N6ng Minh Nggc vd Dig Tap chi KHOA HQC & CONG NGHE 128(14): 199-204 PHirONG PHAP PHAT HIEN VA CHAM DU'A TREN CAU TRUC CAV PHAN CAP G i d l HAN BIEN U N G DUNG KY THUAT HOP BAO THEO HUOtNG Nong Minh Ngoc'', Pham Dinh Lam', D5 Ning Toin^ 'Dgi hpc Thdi Nguyen, ^ Vi4n Cong ngh? thong iin Dgi hoc Qudc gi TOM TAT Tinh toSn va phdt hien va cham giii'a cac doi tuong dang la mot nhiem vu rat quan upne cua m6i h? thong thuc tai ao CSc dSi tugng moi he thong d6 hoa co nhiJng chuySn dong rieng cua n6, chuyen d^ng c6 the va ch^im voi d6i tugng khde, hoSc c6 thS va ch^m vdi moi trucmg, chudng ngai vat Bai bao trinh bay ve mot phuong phSp phat hien va cham dua tren cau triic cay phan cdp gioi han biSn (BVHs) Ung dyng ky thuSt hop bao theo huong nham phat hi?n va cham giiJa c^c doi tuong thuc t^i ko Cite ket qua nghien cuu da chung minh tinh chinh xdc, giam thlSu dfl phiic tap thuat todn, thoi gian tinh todn doi vijri cac phuang phap d3 duoc gi6i thieu Til- kh6a: Bounding volume hierarchies BVHs Collision Detection, OBBs, AABB, Thuc tgi GIOI THIEU Viec mo hinh hoa cac doi tUQug a the giai th\rc vao khong gian kiSn true a thyc t^i ao nhu mo phong ducmg di ciia he Robot, anh xa va mo phong cac doi tugng vat ly tren he th6ng thuc t^i ao da va dang duoc img dung rgng rai hau hk cac ITnh vuc ciia doi s6ng xa hoi: Giao due va dao tao, quan su, y hgc Phuang phap phat hien va cham dua tren cau true cay phan cap giai h?n bien (bounding volume hierarchy - BVHs) da va dang dugc sii dung bien vai viec su dung cac giai h^n bao quanh cac doi tugng dang hinh cau (spheres), dang hop bao theo cac c^nh song song vai cac tryc tga dp (axis-aligned bounding boxes - AABBs), hop bao theo huang cua doi tugng (Oriented Bounding Boxe - OBBs), d6i dac theo k huong cua da giac (k-discrete oriented polytopes- kDOP) Cac phucmg phap dua tren giai han bao quanh doi tugng dugrc dinh nghTa mgt each ro rang cac khong gian chira doi tugng Bai bao tap trung ki8m thir va danh gia thuat toan phat hien va cham giu'a cac doi tugng dua tren cau true cay phan cap giai han bien vai kj thuat sit dung hop bao theo huong OBBs Cac ket qua danh gia se dugc neu ra, dap ung cac yeu cau bai toan ' Tel: 0968 595888 PHUONG PHAP PHAT HIEN VA CHAM U"NG DUNG KY THUAT HOP BAO THEO HUC)NG Dinh DghTa hQp bao theo hvong (Oriented Bounding Boxes-OBBs) Dinh nghTa: hop bao theo huong OBB la hop bao dang dac biet cua hop bao AABB nhung CO huang bat ky ma khong phai huang trimg vai huang ciia true toa Mgt hinh bao OBB dugc dinh nghta thong qua mpt tam C, ba vector chi huong cita hinh hop ^g, ^4,, ^4;, ba dai tuang la kich thuac ciia hinh hop ao>0, ai>0, a2>0 Khi do, dinh ciia hinh hop se dugc xac djnh nhu sau: C + ^ , a , *^, \s, |=1,/ = 0,1,2 (1) 1=0 Viec kiem tra hai khoi da dien loi khong giao neu co the co lap dugc chiing bang mgt mat phang P thoa man mgt hai dieu kien sau: - P song song vdi mgt mat nao ciia mgt hai khoi da dien - Hoac la P chua mgt canh thugc da dien thir nhat va mgt dinh thugc da dien thir hai Tir nhan xet tren, ta thay rang de kiem tra nhanh su giao ciia hai hai khoi da dien loi: Dieu kien can va du de kiem tra hai khoi 199 Nong Minh Ngoc vd Dtg Tap chi KHOA HOC & CONG NGHE da dien loi co giao hay khong la kiem tra giao giQa cac hinh chieu cua chiing Ien