hinh 1-55, hinh tam giric ABC ld mit phdng vi tri xion, mudn bidn ddi n6 thinh
mit drlng chinh ph6i l{y mdt chidu mdi V, thay m{t V. ViQc b6'tri m[t V, ph6i
th6a mdn vrJa vu6ng g6c vdi tam gidc ABC, vt:ta vu6ng g6c vdi mdt H. \n thd, cO tfrd tnJdc ti6n drrng mOt dt/dng bhng trOn tam giric ABC sau d6 dqng m5.t V, vudng g6c
vdi tludng bhng ndy. MEt V, vrla d{ng cfrng nhdt tlinh vudng g6c vdi mdt H. Cric
brrdc dung hinh cu thd xem hinh 1-55(b): (1) D{ng dudng bing bdt ky CD (c.d., cd)
ti6n tam giSc ABC. (2) Dr.tng truc X, vu6ng gdc cd. (B) Cdn crl vdo qui lu4t bidn ddi
tim ra hinh chi6u a,bic, (co tu thdnh tlrrdng thing) cfra tam giric ABC trOn mdt V,.
(a) (b)
Hinh 1 - 55 Bidn Odi mat ph8ng vi trf xi6n thinh m6t rhEng drtng
Ndu mudn bi6n ddi mit phing vi tri xi6n tam gi'ic ABC thAnh m4t th8ng dfng thi ph6i ldy m4t H, thay mit H; giir nguyOn mlt V. Cdn rtidu kign bd tri p4t H,
ld: VUa ph6i vu6ng g6c vdi tam gi6c ABC, vila phAi vudng g6c vdi mit V glr nguy6n.
Do d6, chi c6 khi mit H, vu6ng g6cvdi drrdng song song chinh tr6n tam gi6c ABC thi
Hinh 1 - 56 Bi€in odi mat tn&ng df ng thdnh m{t song song
Hinh 1 - 57 Tim hinh thr,lc c0a tam gi6c
mdt ph&ng vi trixiOn
33
mat Hl mdi c6 thd cing 16c ctrng vuorig g6c voi mat V. Cho nOn, brrdc dgng hinh ddu tiOn bien ddi mat vi tri xiOn tam gi6c ABC thhnh mit thing ditng Id trddc tiOn dung
m6t drJdng song song chinh bdt ky trOn m5.t phing tam gi6c ABC.
4. Bidn tldi mat vuong g6c thdnh mit song song. Nhrr thd hiQn & hinh 1-56.
Tam gi6c DEF Ie mQt m6t drlng chinh. Dd bidn ddi n6 thdnh mit song song thi m{t hinh chiSu mdi lua chon nhdt dinh Id m[t V vuOng g6c v]r song song vdi mlt H, cria
tam gi6c DEF; truc chidu m6i X, nhdt dinh song songvdihinh chidu chinh d'e'f ' cl0'a
tam gtac DEF. Cdc btro-c dqng hinh cu thd la: (1) Dung truc X, song song vdi d {t' . Q)
Can crf vdo qui lu4t bien ddi crja didm tim ra tam gi6c hinh chidu dr"rf, cfra tam gi6c DEF trOn m5,t H,, tam gi6c nhy s6 phAn 6nh hinh thrrc cria tam gi6c DEF.
lll. Vi d9 Ong dVng
Tr6n d6y ddu ld bidn ddi mQt ldn m[t chidu ld c6 thd dat muc dich Si{ii d6;
nhrl tim dO dei thUc cria drrdng thing, hinh thrJc crja m4t phing vu6ng g6c v'v"'
Ddi vdi phuong phdp dqng hinh hai lAn bien tldi chi li dem so t16 hinh chidu
sau mot ldn bidn ddi ldm alidu kiOn girii dd rdi drrng hinh ld.n nfra.
tVi dU 1l Da bidt htnh chidu chinh tam gi6c a'b'c' vd hinh chidu bhng tam
gi6c abc cria tam gi6c ABC mdt phing vi tri xiOn, tim vh d{ng hinh thuc cria tam gidc ABC ftinh 1-57)
Girii: c[n crl vio hinh 1-55 vd 1-56 c6 thd bidt khi bidn ddi mqt ph6ng vi tri
xi6n thdnh mit phEng song song, c6 thd tnJdc ti6n bidn ddi mdt ph&ng vi tri xi6n
thhnh met phdnl thdng drlng , sau d6 lai bidn ddi mdt phing thftng drlng thdnh mat phing .ong rottg. \n thd, nhu thei hien d hinh I-57 , trddc ti6n bidn ddi tam gi6c ABC thdnh m4t thing drlng V,, sau d6 biSn ddi thanh mit song song cria mdt Hr.
