D6 Thi Chi vd Dtg Tap chi KHOA HOC & CONG NGHE 132(02): 17-23
NGHIEN C i r u MOT SO KY THUAT PHAT HIEN VA CHAM AP DUNG TRONG MO PHONG C H U Y E N DONG CO HOC
D§ Thi Chi', LS Son Thai',B6 NSng Toan^
Trudng Dai hoc Cong nglie thong tin vd truyen thong —DH Thai Nguyen Vien Cong nghe thong tin — £)// Quoc gia Hd Not TOM T A T
Phat hien va ch^m la phan quan trong anh huong Ion t6i do chinh xac trong cac tinh toan vS d6ng hgc. Day la m6t ITnh vuc nghien ciiu moi dugc sir quan tam ciia nhiSu nha khoa hoc nhSim mo phong chinh xac su tuong tac vat 1;^ gii^a cac v§t thi tren man hinh miy tinh. Trong ngi dung bai bao tap trung cii d|t thu nghiem, so sanh va danh gia cic ky thuat phat hien va cham. Tir do chon ra dugc kf thuSt phCi hgp cho bai toSn m6 phong dong hoc trong mot so dieu kien cu the. Bdo cao gom 4 phan: Phan 1 gi6i thieu tong quan ve va cham va mo phong co hoc trong thuc t^i ao; Phan 2 la cdc giai phap phdt hien va cham dang dugc nghifin ciru; Ph^n 3 phan tich v^ lira chon phuong ph^p phat hien va cham phii hgp voi bai t o ^ m6 phong co hoc; PhSn 4 kSt luan danh g\A thuat toan.
TCi' kh6a: Phat hien va cham, thuc tai do, khoi bao, khoi bao cau, khoi bao hop, phan vimg khong gian, mo phong
TONG QUAN VE VA CHAM VA MO PHONG CO HOC TRONG THUC TAI AO Thuc tai ao [1][2] la ITnh vuc nghien ciru nham mo phong the giai thuc cua con nguai tren man hinh may tinh. Trong nganh co dien tu, viec mo phong khong chi dirng lai a nhu'ng phan mem m6 phong mach dien ma con CO xu huong phat trien cac he thong mo phong CO hgc, kha nang chiu tai cua may moc trong qua trinh hoat dgng... Tren thuc te, viec che tao cac he ca dien tir phai trai qua giai doan lam ban mau va tien hanh thuc nghiem de kiem tra tinh kha thi truoc khi san xuat hang loat, qua trinh nay doi hoi chi phi Ion.
Nghien ciru, phat trien mo phong giup cho nguoi thi6t ke c6 kha nang kiem chirng san pham thay cho viec tao mau ma do chinh xac CO the chap nhan dugc. Do la nguyen nhan ma ITnh vuc mo phong dugc sir quan tam, nghien ciru ciia nhieu nha khoa hgc va da co nhiJng thanh tuu nh§t dinh.
Trong the gioi thuc ton tai rat nhieu d6i tugng, moi doi tugng co hinh dang va tinh chat vat ly khac nhau. Be mo phong chinh xac cac tucmg tac vat ly, cac nha nghien ciiu quan tam toi hai van de: mot la viec xac djnh chinh xac va cham giua cac doi tugng [3][6][7]; hai Tel- 0985 882793, Email- [email protected]
la qua trinh xii' ly tuong tac dgng hgc khi cac d6i tugng do va ch&m voi nhau [5], Phat hien va cham [6][7] la viec giai quyet bai toan khi hai vat the ran chuyen dgng gan nhau CO xay ra va cham khong. De phat hien va cham giii'a hai d6i tugng mot each chinh xac ta kiem ti-a tii'ng mjt ciia d6i tugng nay co cat m6t mat nao do ciia doi tugng kia hay khong, viec lam nay co uu diem la cho ta chinh xac diem va cham. Tuy nhien, moi doi tugng 3D duac X^o thanh tir Ax nhieu mat [8] (thong thuong la cac tam giac) nen chi phi de kiSm tra giao nhau ciia tirng cap mat rat ton kem v6 mat thai gian. Mat khac, cac he thong thuc tai ao lai doi hoi xir ly trong thoi gian thuc [1].
