Real-Tme Two-way Couplng of Shp Smulator wth Vrtual Realty Applcaton Chen Hsen Chen Natonal Tawan Unversty Electrcal Engneerng Department Tape R.O.C. b91901045@ntu.edu.tw L-Chen Fu Natonal Tawan Unversty Electrcal Engneerng Department Tape R.O.C. lchen@ntu.edu.tw Abstract We present several new methods to promote the shp smulator appled to both physcally and graphcally realtme dynamc rendered ocean. The smulaton system s dvded nto three subsystems, the shps dynamcs system, the hydrodynamcs system, and two ways couplng between them. We apply hydrodynamc and mechancs to smulate the ocean surface and shp model respectvely. In ths paper, wave decay s taken nto consderaton waves propagatng velocty due to sea floor terran, wave generated by object floatng on the ocean and reflecton of wave due to conflct wth the shp. On the other hand, the shp would be affected not only by buoyancy but also vscosty, current, wave and dampng. Fnally we ntegrate ths algorthm to a 6 DOF platform and construct a vrtual shps drvng smulator. (Abstract) Keywords Vrtual realty, two-way couplng, real-tme, render, smulator (key words) I. INTRODUCTION The feld of flud smulaton has become maturer recently. Although the smulaton results has been realstc and appled to many felds such as anmaton, games and moves, they can not avod some lmtaton. Some smulaton results utlze complete physcal equaton and produce excellent renderng performance wth excessve computaton load due to offlne calculaton. Some are well-rendered and real-tme smulated, but the physcal smulaton s apparent that t does the two-way couplng between shps and water. For vrtual realty or other smlar applcatons, we need real-tme calculaton, but the accurate physcal smulaton s computatonally expensve. Therefore, we want to fnd an approxmate method to smulate the flud. We construct a heght map to depct water surface, and apply hydrodynamcs to smulate water surface and waves. The waves would obey physcal rules such as reflecton. When waves conflct wth shps, they change the propagaton velocty by water depth. Then, the shp acts along wth the waves and water surface, generates waves when t moves. In secton we have a bref overvew of prevous work. Secton 3 shows our ocean surface smulaton model, and secton 4 we descrbe the two-way couplng detal. Secton 5 shows the shp model. In secton 6 we mplement the 6-DOF smulator. Secton 7 shows the result. Dscusson, concluson and future work are descrbed n Secton 8. II. PREVIOUS WORK We take an overvew to the prevous work of flud smulaton. Claude Naver (18) and George Stokes (1845) formulated the Naver-Stokes equatons to do the realstc dynamcs of fluds. These equatons are the most common method to do the flud smulaton. They compute the flud grd and update the velocty feld every frame such as [1] There are also many works related to two-way couplng between flud and rgd body by N.V. equatons such as [] and [3]. Snce the N.V. equatons s tme consumng for real-tme smulaton, some methods smplfy the N.V. equatons to D for accelerate purpose lke [4]. Others smulatons use usng surface heght map. The heght map scarfes the precson of real flud to speed up. [5] gves a new method by ths to do the flud smulaton. They convert waves to partcles to mplement the reflecton phenomena. In addton to the two-way couplng smulaton, we also need other elements to buld the smulator. Frst, we need to control the shp nto the ocean surface. Thor I. Fossen gves a complete work to the marne control system. Next, we apply GPU technology to render the ocean [6]. It ntroduces GPU real-tme programmng methods. There are several mplementatons of ocean renderng lke [7]. For hydrodynamcs of the ocean waves, Leo H. Holthujsen eptomzed related work of these and descrbes the detals of the ocean waves propertes [8]. In the shp steerng theory, Hrano and Inoue et al. derved mathematcal models to maneuverng wth theoretcal experment [9-11]. Our work s based on them and can handle complcate terran and two-way couplng based on heght map flud renderng. III. OCEAN SURFACE MODEL We construct a heght feld ocean surface by trangle meshes frst. We contnue to utlze the concept of the wave partcle by [5]. They regard wave as a set of partcles,.e. we can arrange the partcles as a lne to form a wave. We can apply wave propertes based on ths model, for example, reflecton 1568 1-444-384-/08/$0.00 c 008 IEEE
