ADJUSTING DEFORMATION METHODS FOR VIRTUAL REALITY SYSTEMS

Transcription

1 ADJUSTING DEFORMATION METHODS FOR VIRTUAL REALITY SYSTEMS Suene Ferrera Campos 1, Rone Marcos de Moraes 2, Llane dos Santos Machado 3 Abstract Vrtual Realty Systems for tranng have been proposed and developed wth the objectve to smulate real stuatons and to allow the acquston of specfc abltes of crtcal procedures. Bascally a Vrtual Realty System (VRS) s a real-tme system that presents nteracton and mmerson features to provde realsm n the applcatons. In some of these systems, for example the ones used n medcal area, the presence of vrtual models that answer morphologcally to nteractons becomes necessary. These models are known as deformable objects. Ths work presents an analyss of the methods for modelng deformable objects, dentfyng ther most approprate applcaton n VRS. In ths analyss, factors related to the qualty of the mages, methods for collson detecton between objects and computatonal performance s consdered. Index Terms Deformable objects, Methods of Deformaton, Systems of Vrtual Realty. INTRODUCTION Vrtual Realty Systems are computatonal systems used to generate vrtual worlds that present mmerson, nteractvty and real-tme propertes [1]. The combnaton of all these factors s responsble for the realsm n dfferent applcatons. These applcatons reach the most vared scentfc areas wth the objectve to allow acquston of practcal n the executon of crtcal procedures. In many applcatons the presence of vrtual models that present nteractve modfcatons n ther structure becomes necessary, snce objects wth these features are present n real envronments. Objects of vrtual envronments that present deformatons when touched are known as deformable objects. The methods used for modelng these objects are known as Deformaton Methods. There are some methods for modelng deformable objects. These methods can be dvded n two categores: geometrc methods and physcal methods. The geometrc methods are only based on mathematcs and for ths reason present a low computatonal cost and deformatons wth lmted realsm. By the other sde, physcal methods consder some complex physcal prncples n addton of the mathematcs. The physcal methods can offer realstc deformatons but demands a hgher computatonal cost [2]. To ncrease realsm n VRS by the use of deformable models s necessary an analyss to dentfy the most approprate deformaton method to be used. Ths analyss wll verfy the advantages and dsadvantages of each method accordng to the system applcaton. Besdes that, the vsual qualty of the deformatons, the collson detecton method and computatonal cost must be consdered n ths analyss. The choce made from that analyss results make possble the adequate mplementaton of the deformable objects, condton decsve to determne level of realsm of the systems. VIRTUAL REALITY Vrtual Realty (VR) s a recent research area that untes knowledge of many areas such as electroncs, computer scence, robotcs, physcs etc. The objectve of VR s to offer real-tme systems that ntegrate aspects of mmerson and nteractvty to smulate realstc envronments [3]. The qualty of the VR experence s crucal and t must stmulate the user n a creatve and productve way. It means that the vrtual envronment needs to react n a coherent form to the movements of the user, and make the experence realstc [1]. For ths reason t s mportant the presence of models that offer vsual answer to the nteractons n an equvalent way to ts real smlar. DEFORMABLE METHODS Deformable objects are computer generate models that can present deformatons n tme as a reacton of a contact wth them. In some cases the deformatons nclude physcal aspects of the materal of whch the model are consttuted [2]. Several methods have been developed to modelng of deformable objects. The mathematcal theory used as base for them represents a unon of Approach Theory, Geometry and Physcs. Geometry s used to represent the shape of the object, the Physcs mposes restrctons about the behavor n the space along the tme and Approach Theory offers theoretcal support to adapt the models n ts 1 Suene Ferrera Campos, scentfc ntaton student fnanced by PIBIC/CNPq, Department of Mathematcs, Federal Unversty of Paraba, Cdade Unverstára s/n, , João Pessoa, PB - Brazl, suenecampos@yahoo.com.br 2 Rone Marcos de Moraes, Department of Statstcs, Federal Unversty of Paraba, Cdade Unverstára s/n, , João Pessoa, PB - Brazl, rone@de.ufpb.br 3 Llane dos Santos Machado, Department of Informatcs, Federal Unversty of Paraba, Cdade Unverstára s/n, , João Pessoa, PB - Brazl, llane@d.ufpb.br