Vi vay, de giai quy6t vSn de nay, hau het cac he thong deu su dung phuong phap gSn dung d6 phat hien va cham [6]. DiSn hinh la sir dung khoi hinh hgc bao quanh ddi tugng [3].
Voi moi d6i tugng, ta tim mot kh6i bao thich hgp quanh no, viec phat hien va chjtm bay gio dugc dua ve bai toan phat hien giao nhau giira cac khoi bao. Cac loai khoi bao gom: khoi bao theo true AABB (Axis Aligned Bounding Box), khdi bao theo huong - OBB (Oriented Bounding Box), khoi bao cSu - BS (Bounding Sphere), kh6i bao da dien K-Dop (Discrete Oriented Polygon). Trong do, khoi bao cSu [9][10][n], kh6i bao theo true
17
Do Thi Chi vd Dtg Tap chi KHOA HOC & CONG NGHE 132(02) [ 7 - 2 3 [I3][I4] dugc sir dung rgng rai boi sir dan
gian trong viec bieu dien va kha nang phat hien va cham nhanh chong, tuy nhien do chinh xac khong cao. Khoi bao theo huong [8] phat trien tir AABB, bao chinh xac doi tugng ban nhung chi phi ki6m tra va chiim ton kem hon. Khoi bao K-dop bao chinh xac doi tugng hem ca, tuy nhien do phuc tap tinh toan ciing nang len rat nhieu. Tir do doi hoi cac nghien cuu chi tiet ve viec sir dyng khoi bao dS xac djnh va cham.
Viec lira chgn cac loai khoi bao cho mot ung dung nhat djnh dugc xac dinh bdi nhieu y8u to: chi phi tinh toan xay dimg khoi bao cho mot d6i tugng, chi phi cap nhat lai khoi bao trong cac ung dung khi doi tugng di chuyen hoac thay d6i hinh dang hay kich thuac, chi phi xac dinh giao diem va do chinh xac mong mu5n cua viec ki€m tra giao nhau, Dg chinh xac cho viec kiSm tra giao nhau lien quan d6n lugng khong gian ben trong kh6i bao khong lien ket vai cac d6i tugng dugc bao ggi la
"khong gian trdng". Ngi dung phin tiSp theo cua bai bao se trinh bay tong quan ve cac giai phap phat hien va cham.
GL^I PHAP PHAT HIEN VA CHAM Khdi bao cSu - BS
Kh6i bao c5u [4][9] la kh6i bao co dang hinh cau nho nhat bao lay toan bg ddi tugng. Voi mot doi tugng v8 ban chit la mgt tap cac dinh CO quan he vai nhau trong khong gian 3 chi6u. Tir tap cac dinh nay co the xac djnh
d u g c Xn„n, Xmax, ym.n, Ymax, Z,nm, 2m»x l a CaC g i a
tri nho nhat va Ion nhSt theo cac true tga dg.
Kh6i bao cku vai tam C(Xc, y^, Zc) va ban kinh R dugc xac djnh nhu sau:
y-min+ym. 2.B!.: + Z « !
fl = J(^«=« - c^y -h (>km - Cj.)= + C^™.. - c,y Khoi bao d^ng nay rat dl tao ra va don gian trong tinh toan kilm tra va cham. Khi d6i tugng quay hay chuyen dgng thi huong, hinh 18
dang ciia khdi c4u bao quanh khong thay doi va khong phu thugc vao true tga do. Hai khoi cku (C|,Ri) va (C2,R2) la va cham vai nhau khiiC,,C2|<(R,+R2).
Kh6i bao cSu BS dugc sir dung rgng rai, tuy nhien do chinh xac khi phat hien va cham chua cao, dac bidt voi cac vat th6 co dang bet hoac dai.
Hinh \. Svt dung khdi bao cdu-BSdi bao l^ doi tuang con thd
De nang cao dg chinh xac, co the thay the khoi bao cau bdi cac khoi bao khac se dugc trinh bay d phan ti6p theo cua bai bao.