and refracton. We take a bref ntroducton of ther work here. The heght of current poston on the ocean surface x = (x, z) s affected by each wave, η y( x, t) = D( x, t), (1) D( x, t) = aw ( x x( t)) () y s the heght of poston x and tme t. D s the local devaton functon, travellng on the surface. [5] fnally utlzes a π x x() t () t D (,) t = cos + 1 r x x x r where a s the ampltude of the waves and () s the rectangle functon. We can apply ths method to form each partcle to be a wave front. (From fgure 1(a) to fgure 1(b)) The partcles would splt to fll n the gap and avod the partcles dstance s too large and mantan the wave front shape. (3) We also apply other propertes of waves. The wave energy densty (energy per unt area) 1 E = ρga0 (5) (a) (b) Fgure. Theeffect of the ocean floor s terran. In (a), the left part of terran s shallow so the wave propagaton velocty s slower than rght part. (b) s the wave that doesn t affected by the terran. (b) Fgure 1. We can mantan the dstance of two wave partcles to compose a complete wave front. We modfy the wave partcle model of [5] not only reflecton wth boundary but also wth the shp hull and ocean s ntersecton surface, whch we wll descrbe later. Besdes, we also mplement the refracton phenomena by settng the propagaton velocty n dfferent medum. So we can add the effect of ocean floor terran based on hydrodynamcs. g g c= tanh( kd) = tanh( kd) ω k, (4) Here c s the propagaton velocty, k s the wave number, d s the depth of ocean, and g s the gravty acceleraton. The wave propagaton velocty would change any tme due to the depth of current poston. In order to add ths effect to [5] model, we need to modfy ther methods of them to satsfy our functon. The dfference between our method and [5] s the partcle splt condton. [5] calculates when the partcles dstance s too wde, but we calculate how long the partcles travel would cause the dstant too wde. For an unknown or rregular terran, t s mpossble to calculate when the partcles break up. (a) a 0 s ampltude of the wave. Then we can ntegrate t to obtan the sngle partcle s energy by wave shape. Fnally we mplement the attenuaton when the wave propagate. a a e k( t t0 ) current = 0 (6) a 0 and t 0 s the orgnal ampltude and tme, a current and t s the current ampltude and tme, k s the attenuaton coeffcent. IV. TWO-WAY COUPLING A. Object to Flud Couplng The man nfluence of object toward flud s the transformaton of object to flud couplng when the shp moves. It would squeeze the flud or cause flud vacancy. The shp velocty decdes the wave heght nduced by the shp. We utlze a = kv N A (7) 0 water a 0 s the ampltude, k s the coeffcent adjust by user. v s the velocty, N s the normal of the hull surface, A water s the area under ocean surface. In order to smplfy the calculaton, we utlze Awater = ld (8) l s the lne secton of the hull surface and ocean surface. d s the depth of the shp. By equaton (7)(8), we nduced sem crcle waves to be the shp waves. 008 IEEE Internatonal Conference on Systems, Man and Cybernetcs (SMC 008) 1569
B. Flud to Object Couplng Apply to the hydrodynamcs. When the shp travels on the ocean surface, t may have several forces addng on the shp hull. Fb = ρv F b s the buoyancy forces, s the densty of the flud, and V s the dsplaced volume of the flud. We can get V by separatng shp hull to many cubes and calculate ther vertcal poston by orentaton of the shp. 1 F ˆ d = ρv ACdv (10) 1 FL = ρ v ACL (9) (11) F d and F L are drag and lft forces of hydrodynamcs. s the densty of the flud, v s the velocty of the shp, A s the projecton area, C d and C L are drag and lft coeffcents. Drag force s the resstant force of object movng through a flud; t s parallel to the object s moton. Lft force s the force that object moves through a flud. It acts on the perpendcular of the stream flow. Then we process the reflecton of the partcles and shp. We set up the eght summts of the hexahedral shp, and then obtan them at world coordnate. We connect the summts and get twelve edges of the hexahedron, so we can calculate the ntersecton surface of edges and surface (fgure 3). For every edge e, and the two endng pont sa and sb, we can obtan the x and z poston x and z by the followng equaton. t = ( h y )/( y y ) (1) sa sb sa x = x + ( x x ) t (13) sa sb sa z = z + ( z z ) t (14) sa sb sa Where h s the heght of the ocean surface. Fgure 3. we calculate the