C6c brrdc dqng hinh cria n6 la (1) Ldy dudng song song bhng AE trOn tam gi6c ABC,
dUng mdt chieu mdi V, vudng g6c AE, titc dUng truc Xr vuOng g6c ae, sau d6 tim ra hinh chieu mdi a,brc; itri"f, chiSu trirng chap thdnh mOt drJdng th8ng) cria tam gi6c
ABC tron mlt V,. i'Zi O,l"g mbt chidu mdi H, song song vdi tam giSc ABC, titc dung truc X, .orlg .ottg v6i qb'rc'r, sau d6 tim ra hinh chidu mdi cfra tam gi6c ABC trOn m4t Hr; hintr chidu mdi tam gi6c arb,cr PhAn 6nh hinh thr,tc cria tam gi6c ABC'
[Vi du Z] De bidt hai m{t ph8ng tam gi6c MNF vd MNG cdt nhau d MN,
hinh chidu chinh cfia chrlng Id m' g'n'f
"
hinh chidu bhng ld mgnf; tim g6c kgp gitra
hai m{t ph8ng (hinh 1'58). I
(a) (b)
Hinh 1 - 58 Tim goc kep gifa hai mAt ph8ng
^1)+
Gizii: Khi giao tuydn MN cria hai mat phing vudng g6c vdi mrt chidu thi hinh chidu cria hai mrt phing trOn mdt chidu niy trd thanh hai dudng thing c6t nhau. G6c
kep 0 gifra hai drrdng thing cdt nhau chinh ld g6c kep ctia ttui -+iph8ng cdn tim.
Nhrr thd hien d hinh 1-58(a). Do giao tuydn MN .f," tam gi6c MNF vd tam gi6c MNG ld drrdng song song chinh, chi cdn bidn ddi m6t ld.n, ui tfrA bidn ddi n6 thdnh dudng vu6ng g6c cria mit H, ld duoc. Cric budc d{ng hinh cu thd cria n6 ld: (1) dung truc chidu mdi X, vudng g6c m'n'. (2) Tim ra hinh chidu cria tam gi6c MNF vd tam gi:ic MNG tr6n mdt H,, chrlng ld.n luot co tu thdnh cdc doan thing (nr) mrf, vd (nr) DrB,. .f,-,9, ld g6c kep 0 gifra hai mdt rhing cdn tim,
lvi d9 3] Tim g6c kep 0 gifra hai m6t canh cfra ddu ndi bieh d?ng.
. Hlnh 1 . 59 Tlm g6c rgp gi8a hai m{t b6n cOa ddu ndi bidn dgng
Gi6i: Hinh 1-59 (a) thd hign mQt dAu ndi bidn d+ng. Khi chd tqo, y6u cdu
kidm tra dQ ldn cria g6c kgp gifla hai m{t b6n ABCD vA ABEF. Mdu chdt cria viQc
gi6i dd niy ld tim crich bidn tldi giao tuydn AB thdnh drrdng vudng g6c. eua hinh
bidt giao tuydn t bOn
dn ddi mdi thdn vu6ng
giao tuydn AB c ng AB
H' rdi lai bidn ludng vudng g6c cfia mit v,. cdc brrdc cfia
n6 ld: (1) Dung truc X, song song vdi hinh chidu chinh a'b' cfia giao tuydn, tim ra hinh chidu mdi a,brf,e, vd a,brd,c, cria hai mdt phing trOn mit H,- (2)Lqj drlng truc X, vu6ng g6c vdi hinh chi€'u mdi arb, cria giao tuydn, tim ra hinh chidu mdi arb,fi e, vd arbrdrc, cfra hai m6t phing tron mdt v,. G6c eiblc, Id g6c kep gifra hai mat bOn cria dAu ndi bidn d?ttg.