Khoi bao theo true - AABB
Khdi bao theo tryc [13][14] la khdi bao co dang hinh hop chCr nhat nhd nh5t bao ISy doi tugng va cd cac canh song song vdi cac true tga do. Khdi bao gdm mgt tam C, ba he s6 ao, aj, a2 tuong ung theo 3 true tga do x, y, z. Hai khdi bao AABB xac dinh bdi [Cj, a^ a,, 32]
va [C2, bo, b,, hi] vdi ai > 0, bj > 0; ij - 0, I, 2. Trong khong gian 3 chidu, AABB dugc xac djnh bdi 2 dinh: dinh cd tga do nhd nhat
Pminl(Xm,nl, y m m l , Zmmi) V a d i u h CO tOE d o lOH
n h a t Pmaxl(Xmaxl, y m a x l , ^ m a x l ) CUa k h d i b a O CO
tam Ci- Trong do:
^ 2 :.1 = C, + -
-Ci-- a,
maxi. 1 —
Hinh 2. Xay dung hgp bao AABB
DoThiChivd£>rg Tap chi KHOA HOC & CONG NGHE 132(02): 17-23 Ddi vdi khdi bao AABB cac cgnh cua khdi
bao song song vdi cac true tga do, vi vay tir 2 dinh Pmax va Pmin cd the de dang tinh dugc 6 dinh con lai cua khdi bao. De xac djnh va cham giiJa hai khdi bao, thuat toan kiem tra xem mgt trong 8 dinh cua kh6i bao thu nh4t cd nam trong khdi bao thii" 2 hay khdng (dua tren viec so sanh tga do dinh dang xet cua khdi bao thu nhit vdi gia tri 2 dinh P^ax, Pmm ciia khdi bao thu 2). Khdi bao AABB so vdi khdi bao cau cd dg phuc tap tinh toan Idn hon, tuy nhiSn do chinh xac trung binh khi phat hien va cham la cao hon ddi vdi hSu het cac hinh dang (do khdng gian thua khdng phai cua ddi tugng khi bao la it han).
Hinh 3: Mgi so gdc nhin sie dung khdi bao hop de bao /ay ddi tuang con thd Khoi bao theo hirdng - OBB
OBB [21] ia khdi bao AABB nhung true cd hudng bit ky. Khdi bao hop nay dugc xac dinh khi no xoay theo chidu cua ddi tugng va dm sat ddi tugng nhat. OBB cd uu diem hem AABB la giam khdng gian trdng giua vat the va khdi bao. Mgt khdi bao OBB gdm mgt tam C, 3 vec to At], Ai, A2 chi hudng cua hinh hop va 3 he sd dg dai tuong ung vdi kich thudc ciia hinh hop la ao > 0, ai > 0, a2 > 0.
Khi do, 8 dinh ciia khdi bao se dugc xac dinh nhu sau:
C + 'j^s,a,*A, [5, 1=1,/= 0,1,2.
(=0
Viec tao ra va tinh toan va cham tren khdi bao loai nay phiic tap hon AABB nhilu, tuy nhien cac chuang trinh md phdng sir dung OBB nhilu han so vdi khdi bao cau va khdi bao AABB vi do chinh xac tuong ddi cao va tinh
toan khdng qua phuc tap. Tuy nhien hgp bao nay van bdc Id khdng it nhugc diem khi ap dung vdi cac doi tugng cd nhieu dinh hoac nhieu khoang Idm.
Khoi bao dang da di^n loi K-Dop De nang cao do chinh xac trong qua trinh phat hien va cham, cac khdi bao dugc su dung la cac da dien. Tren thuc te dl don gian cho viec tinh toan va ch^m, cac h? thdng thudng sir dung cac khdi bao la da dien loi K-Dop [15][I8]. Viec tao ra cac khoi bao nay ddi hdi xac dinh rat nhieu cac thdng sd, khdi bao cang phuc tap thi cang giam dugc khoang khdng gian trdng giua ddi tugng va hop bao. Tuy nhien, chi phi de tao ra hop bao va phat hien va cham vdi K-Dop la rkt Idn.