ntersecton (x, z) of the shp s edge(lne sa sb) and ocean surface. Fnally we detect the edge of the ntersecton polygon and complete the settngs. Reflecton would happen when partcles contact the edges. When the partcles conflct wth the shp, t would add force to the shp hull, the amount of the force F w s decded by the velocty and the energy of the partcles. By F b, F d, F L and F w the flud. V. SHIP MODEL The followng shows the general equaton of the shp. M ν + C( νν ) + D( νν ) + g( η) = τ+ g + w 0 (15) s the shp s velocty and angle velocty. M( ) s the nerta matrx, C( ) s the Corols-centrpetal matrx. D( ) s Fgure 4. The ntersecton surface (green) between the shp and the ocean surface (blue). the dampng matrx, g( ) s the vector of the gravtatonal / buoyancy forces and moments. s the vector of control nputs. g 0 s the vector used for pretrmmng, w s the vector of envronment nterference. Here we neglect the C( ) and g 0 terms, the dampng matrx s gven by hydrodynamcs. We segment the shp nto many small cubes, calculate each cube s poston. We gve a buoyancy force and torque f the cube s under the surface. (Fgure 5) the g( ) term can be presented by F F buoyancy gravty buoyancy = Fb (16) = Fg (17) τ = τb (18) gravty τ = τg (19) The total force and torque s 1570 008 IEEE Internatonal Conference on Systems, Man and Cybernetcs (SMC 008)
Ftotal = Fbuoyancy + Fgravty + Fd + Fl + Fw + Fshp (0) τtotal = τbuoyancy + τgravty + τw + τshp (1) F d and F L are drag force and lft force by equaton 10-11, F w s the force of the wave, and F shp s the force of the shp motor and propeller. We apply dynamcs on the rgd body by [1], I 1ω1 ωω3( I I3) = τ1 I ω ωω 1 3( I3 I1) = τ () I ω ωω ( I I ) = τ 3 3 1 1 3 I 1 ~I 3 s the nerta tensor s term (I s the nerta tensor s matrx I term), s the angle velocty. We utlze ths equaton on our shp model by summng up the buoyancy, drag, lft, waves, gravtaton, propellers forces and moments. Update the poston and orentaton. The physcal part of smulator s complete. The washout flter controls moton on the 6-DOF platform wll let people n the cabn feel the acceleraton and angle velocty (fgure 7). We can control the joystck on the cabn. Drve the shp and sal on the ocean. The scene of ocean would be projected by the projector fxng on the top of cabn. The vrtual realty shp smulator s complete. The ppelne of our graphcal and physcal system s: For each frame () Generate Waves () Detect Wave Collson () Add Forces and Moments () Update Poston and Orentaton () Transfer data to Washout Flter () Renderng by Cg () Renderng by OpenGL () Frame end () Generate Waves () ncludes the partcle generaton and renew the heght feld. Detect Wave Collson () handle the wave partcle reflect detecton. For extractng the angle velocty and acceleraton of the shp, we need excute all of these functons (expect Renderng by GPU ()) on the CPU. We only handle the ocean renderng on GPU. We get the ocean scene (Fgure 8) by summng up wave partcles heght of the ocean, and then nteract wth our shp. The platform wll do moton when the hull moves. People can feel lke drvng a shp n the ocean now. Fgure 9 shows the smulaton result. We gve a large z drecton sngle snusodal wave to the shp wthout reflecton, and observe the respond of the shp. We compare the smulaton angle velocty and the rotaton of the vrtual shp and the measured values of the Stewart platform. By ths way, we can analyss the fdelty of our smulator. Fgure 5. The blocks above the surface (black) and the blocks under the surface (red). Only the red blocks would add buoyancy force and torque. VI. 6-DOF STEWART PLATFORM SIMULATOR Next we ntegrate the ocean scene to our 6-DOF moton smulator (Fgure 6). General vrtual realty smulator wll make our model looks realstc. The physcal part of smulator s descrbed n the last secton. The graphcal part s done usng GPU operatons. The work of feelng realstc would be descrbed n next secton. We extract acceleraton and angle veloctes, whch are senstve to human, from one computer handled graphcal and physcal smulaton. We transfer these data to the other computer whch processes the washout flter. When we do moton on the lmted range moton platform, we need flter to retan parameters that s perceptual by human and washout other unnecessary parameters. Fgure 6. The hardware and software structure of our smulator. 008 IEEE Internatonal Conference on Systems, Man and Cybernetcs (SMC 008) 1571