duang thang vuong goc voi m§t phang P a tren, duang thang duge ggi la true co lap Ta thSy r^ng cac hop bao OBBs la nhirng khoi da dien 161, boi vay ta hoan toan co the ap dung djnh ly h^n 6.k ki§m tra va cham giua chiing 128(14): 199-204 Theo [xxx] ta co bang tinh toan l^m can cu ki6m tra va cham giira hai hop bao OBBl va 0BB2 nhu o bang CAU TRUC CAY PHAN CAP Gl6l HAN BIEN (BOUNDING VOLUME HIERARCHIES -BVHS) Cay phan cap gioi ban (bounding volume hierarchies-BVHs) Cay phan Icfp gidi han (bounding volume hierarchies-BVHs) la mpt cau triic cay doi vofi I nhom cac d6i tuang hinh hgc Cac doi tugng hinh hgc dugc bao cac hinh bao (bounding volumes) Cac hinh bao cac Node la ciia cay Cac Node sau dugc gom cac nhom nho va dugc dong kin cac hinh bao lan hon TuSn tu nhu vay, chung Hinh True cd Idp (Separating Axis) de kiem tra ciing lai dugc gom lai va dong kin cac hinh bao Ion han nita theo kieu lap lai Cuoi su va cham cua OBBl vd 0BB2 cimg se tao nen mgt cau triic cay voi mpt hinh Phuong phap kiem tra va cham giira hai bao dan tai dinh ciia cay Cau tnic hinh bao hop bao OBBs tuan tu dugc diing dS hg trg mgt vai phep Cho hai hinh bao OBBs xac djnh bai eac toan Ien tap hgp cac hinh kh6i mgt each hieu thong so OBBl: [Co,Ao,A|,A2,ao,aba2] va qua tieu bieu nhu giai quyet bai toan phat 0BB2: [C|,Bo,Bi,B2,bo,b|,b3] Ta thay rang hien va cham (collision detection) cac tinh huong ma hai OBBs tiep xiic voi Xay dumg cay phan lorp gioi ban (khong c4t nhau) chi eo th6 la mgt De xay dimg cay phan lap giai han, nhieu truong hgp sau day: mat - mat, mat - c^nh, nhom tac gia da d6 xuSt cac phucmg phap tinh mat - dinh, canh - canh, canh - dinh, dinh dinh Do vay, tap ung cu vien cac true co lap toan nhu: Chia cat a giifa cac true dai nhat, chi toi da la 15 true sau: Chia cat o gia tri trung binh, Chia cSt dua tren thuat toan SAH (Surface Area Heuristic) - true chi huong ciia hop bao thii nhit (A^) Trong bai bao nay, phuang phap xay dung - true chi huong cua hgp bao thir hai (Bj) cay phan lap gioi han dua tren thuat toan chia - true tao boi tich co huong cua mgt true cat Node goc cac Node (trai/phai) can thugc hop bao thir nhat va mgt true thugc hop cii- vao gia tri trung binh ciia khoi bao bao thir hai {A,®Bj) (Median-Cut): Mat khac, ta biet rang neu mgt true la true co Y tuong cua phucmg phap dugc neu nhu lap thi tjnh tien den vj tri nao, no van la sau: Cac doi tugng dupe sap x€p dgc theo true CO lap Bai vay, khong mat tinh tong quat mgt ba true tga x,y,z Khi do, xac ta se ggi true co lap co vector chi phuong la V djnh dugc gia tn trung binh tga dp ciia cac d6i va di qua tam CO cua hop bao thu nhat, tugng tren true tga dg da lya chon, dong thcri vay no co phuang trinh nhu sau: tiSn hanh c5t d6i tupng hai Node &^C^+X*V (2) tuang ung la Node trai va Node phai thong qua gia tri trung binh da dugc tfnh toan, xac Trpng do: t la tham so V la A^ hoac S^ dinh o tren hoac A, ®B^ vai i,j = 0,1,2 N6ng Minh Nggc va Dig Tsp chf KHOA HOC & CONG NGHE 128(14): 199-204 Bang I Cdc gid Irj R, R,,, R, cho thdy viec cd va cham giira OBBs xdy khi: R> Rn+R, V i?i R &jkool + 6lkc,i|-|-t2k32l \Ao-D\ &)kiol + fiikiil + (^zkijl \Ai-D\ hj|'J20| -I-61IC21I +'l2k22| \A2'D\ Bo AJ Oo 4i m A ao iSj ookwl + i i k i o l + aalcjcil bo \BoD\ Bl CIok(3l| + «lk-ll|+.