18-DOP ^ * ^ ^ G 3 26-DaP Hinh 4: Minh hoa mot sd hop bao k - Dop gdm: 6
- Dop, 14 - Dop. 18 - Dop vd 26 - Dop Khi khdng gian trdng giiJa hop bao va ddi tugng cang nhd thi do chinh xac trong xac dinh va cham cang cao. Nhung de dat do chinh xac cao vdi K-Dop thi cac da dien cd sd mat fit Idn, dac biet vdi cac vat the phijtc tap viec xay dung K-Dop dan tien tdi viec xac dinh va cham cua tat ca cac mat hinh thanh len ddi tugng 3D. Vi vay nhugc diem Idn nhat cua K-Dop la thuat todn tien tdi vet can tat ca cac mat, dieu nay la khdng thuc te vdi mgt he thdng md phdng doi hdi do chinh xac cao, khi phat hien va cham phai tra mgt chi phi thai gian Idn.
S o pliitc Inp bong tuill to ^11
k-Dop
Hinh 5: Minh hoa do phiic tap tang ddn cua mot so hop bao
Q6 Thi Cht vd Dig Tap chi KHOA HOC & C 6 N G NGHE 132(02): 17-23 Tir nhirng nhugc diem ve do chinh xac va thai
gian thuc thi cua cac thuat toan xac dinh.va cham da dugc de xuat, ddi hdi phai cd nhung nghien ciru xay dung cac phuong phap va cham cd do chinh xac cao nhung van dam bao thai gian tinh toan Phan tiep theo cua bai bao trinh bay cac giai phap dam bao md phong cac tuong tac co hgc tuong ddi chinh xac trong thoi gian thuc.
M O T S O KY THUAT PHAT HIEN VA CHAM NANG CAO V6I BAI TOAN M O PHONG CO HOC
Sir dung ket hop cac khdi co so Khi cac ddi tugng cd hinh dang phirc tap, viec sir dung mgt khdi bao co sd se mang lai ket qua tinh toan va cham khdng chinh xac, De nang cao do chinh xac, ddng thai dam bao thoi gian tinh toan d mirc chap nhan dugc, cac nha nghien ciru da dua ra y tudng sii' dung ket hgp cac khdi bao co sd [8][9][13][I6]. Mdi khoi bao ca sd (khdi cau hoac khoi hdp) deu cd do phirc tap trong xay dung va tinh toan thap. Viec sir dung ket hgp nhilu khdi bao co sd cai thien dang ke dd chinh xac trong qua trinh md phdng va dd phuc tap trong tinh toan tang len it
Hinh 6 Bat loan minh hoa each su dung ket hap cac khoi bao ca sa cho mot sd doi tuong Theo dd, khi phat hien sir va cham giiJa 2 doi tugng chinh la phat hien xem cd mgt khdi bao CO sd nao ciia ddi tugng nay va cham vdi khdi bao CO sd ciia ddi tugng kia hay khdng. Mac du tinh toan phat hien va cham cua nhieu khdi bao CO sd se phuc tap han la viec su dung duy 20
nhat mgt khdi bao ca sd. Tuy nhien vi moi phep toan xac djnh va cham don vi (phep toan xac dinh va cham giua hai khdi co ban) lai dan gian, do dd toan bg qua trinh phat hien va cham cd tdc do nhanh hon viec sir dung kh6i bao K-Dop.
Khi kit hgp cac khdi bao don gian vdi nhau, khoang trdng giira ddi tugng va khdi bao se giam di nhieu, tir dd nang cao dg chinh xac trong qua trinh xac dinh va cham. Ddi vdi nhu'ng ddi tugng cd hinh dang dai hoac nhieu gdc canh, phuong phap nay cho kha nang phat hien va cham vdi do chinh xac tuang ddi trong thoi gian tinh toan thap. Phuong phap su dung kit hgp nhilu khdi bao co sd da khac phuc dugc CO ban nhugc diem ciia phuong phap chi six dung mgt khdi bao duy nhat. Tuy nhien ddi vdi cac bai toan yeu cau dd chinh xac cao van can cd nhung cai tien trong each xac dinh va cham.