35
BAr rAp
1. Tim dO dai thgc c0a tlrrdng th&ng EF z
(a) (b) (c)
2. Tim hinh thqlc cria m4t ph8ng hinh tam giric ABC vd hinh thang ABCD'
(b) (c)
3. Kidm chfng tt gi6c CDEF sau ddy c6 phAi li m[t chung'
(a) (b) (c,
4. Tim g6c kep 0 giira hai m{t ph&ng (giao tuydn crlra hai m4t phf,ng lt AB)
c
36
(b) (c)
CHUOT',JG 2
2 - | Hinh chidu c&a dudrng con$
Dudng cong c6 thd xem nhrr qul tich chuydn dQng cfia tlidm. Dttdng cong cfia didm chuydn dO"J trong m[t ph&ng t?o n@n thi goi Id tlrrdng cong ph&ng, nhu drrdng
trbn, drrdng elip, dudng thAn khai, dUdng paraboi v.v... Drtdng cong cfia didm chuydn
dOng kh6n! d trong cr)ng mQt mdt phing,tao n6n thi gpi ld cltrdng cong khdng gian
,rirriauUngloSr.r dc tru trdn, dudnf *o6tt dc n6n v.Y... Cirng mqt dudng cong c6 thd
dugc hinh- thdnh bdi nhidu pn.rong phdp kh6c nhau; nhrr hinh elip vira c6 thd xem ld
qui ti.h chuydn dQng theo qui tuat ntrdt rrinh cira didm trong mAt ph8ng, l+i vira c6
thd xem ld giao tuydn girla mdt ph&ng vdi mdt hinh tru. Drrdi dAy sE gidi thiQu m6t so tludng cong thrJdng g?p.
l. Hinh chidu crio dr.ldng lr6n.
Vi tri kh6ng gian cfia drrdng trbn kh6c nhau thi hinh chidu cfia n6 cfing khdng gidng nhau. Khi tludng trdn vuOn! g6c vdi mdt chidu thi hinh chidu trOn m{t chidu
,ray tO co tr,r thdnh mQt dudng th!n--g Khi dubng trbn song song vdi mQt m4t chidu ndo d6 thi hinh chidu tren m41 nay ptrdn 6nh ld hinh thuc. Khi drrdng trbn xi6n vdi m4t chidu thi hinh chidu trOn mdi
"ay ta hinh elip (hinh tdong tr,r cfia hinh trbn)'
1 Hinh chidu c0a tlrrdng trbn khi 6 vi tri song
song vdi mdt chidu: Ktri cludng trdn song song vdi mQt mdt chidu niro d6 tdt phai vu6ng g6c v6i hai m4t chidu kia cfia n6. Hinh chidu cria drrdng trbn tr0n m{t
chidu niy ph6n 6nh
mdt chidu khdc co
hiendhinh2-t,d,
2. Hinh chidu cria cludng trbn khi A vi tri vudng g6c vdi mft chidu' Khi dudng trbn 6 vl tri m4t th&ng
a*g thi hinh chidu cria drrdng trbn nhy tron mf,t chidu
Hinh 2 - 1 Hinh chidu c0a dudng trdn khi song song vdi mit chi€lu
37
mh n6 vu6ng g6c sE eo t9 thdnh mQt drldng th&ng, cbn hai hinh chidu kia Ih drrdng elip.
Nhrr thd hiQn 6 hinh 2 - 2, mlt phhng hien tai cria hinh trbn lir mQt mlt thhng drlng.
Vi thd, hinh chidu bhng ab cfra hinh trbn co tu thhnh mQt dudng thing, tlQ dei cfra n6 lh
drrdng kinh D cfia tlrrdng trbn; hinh chidu chinh cria dtrdng trbn ld hinh bAu duc, truc ddi
cria hinh bAu dgc nhy lh hinh chidu c'd' cfia dudng kinh th&ng dwrg CD cira tludng trbn,
d0 ddi cfia n6 bhng dudng kinh D cfra dudng trbn. Tnrc ng6n Ii hinh chi6u a'b' cira dtrdng
kinh bhng AB drrdng trdn, dO dei cria n6 c6 thd c[n crl vdo quan hQ hinh chidu ild dung ra.
Sau khi tim drloc tryc diri, t4rc ngSn thi c6 thd dung ttrrgc hinh bAu dqc.