(a) Fgure 7. The 6-DOF Stewart Platform (up and the cabn (down). VII. RESULT (b) Fgure 8. The ocean scene of our vrtual envronment. Because the physcal unt n the smulaton system s dfferent to the real MKS unt, so when we send data to the platform, we need to scale the parameters to ft the real scale. The coeffcents need to be adjusted to make the results close to the human percepton. Comparng wth the sx curves, we can fnd out the parameters tendency that platform measured s approxmate to the smulaton feed. The undulaton of the platform curves happen before the rase of the angle velocty a rotaton values s that the acceleraton of the shp s also be detected. Due to the lmted range of the platform, the washout flter does somethng beforehand to ft the human percepton. The speed of our two-way couplng shp smulator s nearly 40 frames per second on our laptop wth a 1.73GHz sngle core processor 1 GB RAM and ATI RADEON X700 64MB graphcs card. (c) Fgure 9. The upper fgure s the platform motons; the lower fgure s the parameter graphc system feed. Horzontal axs s smulaton frames (a) The angle velocty of yaw, the vertcal axs s degree/s; (b) the rotaton responds to z axs, the vertcal axs s degree (c) the rotaton responds to x axs., the vertcal axs s degree. VIII. DISCUSSION AND CONCLUSION The wave partcle method can acheve our goal of two-way couplng wth the shp and waves. Partcles are more flexble and faster than other methods such as summng up snusod waves or Naver-Stoke smulaton. Based on Naver s method, we can apply t on a varety of applcatons, and successfully construct a real-tme two-way couplng ocean scene. Wth our smulator, we can construct more realstc envronment of ocean scene by hydrodynamcs. It combnes 157 008 IEEE Internatonal Conference on Systems, Man and Cybernetcs (SMC 008)
graphcs and control foundaton to acheve the physcs, vsual and physcal effects. The system can be wdely used for other applcatons. It can be developed to the shp operaton tranng smulator, entertanment machne, dynamc anmaton theatre and even help people get over seasckness by combnng wth medcal scence. Because we need to extract the parameters from the GPU, we do lttle computaton on the GPU whch s only used for renderng the ocean surface. Base on ths model, we can add more effects wth GPU n the future. The foam and splash of the waves are approprate. In addton, the hgh dynamc range scene and other surroundng objects wthout nteracton wth the hull and ocean surface can enhance the vrtual realty scene. ACKNOWLEDGMENT We would lke to thank Can Yuksel for hs help. Ths work was supported by Natonal Scence of Councl under the grant NSC 96-18-E-00-033. REFERENCES [1] M. Matthas, C. Davd, and G. Markus, "Partcle-based flud smulaton for nteractve applcatons," n Proceedngs of the 003 ACM SIGGRAPH/Eurographcs symposum on Computer anmaton San Dego, Calforna: Eurographcs Assocaton, 003. [] C. Mark, J. M. Peter, and T. Greg, "Rgd flud: anmatng the nterplay between rgd bodes and flud," ACM Trans. Graph., vol. 3, pp. 377-384, 004. [3] B. Chrstopher, B. Florence, and B. Robert, "A fast varatonal framework for accurate sold-flud couplng," n ACM SIGGRAPH 007 papers San Dego, Calforna: ACM, 007. [4] J. X. Chen, N. d. V. Lobo, C. E. Hughes, and J. M. A. M. J. M. Moshell, "Real-tme flud smulaton n a dynamc vrtual envronment," Computer Graphcs and Applcatons, IEEE, vol. 17, pp. 5-61, 1997. [5] Y. Cem, H. H. Donald, and K. John, "Wave partcles," ACM Trans. Graph., vol. 6, p. 99, 007. [6] T. I.Fossen, Marne Control System: Marne Cybernetcs, 00. [7] C. Johanson, "Real-tme water renderng," n Department of Computer Scence. vol. Master: Lund Unversty, 004. [8] L. H. Holthujsen, Waves n oceanc and coastal waters Cambrdge : Cambrdge Unversty Press, 007. [9] M. Hrano, "Calculaton Method of Shp Maneuverng Moton at Intal Desgn Phase," J. SOC. NAVAL ARCHIT. JAPAN, vol. 147, pp. 144-153, 1980. [10] J. T. M. Hrano, and Y. Takash, "Shp turnng trajectory n regular waves," Transacton of the West-Japan Socety of Naval Archtects, vol. 60, pp. 17-31, 1980. [11] M. H. S. Inoue, K. Kjma, and J. Takashna, "A Practcal Calculaton Method of Shp Maneuverng Moton," Internatonal Shpbuldng Progress, vol. 8, pp. 07-, 1981. [1] H. Goldsten, Classcal Mechancs: Addson Wesley, 199. 008 IEEE Internatonal Conference on Systems, Man and Cybernetcs (SMC 008) 1573