre 9 it shows the normal line harateristi to an ellipti paraboloid, when the tangent point was determined sing an instane of Parametr lass, appling the defalt projetion (α-135, β-3, γ9). If it is desired the iewing sing the projetion angles (α -5, β 45, γ 16), the ellipti paraboloid with the normal line will hae representation shown in figre 1. Figre 7. Tangent plane of an ellipti paraboloid Figre 8. Tangent plane of an ellipti paraboloid Figre 9. Normal line of an ellipti paraboloid Figre 1. Normal line of an ellipti paraboloid Figre 11. Hperboli paraboloid obtained b smmetr Figre 1. Hperboli paraboloid obtained b smmetr 67 Fasile 4

6 ISSN: [CD-ROM]; ISSN: [online] In figre 11 is represented a hperboli paraboloid obtained b appling a smmetr abot a plane, sing the defalt projetion (α- 135, β-3, γ9). If it is desired the iewing appling the projetion angles (α -5, β 45, γ 16), the hperboli paraboloid will hae representation shown in figre CONCLUSIONS Bease the representation of the diagrams orresponding to all three phases: analsis, design and implementation, the interatie software has been desribed in an obios and objetie manner, withot ambigit. The se of the nified modelling langage for the ahieement of the diagrams is harateried b rigoros sntati, rih semanti and isal modelling spport. The diagrams hae been ahieed sing a new approah, mltidisiplinar of the interatie software, groping both modern pedagog methods and disipline-speifi omponents. The onnetion between teahing atiities and sientifi goals and objeties was established throgh the deelopment of the new methods and the assimilation of new means, apable of enhaning shool performane, enabling stdents to aqire the knowledge and tehniqes reqired and appl them in optimm onditions. REFERENCES [1]. J. Gra, M. Esplen, D. Brannan, Geometr, Cambridge Uniersit Press, 11 []. W. MCrea, Analtial Geometr of Three Dimensions, Doer Pbliations, 6 [3]. A. Chrh, Elements of Analtial Geometr, 14 [4]. M. Fowler, K. Sott, UML Distilled: A Brief Gide to the Standard Objet Modelling Langage, Pearson Edation, 3 [5] J. Hnt, Gide to the Unified Proess featring UML, Jaa and Design Patterns, Springer London Ltd, 14 [6] K. Lnn, J. Skelton, S. Bennett, Sham s Otline of UML, MGraw-Hill Edation, 4 [7] B. Bregge, A. Dtoit, Objet Oriented Software Engineering Using UML, Patterns, and Jaa, Pearson Edation, 13 [8] A. Dennis, B. H. Wixom, D. Tegarden, Sstems Analsis and Design with UML, John Wile & Sons Ltd, 1 [9] P. Jalote, A Conise Introdtion to Software Engineering, Springer-Verlag, 8 [1] J. Brant, Jaa 7 for Absolte Beginners, Springer, 1 [11] J. Gosling, B. Jo, G. Steele, G. Braha, A. Bkle, The Jaa Langage Speifiation, Orale, 13 ANNALS of Falt Engineering Hnedoara International Jornal of Engineering opright UNIVERSITY POLITEHNICA TIMISOARA, FACULTY OF ENGINEERING HUNEDOARA, 5, REVOLUTIEI, 33118, HUNEDOARA, ROMANIA 68 Fasile 4