Research on Real-Time Collision Detection Based on Hybrid Hierarchical Bounding Volume

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1 20 2 Vol. 20 o Joural of System Simulatio Ja., SphereOBB X Z X Sphere OBB-Sphere Z OBB Sphere Sphere OBB OBB OBB OBB TP9.9 A 004-7X (2008) Research o Real-Time Collisio Detectio Based o Hybrid Hierarchical Boudig Volume ZHU ua-feg, MEG Ju, XIE Guag-hua, MA We-jua Departmet of Computer Sciece ad Egieerig, Dalia Uiversity of Techology, Dalia 6024, Chia Abstract: Aalyzig the performace of various hierarchical boudig volumes (HBVs), a fast algorithm for real-time collisio detectio (CD) was proposed usig a structure of hybrid hierarchical boudig volume (HHBV) based o OBB ad sphere BV. The HHBV tree for CD falls ito three successive layers i a top-dow maer, which are Layer X usig sphere as its tree ode, Layer usig OBB-Sphere BV ad Layer Z usig OBB. The itersectio test uses sphere vs. sphere or sphere vs. OBB method for fast overlap test i upper layers, elimiatig the possibility of collisio betwee objects far apart; the it accurately determies the cotact status amog objects i closer proximity by OBB vs. OBB test i lower oes. Experimets were compared with other competitive algorithm (OBB) to aalyze the performace. Results show the algorithm is as efficiet i precisio as OBB, ad faster i complex virtual eviromet. Key words: collisio detectio; hierarchical boudig volumes; sphere boudig boxes; OBB X Sphere OBB-Sphere Z OBB Sphere-Sphere OBB-Sphere [] OBB O( 2 ) Sphere OBB [2] Sphere BSP K-DOP [] OBB Sphere AABB FDH [4] OBB [5] AABB (axis -aliged BVT boudig boxes) (spheres) OBB(orieted boudig boxes) () (982-) T= v Cv+ p Cp+ u C () u, (964-), 98- T v (98-) C v p 72

2 20 2 Vol. 20 o Ja., 2008 C p CDSphere_Sphere() Sphere-Sphere u C u CDSphere_OBB() OBB-Sphere CDOBB_OBB() OBB-OBB CDTraverse(a i b i ) START. (AABB) a i b i a i, b i Layer X or AABB (a i Layer X, b i Layer Z)or(a i Layer Z, AABB b i Layer X) [6].2 (Sphere) (box(a i ) box(b i )) CDFlag= =true BV a i a i a i Sphere [7] START b i b i b i. OBB P ai S ai, P bi S bi P ai P bi?f Φ HBVT CDTraverse 2.2 HBVT A X B X OBB Sphere-Sphere [8] CDSphere_Sphere() 2 A X B A X B X Sphere 2. Sphere-Sphere HBVT A X B X Sphere Sphere Sphere-Sphere OBB-Sphere Z OBB A X B Z X Z OBB-Sphere CDSphere_OBB() A X B Z OBB-Sphere HBVT Sphere-Sphere Sphere-Sphere OBB-Sphere OBB-OBB OBB-OBB OBB-OBB 5 ( OBB HBVT CDTraverse() a i b i 6 OBB 9 A, B box(a i ) box(b i ) 5 ) OBB-Sphere Layer X Z X Z CDFlag 7 Bool CDFlag=false Bool CDSphere_Sphere() CDFlag=CDSphere_Sphere CDFlag=CDSphere_OBB (box(a i ) box(b i ) Bool CDOBB_OBB() Bool CDSphere_OBB() a i,b i Layer or Layer Z, a i,b i Layer CDFlag=CDOBB_OBB (box(a i) box(b i)) ED

3 20 2 Vol. 20 o Ja., 2008 A OBB Sphere OBB A Z B Z OBB OBB-OBB CDOBB_OBB() OBB BV X Z X OBB-Sphere X Z Z OBB X.2 OBB OBB-OBB Z Z OBB X OBB-OBB 2 2 s (s>2) s>=2 s (s-) f(s)=(s-)*log 2 BV BVT(S) S s ( + ) f'(s)>0 f(s) s =2 f(s). HBV BVT BVT(S) S S. BV HBV BV BV.4 BV BV BVT BVT BV BV BV Z BV Sphere 2 S HBV HBV BV BV X OBB OBB 74