2 dmensons/measures and become possble the computatonal mplementaton of them [4]. Deformable methods can be classfed as geometrc methods (non-physcal) and physcal methods, and ther applcaton s based on requrements from the VRS where the model wll be used. Geometrc Methods (Non-Physcal Methods) Geometrc Methods use geometry foundatons n ther modelng process. In these methods, objects or the space around them are modfed due to manpulatons exerted on ther vertex and control ponts [5]. Generally, these technques present a low computatonal cost due to the concepts they are based on. They are adequate to systems that do not demand hgh levels of realsm [2]. Amongst the geometrc methods two can be hghlghted: Splnes and Free-Form Deformaton (FFD). - Splnes Splnes method works on the modelng of segments of curves from a process based n the Bézer method. It presents some mprovements as local control and hgher smoothness n the drawng of curves [6]. There are several types of Splnes but, n general they work on the form: Let be P 0, P 1, P 2, P 3..., Pn ponts n the R 3, P P +1 segments wth =0,1,2...,n-1 are consdered polygon lnes. By lnear nterpolaton for each t [0,1], one P pont s defned n each P P +1 segment through P = tp + (1-t)P +1 (1) to form new polygon lnes from the P 0,P 1,P 2,..., P n-1 ponts. After n steps, a polygon named as control polygon s generated and from t s obtaned a P 0 n pont. Ths pont s the value of P(t), a polynomal functon wth parameter t and degree n, that defnes the segment of curve to be formed. Takng an nteger k of 2 k n+1 and (x n ) an fnte ncreasng sequence called knot vector composed by n+k+1 real numbers, the functon P(t): [0,1] R 3 s defned by, n + 1 P(t)= P N (t), t mn t t max (2) k = 1 where N k s a polynomal functon defned n successve steps and represented by, N k 0, f ( t) = 1, f t [ x, x t [ x, x The knot vectors can be expressed on dfferent manner and could be unform or not. These varatons cause severe changes n the format of N k basc functons and modfy the ] ] (3) nfluence area of the control ponts. Due ths fact, there s a collecton of Splnes where the most popular are the B- Splnes, the ratonal B-Splnes, the non-unform ratonal B- Splnes (NURBS) and the Cubc B-Splnes [7]. A Splne model s formed by the assembled of several Splnes curves. The movement of the control polygons from the dfferent curves that generates the model allows ts deformaton. It does not gve an ntutve control of the movements to the user and, consequently, does not provde realsm to the model. Ths method s qute used n computer aded geometrc desgn (CAGD), manly n systems that requre computatonal effcency. - Free-Form Deformaton Free-Form Deformaton (FFD) method acts drectly on the vertex of the objects that need to be deformed. In ths method the object to be deformed s embedded n a standard geometrc lattce of control ponts, such as a cube. Soon after, the ponts of the lattce are connected through functons to the ponts of the object. The ntal form of FFD was ntroduced by Sederberg and Parry [8] and used the trvarate Bernsten polynomals: n n 1 B n( t) = t (1 t) (4) The space nsde the lattce s deformed when the control ponts of t are manpulated, what also deform the object contaned n the lattce. In other words, ths deformaton method works deformng the space where the objects s contaned. For a better refnement of the object deformaton s necessary a great amount of control ponts that wll turn more dffcult ts manpulaton as well as t wll ncrease the processng cost [2][8]. FFD has been used n assocaton wth other deformaton methods and also to modelng complex forms from ther geometrc prmtves. FFD are more ntutve than deformatons based on Splnes and they can be appled n dfferent graphcal representatons. Physcal Methods Physcally based methods can model objects by the restrcton of ts movements accordng to the physcs and dynamcs nvolved n nteractons wth them. Thus, nternal and external forces are consdered durng the smulaton what provdes more realstc behavors to the objects [6]. These methods use computatonal technology wth physcal prncples to develop realstc smulatons that demand hgh fdelty n the deformaton of objects. Most of the technques used for physcal objects modelng s reduced to two general categores: Mass-Sprng Systems and Fnte Elements Methods (FEM).