Hinh 2 - 2 Hlnh chidu c0a hinh tron khi vuOng g6c vdi mqt chieu
3. Hinh chidu cria tlrrdng trbn khi dr vi tri xiOn. Khi hinh trbn d vi tri xi6n, thi
c6c hinh chidu cria drrdng trbn ld dudng elip. Nhrrthd hien d hinh 2 - 3(a), hinh trdn
c6 drrdng kinh li D nhm tr6n m5.t phing vi tri kh6ng dac biQt ZMNKL, hinh chidu
cria drrdng trdn ndy tr6n m6.t V vd m4t H ddu ld dudng elip. Khi cho trrldc hai hinh
chidu D m'n'k'l' vd,D mnkl vd tAm O(o,o') cria drrdng trbn tr0n mdt phlng thi c6
thd dtrng phrrong ph6p ho6n ddi mat dd tim ra phrlong vd dQ ldn cria truc dii, vi
truc ngdn cria elip. Trong hinh 2 - 3(b), dd tim hinh chidu chinh cria drrdng trbn, trddc tiOn bidn ddi m[t hinh binh hinh z7 MNKL thdnh mlt th&ng drlng, trlc ldy H,
(a) (b)
Hinh 2 - 3 Hinh chidu cOa dr.tong trdn khi nbm xiBn vdi m{t chidu
38
thay H, thi trong h0 thong V/H, drrdng trdn vu6ng g6c v6i H' ltic ndy c6 thd cdn cf
vdo phttong ph6p d{ng hinh cria hinh chidu drrdng trdn tr6n mdt th8ng drlng dd tim ra hinh chidu - elip cria n6 tr6n m4t V. Dtrng phuong phrip tuong tt/ c6 thd tim ra hinh chieu - elip cria hinh trdn trOn mit FL
ll. StJ hinh thonh, hinh chidu vo hinh khoitridn drJdng xodn dc trr,r tr6n (dUdng dinh dc).
I(hi mdt tlidm trOn bd mit hinh tru trdn chuydn dQng ddu quanh truc, ddng thdi chuydn dQng thing ddu theo phuong drrdng truc cfia hinh tru, thi qui tich chuydn
dQng crja dieim dOng tr6n bd mit hinh tru trdn goi ld tludng xoSn dc tru trbn. Qui tich
cria didm A thd hien 6 hinh 2 - 4(a) chinh Id mOt drrdng xodn dc tru trbn. Kho6ng cdch
di chuyeln hrrdng truc cria didm A khi chay quanh dugc mQt vdng (nhrr AoA, r) gOi lA bddc
cria drrdng xoin dc tru trbn khi da bidt dudng kinh d cria hinh trg trbn, chidu quay (quay tr6i ho5,c quay ph6i) cria didm A vd dQ ldn cria brrdc S thi c6 thd vE ra hinh chidu
cria dudng xoSn dc tru trdn (drrdng dinh 6c). Cdc brrdc drrng hinh cria n6 (hinh 2 - 4(b))
ld: (1) tnjdc tiOn dung hinh chidu hai mdt cria m4t tru trbn c6 dt/dng kinh lA d, sau d6 chia brrdc S trOn hinh chidu bbng (drrdng trbn) vh hinh chidu chinh cria n6 thinh cdc
phdn bbng nhau (trong hinh chia thdnh 12 phAn) (2) TU cdc phdn tr6n budc S dgng tludng song song ngang bbng vd til c6c phAn tr6n chu vi drrdng trdn dqng tlrrdng thing
drlng, c6,c giao didm trJong rlng cria chfng nhu: ai, a, ai...ld hinh chidu chinh c$a ct.c
di6m tr6n dudng xoSn dc. (3) Ldn luot ndi trbn hinh chidu c6c didm niy, sE drroc hinh
chiSu chinh cria ,iltrdng xo6n dc. Dudng xodn dc tr0n mit hinh tru nita phia tnrdc c6 thd
nhin thay, vd thd.nh dudng n6t lidn dQm, dudng xo6n dc tr6n mIt hinh tru nira sau khdng nhin thdy thi vE thdnh dudng n6t drlt. Hinh chiSu bing cua drrdng xoin dc co
tu thdnh itrrdng trbn. Ndu khai tridn mdt hinh tru, thi tludng xoSn dc tr6n n6 trd thdnh mQt dt/dng thing 6inh 2 - 4 c). Drrdng th&ng niy lh canh huydn cfra tam gi6c
vuOng. MQt canh g6c vuOng cfia tam gi6c vudng ld dQ ddi chu vi nd cfra dttdng trdn t161'
hinh tru trbn, m6t canh g6c vudng khdc li budc S crja tlttdng xoSn dc. D0 dhi cria brrdc S dtldng xodn tr6n dc fa fflrd)a$ , g6c kep gifra canh huydn vd canh d6y cria tam gi6c vu6ng goi ld g6c l6n (ddc) cria dttdng xodn 6c, g6c kep I gif,a canh huydn vdi mQt canh
g6c vuOng kh6c goi Id g6c xo6n cria drrdng xoSn dc, c5'n cr1 vdo nguy0n lf tr6n, ndu
qudn mQt mAnh giay hinh tam gi6c vu6ng I6n mit hinh tru trdn thi trOn mqt hinh tru trdn, canh huyAn sE quay thhnh m6t dUdng xodn dc tru trdn (drJdng dinh dr).