4 20 2 Vol. 20 o Ja., 2008 OBB BVT OBB i L i [9] i= 2 L i L i.4 X di= /2 Li i= 2 Z i HBV 4 4. BV v Sphere-Sphere OBB-Sphere OBB-OBB vv Sphere-Sphere (4) HBV oo 2 > r + r + 2rr (4) 2 o X Sphere o 2 o o 2 r r OBB-Sphere Z OBB 2 X 4..2 OBB-OBB OBB-Sphere OBB 2(a) OBB A B a i OBB sphere OBB b i A B i=, 2, A i B i A B 2 2 R= a + b + c 2 2 a b c OBB i=, 2, T A B L r A A L OBB i p i q i r B B L r i T L (r A +r B ) (2) (5) i i i m= ( p + q + r ) (2) ra= aiai L, rb= bb i i L (5) i= i= i = () i j i j i j C jk = p j pk + qjqk + rj rk, j, k () i i i i i i i TL > ra+ rb= aal i i + bbl i i (6) i= i= p = p m, q = q m, r = r m, A C B 4 C 5 A B OBB a b c X.4 Z OBB (a) (b).4 Z 2 75 (6) A B L 5

5 20 2 Vol. 20 o Ja., OBB-Sphere 2(b) OBB A (Sphere OBB) Sphere B a i A i=,2, r B A i OBB A i=,2, T A B Z OBB L r A r B A B OBB OBB L (7) OBB ra= aiai L, rb= r (7) i= T L (r A +r B ) 2 BV BV (8 A B L OBB OBB TL > ra+ rb= aal i i + r (8) BVT i= A B A B 2 A B A B B 4.2 HBV HBV BV 5 BV HBVHS AMD 64bit BV (AMD 64bit 000+ CPU, VIDIA 6800GT 2 BV GB DDR400 ) VC 8.0 BV BV BV HBVHS (a) (b) HBV Sphere OBB (c) (d) HBVHS RAPID X OBB HBVHS RAPID OBB X BV (fps) RAPID HBVHS

6 20 2 Vol. 20 o Ja., 2008 OBB 4 HBVHS RAPID OBB 5 HBVHS HBVHS FPS 0FPS HBVHS.76 HBVHS OBB 0 FPS (a) 496 (b) 694 (c) 96 (d) 06 / vs RAPID vs HBVHS / / FPS vs (FPS) / , 8(S) (ZHOU u-bo, A Qig-dog, HBV X BV LI Hog-cai. Collisio Detectio Algorithms Aalysis i Virtual BV Eviromet [J]. Joural of System Simulatio, (S) OBB-Sphere 0-07.) [4],,. [J]. OBB-Sphere OBB, 200, 2(2): [5],,. [J]. OBB 2006, 8(4): (MA Deg-wu, E We, LI ig. Survey of Box-based Algorithms for Collisio Detectio [J]. Joural of System Simulatio, 2006, 8(4): ) X Z [6] Larsso T, Möller TA. Collisio detectio for cotiuously deformig bodies [C]// The Proceedigs of Eurographics 200, Machester : Eurographics Associatio 200: 25-. [] M Li, S Gottschalk. Collisio Detectio betwee Geometric Models: A Survey [C]// The Proceedigs of IMA Coferece o Mathematics of Surfaces, Birmigham, UK, 998. Birmigham Eurographics Associatio 998: [7] [8] Palmer I J, Grimsdale RL. Collisio Detectio for Aimatio Usig Sphere-trees [J]. Computer Graphics Forum(S ), 995, 4(2): 05-6.,,. OBB [J]. [2], 200, (l): ,,,. [J]., 2005, 7(9): (ZHEG i, IG Ru-xi, LIU Jia-hua. Research o Fast Collisio Detectio Method i Virtual Assembly Eviromet[J]. Joural of System Simulatio, 2005, 7(9): ) [],,. [J]. [9],. [J]. 2005, 4(5):