3 - Mass-Sprng Systems In a mass-sprng systems object geometry s represent by a three-dmensonal structure (lattce) composed by n mass ponts connected by sprngs what forms a regular polygon on ts surface. Each mass pont s the mappng of a specfc pont on the object surface. For ths reason, a mass pont dsplacement wll descrbe an object deformaton. The mechancal propertes of the object are descrbed by data stored n the mass ponts and sprngs. That s made through the assocaton of mass, dampng and stffness to the mass ponts and sprngs [9]. In dynamc mass-sprng systems, Newton's Second Law (F=ma) governs the moton of each mass pont n functon of the tme what generates a second order dfferental equaton. The moton of the whole body s calculated by the concatenaton of the moton equatons of all mass ponts n the lattce. It generates a dfferental expresson formed by mass (M), dampng(c) and stffness (K) matrces: Md 2 x/dt 2 + Cdx/dt +Kx =f (5) where f s a three-dmensonal vector of the sum of external forces actng on the ponts and x s a three-dmensonal poston vector formed by the concatenaton of the poston vector of all the mass ponts. The expresson (5) can be solved through a varety of numercal ntegraton methods to obtan the poston and velocty values of each pont n functon of tme and to determne the model deformaton [2]. Ths method can be used for soft deformatons modelng as well as for deformatons related to the human organsm. The approxmaton of the dfferental equatons solutons offers mages wth satsfactory qualty of realsm wth a tme of processng that doesn't commt the propertes of real-tme of the VRS. - Fnte Elements Methods Fnte Elements Methods (FEM) combne concepts of Mechancal Contnuum wth fnte elements methods for numercal approxmaton [2]. The contnuum propertes govern the deformaton process that wll be developed. Thus, FEM dscretze these propertes and allow the computatonal mplementaton of the method. The contnuum model of a deformable object consders the equlbrum state that can be nfluenced by external forces. Ths equlbrum state n dynamc systems s calculated through the potental energy ( ), determned by the stran (Λ) and work (W) appled to the object: = Λ - W (6) An object reaches equlbrum when ts potental energy s mnmum. The stran and work are expressed n terms of the object deformaton, whch s represented by a functon of the materal dsplacement over the object. Ths physcal process s mathematcally represented by a dfferental equaton that s approxmated by the fnte elements method. FEM dvde the object contnuum nto reduced dscreet ponts (fnte elements) and approxmate the equlbrum functon for each one of them. The model s represented by the jon equlbrum equatons that are expressed by several calculatons nherent to the strans and works generated by the system. The use of FEM has been lmted n VRS due to the contnuous re-calculaton of the equlbrum equatons for each manpulaton what commts the real-tme necessary for ths knd of applcaton [2]. DEFORMATION METHODS IN VRS Implementatons of deformable methods n VRS s a process that requre the combnaton of dfferent types of knowledge: - Computer Graphcs, to the vsualzaton and manpulaton of the vrtual models presented nto threedmensonal envronments; - Physcs, that models behavor features of objects and envronments propertes where the objects are nserted; - Mathematcs, that provdes the mathematcal descrptons of the physcal mechansms, of the generated models and all other foundatons used n the development of these types of systems, besdes the optmzaton of the systems; - Specfc knowledge of the scentfc area of VRS applcaton to provde the data and necessary nformaton about the objects features and envronments that composes the vrtual worlds to be generated. Ths assocaton allows the concepton of realstc systems and provdes solutons for several applcatons and specfc problems. However, a metculous analyss of the deformaton methods must be accomplshed to dentfy ts benefts n the VRS and do not compromse the real-tme of the applcaton. In a VRS a deformaton s related to nteractons wth and between objects and also to movements and forces appled durng these nteractons. A deformaton wll occur only when a contact exsts and a collson detecton method must be used to dentfy the contact poston and ts propertes. Ths fact make the mplementaton of the collson detenton algorthm a crtcal factor because ts bad use can compromse the real-tme feature of VRS [10]. In these systems, collson test routne uses the nteractons to dentfy contacts and calculate possble deformatons. Due to ths, the collson test routne s contnuously processed. Fgure 1 presents a dagram to llustrate how collson detecton and deformaton routnes are related n a VRS. Durng the system executon, when an nteracton occurs the collson detecton routne s called to verfy f there s contact between objects of the scene. When a contact happens, the propertes of the collson are provded to the