(b) (c)
39
Hinh 2 - 4 SU hinh thdnh hinh chieu vd hinh khai tridn dUdng xoin cic tru trdn (drldng dinh cic)
-
tlt. Sg hinh ihonh vo hinh chidu cfio dr;dng xo6n dc hinh non.
ICri mQt dOng tlidm d trOn mdt hinh n6n chuydn dQng ddu quanh drldng truc, ddng thdi chuydn clOng thing ddu theo phrrong dttdng truc ctra hinh n6n, thi qui tich
.t rid1 dong cfra dQng didm tr6n mit hinh n6n goi ld drldng xoSn dc hinh n6n.
rcroang c6ch di chuydn hudng truc cira didm A khi chay quanh d'ttoc mOt vbng goi lh
brrdc cira drrdng xodn dc hinh n6n (S). Khi da bidt dudng kinh d cria drrdng trbn mdt
driy cria hinh n6n chinh, dO cao H cria n6n. Vd chidu quay (tr6i, phii) cria ctidm di
dOng vd rlQ ldn cfra budc S thi c6 thd vE ra hinh chidu cria dudng xo6n dc hinh n6n.
Cdc brrdc dqng hinh cria n6 lh (xem hinh 2 - 5) (1) Drrng hinh chidu hai m4t cria mdt
hinh n6n chinh c6 dtldng kinh tludng trbn d5'y le d, tlQ cao H cria n6n li H. Sau d6 chia cria
hinh chidu bXng (tlrrdng trdn) vd budc S tr6n hinh chidu chinh thdnh cric phdn bing nhau.
(trong hinh lA 12 phdn bdng nhau). (2) TrOn mdt n6n dqng hinh chidu cfia c6c dudng sinh (S'1' , S'2'... S'L2' vit 51, S2... S12 v'v.'.) giao
didm {0, {r, ar... arL gifra hinh chidu chinh cria
cdc tludng Sinh S'1', S'2' ... S'12' tr6n mbt hinh n6n vd c:ic dudng ngang tudng fng dqng dttoc til
c6c phdn bhng nhau trOn budc S, Ie hinh chidu chinh cfra cdc di6m tr6n d.ttdng xo6n dc n6n, lAn
.lrrot ndi tron lidn cric didm ndy sE dugc hinh
chiSu chinh cria dudng xodn dc n6n, drrdng xodn dc trOn mdt hinh n6n nilta trudc thinh tltrdng
n6t lidn, tlrrdng xodn dc tr6n mit hinh n6n nila
sau drJoc vE thdnh drrdng n6t dft. (3) Do cdc
didm A0, A1, Ar... trOn ttudng xoSn dc lAn lrrot d tr6n ttubng-Sinh trrong ftng S0, SI, SII..., c6 thd trl c6c didm ai, a'r, {2... dab du
bhng osr a1, ar... tdong r1ng, dn
lidn c6c didm ndy sE drJgc ria
'tlttdng xodn dc n6n. Tit phuong phdp dUng hinh ta bidt, n6 ld mQt ihrdng xodn dc Acsimet.