Su- dung phSn vung khdng gian Lay y tudng tu viec phan chia khdng gian quanh ddi tugng thanh tii'ng viing, thuat toan phan viing khdng gian [3] doc lap vdi cau true ciia cac ddi tugng chu khdng phai la phan chia ddi tugng thanh cac vung. Khi chia khdng gian thanh cac vimg, cac ddi tugng dugc coi la va cham vdi nhau neu trong cimg mgt viing khdng gian chua tii 2 ddi tugng trd len. Ddi vdi phuong phap phan viing khdng gian cd hai loai cau true dien hinh thuong dugc su dung: clu true ludi va cau true cay, Ddi vdi cau triic ludi, khdng gian quanh ddi tugng dugc chia deu thanh cac viing nho, do chinh xac tinh toan va chiim va thoi gian tinh toan phu thugc vao kich thudc ludi. Ben canh do cau triic cay phan chia khdng gian phu thugc mgt phan vao ddi tugng, nhQ-ng vung gan be mat doi tugng dugc chia nhd hon cac viing khac. Vi cau true phirc tap hon nen cku true cay tdn thcri gian hon so vdi c4u true ludi trong qua frinh xay dung, tuy nhien khi kiem tra va cham cau true cay lai tdi uu hon vl mat thoi gian do khdng gian dugc phan loai tdt hon.
06 Thj Chi vd Dtg T^p chi KHOA HOC & CONG NGHE 132(02): 17-23
Hinh 7: Minh hoa thudl todnphan viing khong gian tren ddi tuang con (hd MO PHONG, D A N H G I A X A C DINH VACHAM
Chuong trinh md phdng mgt doi tugng cd hinh dang phirc tap trong qua trinh nem xien va roi tu do dugc cai dat bang ngdn ngif lap trinh Visual C# va thu vien do hoa 3 chilu XNA. Trong dd, ddi tugng dugc nem xien tir vj tri each mat dat 2m, vdi tde do hudng len cao (theo true y) la lOm/s, van tdc theo nem ngang (theo true x) la 2m/s. Khi tien hanh thi nghiem mdi Ian tinh toan ddi tugng tu quay quanh 3 true tga &o mgt gdc O.OI radian. Ddi tugng sir dung ddng nang chuyen thanh the nang, khi toan bg dgng nang bien thanh the nang qua trinh rai bat dau (chuy8n tir the nang thanh ddng nang). Qua trinh roi ket thuc khi ddi tugng va cham vdi mat dat, 30% gia tri nang lugng se bj' mat dat hap thu cho bien dang, phan con lai trd thanh phan luc de ddi tugng bat ngugc len theo gdc phan xa vdi gdc rai xudng. Qua trinh mo phdng khdng tinh tdi ma sat khdng khi.
De danh gia do chinh xac ciia cac ky thuat xac dinh va cham, chiing tdi cai dat mgt chuang trinh md phdng nem xien, sau do sir dung cac ky thuat xac djnh va cham khac nhau.Thdi gian mdi khi ddi tugng xay ra va cham duoc luu lai va so sanh vdi thai gian xay ra va cham khi sii' dung ky thuat kilm tra timg mat.
Ky thuat nay xac djnh va cham bang each kiem tra vet can tat ca cac mat cua ddi tugng nay cd giao vdi mgt mat nao cCia ddi tugng khac hay khdng. Phuong phap vet can nay cd do chinh xac gan nhu tuyet ddi nhung thoi gian tinh toan la rat Idn, Chung tdi sii' dung ky thuat vet can lam mdc so sanh, cac ky thuat
khac cd sai sd vdi ky thuat nay cang Idn thi do chinh xac cang giam.
Cac ky thuat sir dung khdi bao co sd, ky thuat ket hgp cac khdi bao co sd, phan vimg khdng gian dugc thuc hien trong thai gian thuc vdi tdc dd xu ly 30 hinh/ giay (mgt giay cac tinh toan va cham dugc thuc hien 30 Ian), ky thuat vdi do chinh xac cao khi kiem tra timg mat cua ddi tugng dugc thuc hien 3 Ian/ giay de lay ket qua thuc nghiem chinh xac nhung khdng dam bao tinh thdi gian thuc
Hinh S Thu n'III. II i ' t ^ i i cham Chiing tdi da tien hanh md phong va su dung ket qua thu dugc la thdi gian mdi khi ddi tugng va cham vdi mat dat. Dua tren ky thuat kiem tra tung mat ciia ddi tugng de so sanh dd chinh xac vdi cac ky thuat khac Tam Ian va cham dau tien thu dugc ket qua ve thdi gian dugc md ta trong so dd sau:
— PlilnTngptiapW
Hinh 9: Sai sd giira cdc if; thiidt K8t qua md phdng cho thiy: ky thuat xac dinh va cham su dung duy nhat mgt khdi bao cku cd sai sd Idn nhat. Sai sd tai Ian va cham cuoi ciing dugc ghi lai la 0.26 giay, tdng sai so sau 8 Ian va cham len tdi 1,31 giay. Tiep dd la ky thuat sir dung duy nhat mgt khdi bao hop vdi tdng do lech ve thdi gian sau 8 Ian va cham la 0.91-giay, sai sd Idn nhat d \hn va cham cuoi ciing la 0.2 giay.