4 deformaton model to process the deformaton of the 3D model. FIGURE. 1 INTEGRATION OF COLLISION DETECTION AND DEFORMATION IN A INTERACTIVE VRS. CONSIDERATIONS ABOUT DEFORMATIONS METHODS IN VRS APPLICATIONS The qualty of deformaton provded by each deformaton method must be combned to the performance expected by the applcatons. The correct combnaton of these factors s possble wth the prevous plannng and study of the process to be smulated. It s mportant to dentfy the possbltes that each one of the deformaton methods can offer and how to adapt them to dfferent VRS. Because geometrc methods for deformaton are ndependent from materal characterstcs and external forces from the envronment where the object s nserted, they are not very realsts. By the other sde, they can be qute useful n systems that prortze the vsual renderng and do not depends on hgh levels of detals n the objects deformatons. CAD (Computer Aded Desgn) systems are one example of these systems. They make an extensve use of Splnes methods and request relatvely smple mathematcal foundatons, as functons, dstances and lneal transformatons to allow the modelng of complex objects by the composton of curves. When compared to the Splne method, FFD provdes a hgher and more powerful level of control about the deformatons. Besdes ts use for generaton of models n systems of geometrc modelng, Free-Form Deformaton method has also been used n assocaton wth other methods for deformaton, as masssprng methods for elaboraton of complex anmatons. In Physcal methods, the qualty of the deformatons s hgher when compared to deformatons based on geometrc methods. In Physcal methods, the computatonal cost requests care due the quantty of calculatons to be executed n each cycle of the VRS. In ths context, mathematcal technques for approxmaton are used to optmze results and then promote the non-commtment of the VRS real-tme. In general, VRS that ncorporate a physcal method of deformaton for objects present realstc deformatons due ncorporate nherent characterstcs of the materal that compose the objects and envronments n that they are nserted. The Mass-Sprng method s relatvely fast and easy to construct and allows realstc smulatons for vared objects, ncludng vscous and elastc tssues usually appled n medcal smulatons [11]. Ths method has been used n facal anmatons to model the smooth human facal expressons. The objects can be anmated at rates not reached wth FEM and present vsual realsm and low processng cost that does not commt the real-tme propertes of the VRS. The use of Fnte Elements methods n realtme systems s lmted due to the computatonal requrements demanded by the same. Ths occurs because FEM requre complex calculatons for each pont of an object to determne the deformaton of the whole object at each user nteracton. In spte of ths, the use of deformaton based on Mechancal Contnuum provdes objects wth accurate physcal propertes when compared to objects deformed by other methods. The applcaton of a specfc deformaton method n a graphcal system cannot be dscussed n an ndependent way. The advantages and dsadvantages that each one presents need to be dscussed n relaton to the specfc applcaton. It means that the method wll depends on the graphcal qualty related to the physcal propertes of the object and the performance of the system. The most mportant s to mantan the real-tme feature of the applcaton when deformable objects are present n a VRS. Because VRS are nteractve applcatons, a collson detecton method must be present to actvate the deformaton when a contact occurs between two objects. So, an deal deformable method must guarantee real-tme and graphcal qualty when runnng together wth a collson detecton model. The purpose of the applcaton must serve as base durng the choce of the deformaton method to allow the balance between cost and benefts and to avod any delay n the fnal result. ACKNOWLEDGMENT Ths research s partally supported by CNPq / and FINEP ref. 1898/04. REFERENCES [1] Netto, A.V., Machado, L.S., Olvera, M.C.F., Realdade Vrtual. Floranópols: Vsual Books, [2] Gbson, S., Mrtch, B. A Survey of Deformable Modelng n Computer Graphcs. Techncal Report. No TR Mtsubsh Electrc Research Laboratory. November [3] Machado, L.S., A Realdade Vrtual no Modelamento e Smulação de Procedmentos Invasvos em Oncologa Pedátrca: Um estudo de caso de Transplante de Medula Óssea. PhD Thess. Escola Poltécnca da USP

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