Hinh 2 - 5 SU hinh thdrnh vd hinh chieu c0a dudng xo6n tr6n oc hlnh n6n
tV. Hinh chidu cfio dUdng cong khong gion bdt quit6c vo sgkhoitridn gdn dOng
Hinh chidu cira Cludng cong khOng gian c6 drlgc bdi ndi tron lidn tudn tr/ hinh chidu cing m6t cfra cdc tlidniauUtg .orrg. Odi uOi tlrrdng cong kh6ng gian bdt qui t6c, ngodi vi6c c[n crl vdo hinh chidu cira tlrrdng cong dd bidu thi hinh d6ng cria n6 ra co1 phei d6nh kf hi€u ddi vdi c6c didm tlac biet nhu ttidm tldu, didm hinh chidu
trirnl v.v... cria dudng cong. Nhu trong hinh 2 - 6(a), (b) hinh chidu cria hai hinh v6
gidng nhau, nhtrng kf hiQu cria chring khdc nhau. Vi thd, hinh ddng kh6ng gian cfia hai drrdng cong cfrng dai thd khdc nhau. Nhu ndu de bidt hai hinh chidu cfra dudng
do dei khai tridn cfi Trong hinh 2 - 7(d d'e
6t cria mot dudng co BIXC, tld khai trid.n n6
6 thd dDng ntridu tl 6ng gian thay the gAn
dring drrdng corrg kh6ng gian (trong hinh chia ra 11 doan drrdng gdy), sau d6 dirng 40
11 210 39 48 5
t
(a) (b)
Hinh 2 - 6 Hinh chieu c0a dudng cong kh6ng gian bdt quit6c
phtrong ph6p hinh tam gi6c vuOng lAn luot tim ra dO dai thr,Ic cria m6i doan tlrrdng gdy thdnh drrdng thing nhrr thd hiQn 6 hinh 2 - 7(c).
(a) (c)
Hinh 2 - 7 Phudng phdp khqi tridn gdn d0ng thdnh dudng thtng c0a dudng cong khong gian bdt qui t6c
V. Tidp tuydn crio drldng cong
Trong tinh hinh chung, bdt kd Ie dudng cong mdt phing ho4c dttdng cong kh6ng gian
thi hinh chidu crta c6t tuydn vd tidp tuydn cria drrdng cong lh kh6ng thay tldi, hinh chidu cria
clidm c6t va tidp didm v6n ld tlidm cdt ve tidp didm tr6n hinh chidu cria dudng cong nhy. Nhu thd hign d hinh 2 - 8, giao tlidm gif,a dudng cong khdng gian K vdi c6t tuydn L la C vD. D,
hinh chidu 1 cira c6t tuydn L vAn ld crlt tuydn
cira hinh chidu k cria dudng cong, giao didm lh c
vi d. Khi tlidm C chuydn tlQng theo dtrdng cong gdn vd phia D, thi c6t tuydn L bidn thdnh tidp tuydn T, hinh chidu 1 cfia n6 cfrng trd thinh tidp tuydn t cria hinh chidu drrdng cong; hinh chidu d cria tidp tlidm D cflng Id tidp tlidm giita tidp tuydn t vdi drrdng cong k.
40 50 bo 60 70
Hinh 2 - S Tidp tuYdn c0a dudng cong
4l
ivi du 1l: Tim vh dung tidp tuydn cria dttdng xo6n oc tru trbn-
Gi6i: Til tinh chdt cfia dddng xodn oc tru trdn vd hinh 2 - 9(a), ta c6 thd bidt
g6c nghiOng c0a tidp tuydn IA,, IIA2... cria m6i didm trOn dudng xodn dc trg trbn v6i
ir+t fr ac1,"Uhng gOc ttrang a(g6c I6n, g6c ngdng) cria drrdng xo6n oc, cl6 dii cira tidp
LAr, 2A2... (tr1c tid
g theo sd tdng cao
trdn. Cin cfi ddc
dc tru trdn. Cdc bttdc d{ng hinh cfra n6 lir (hinh 2 - gb). (1) Vd ra hinh chidu cria drrdng xodn dc tr6n m4t hinh trg vdi budc
x.ra,.., le S, dtrdng kinh Ie d, vd drrdng thAn khai cfia hinh trbn d6y. (2) Do hinh chidu cira tiep tuydn drrdng cong nhat tlinh c6t vdi hinh chidu cing mbt cfra dudng
cong, cho nOn khl drlng hinh, trddc ti6n tit c6c phAn bhng nhau: l, 2, 3"' tr6n hinh chidu bhng, dgng tidp tuydn cfia hinh trbn. Nhrr a hinh trbn dttng qua