21
Do Th'iCh'ivd Dtg Tap chi KHOA HOC & CONG NGHE 132(02) Phuong phap ket hgp cac khdi bao co sd cd
do^cyi^xac ve va cham tuong ddi tdt, tdng
"Bg feefcrvffthdi gian vdi ky thu|it vet c^n chi cd 0.39 giay. Ddng thdi ket qua thuc nghiem cung cho thay, ky thuat phan viing khdng gian cho ket qua md phdng vdi do lech sau 8 Ian va cham !a nhd nhat vdi 0.23 giay. Sai sd trong Ian va cham cudi ciing la 0.06 giSy.
Nhu vay, ddi vdi bai toan md phdng dgng hgc ky thuat xac dinh va cham dua tren phan vimg khdng gian cho kit qua tdt, mat khac thda man tinh tiidi gian thirc trong qua trinh md phdng.
KET LUAN
Bai bao trinh bay cac ket qua cai dat phat hien va cham ap dung cho bai toan md phdng dgng hgc. Cd nhieu phuong phap khac nhau de xac djnh va cham giu"a cac ddi tugng: su dyng cac khdi bao doc lap, kit hgp giira cac khdi bao, phan viing khdng gian... Mdi phuong phap dIu cd nhitng uu diem va nhugc dilm rieng, tuy nhien trong md phdng va cham cung vin cin cd nhiJng nghien ciru dl phat trien va cai tiln de thu§t toan tdi uu hon. Ciing vdi su phat triln ciia cdng nghe md phdng, vi$c phat hien va cham ddi vdi cac ddi tugng cd hinh dang thay ddi thuong xuyen nhu chSt long, chat khi, vai, lua ... van con la mgt thach thii-c.
Do vay, de dam bao tinh chinh xac trong md phdng van can cd nhiing nghien cuu chuyen sau hon nira vl vSn de xac dinh va cham va xir ly dgng hgc trong thuc tai ao.
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D6 Thi Chi vd Dtg Tap chi KHOA HOC & CONG NGHE 132(02): 17 - 23
SUMMARY
RESEARCH SOME TECHNIQUES COLLISION DETECTION APPLIED TO SIMULATION OF MECHANICAL MOTION
Do Thi Chi'', Le Son Thai', Do Nang Toan^
College of Information and Communication Technology - TNU 'Institute of Information Technology- VNU Collision detection is an important part, which influences to the precision of the calculations on the dynamics. This is a new research field of interest of many scientists to describe accurately the physical interactions between objects on a computer screen. In content of articles focused installation testing, comparison and evaluation collision detection techniques. From there, select the appropriate technique for kinematic simulation problem in some specific conditions. The report consists of 4 parts: Part 1 introduction overview of collision and mechanical simulation in virtual reality; Part 2 the collision detection solution is being studied currently; Part 3 analyse and select the collision detection method suitable for mechanical simulation problem; Part 4 the conclusion and evaluation algorithm.
Keywords: Collision detection, virtual reality, bounding volume, bounding sphere, bounding box, spatial partitioning, simulation
Ngay nhdn bdi: 18/10/2014; Ngayphdn bien:06/11/2014; Ngay duyet ddng: 05/3/2015
Phan biin khoa hoc: TS. VS Due Thdi - Tntdng Dgi hoc Cdng nghe Thong tin & Truyen thdng - DHTN ' Tel: 0985 882793. Email: dtchi@ictu edu vn
