Feiner and his colleagues developed a laser printer .... The corresponding viewport coordinates (u, v) are iv iv ..... 5Y10, October 29Y30, 2001, New York, NY.
(DV\&DOLEUDWLRQRID+HDG0RXQWHG3URMHFWLYH'LVSOD\IRU $XJPHQWHG5HDOLW\6\VWHPV
&KXQ\X*DR +RQJ+XDDQG1DUHQGUD$KXMD
%HFNPDQ,QVWLWXWH8QLYHUVLW\RI,OOLQRLVDW8UEDQD&KDPSDLJQ8UEDQD,/ 'HSDUWPHQWRI,QIRUPDWLRQDQG&RPSXWHU6FLHQFH8QLYHUVLW\RI+DZDLLDW0DQRD+RQROXOX+, (PDLO +KXD#KDZDLLHGX
$EVWUDFW
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
,QWURGXFWLRQ
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±DLGHG VXUJHU\ >@PHGLFDOWUDLQLQJ>@DQGWHOHPDQLSXODWLRQ>@
Proceedings of the IEEE Virtual Reality 2003 (VR’03) 1087-8270/03 $17.00 © 2003 IEEE
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¶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
5HODWHGZRUNDQGPRWLYDWLRQ
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
&DOLEUDWLRQUHTXLUHPHQWV
,Q WKLV VHFWLRQ ZH EULHIO\ UHYLHZ WKH +03' WHFKQRORJ\ DQG FDOLEUDWLRQ UHTXLUHPHQWV IRU DQ $5 V\VWHP
2YHUYLHZRIWKH+03'WHFKQRORJ\
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¶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
3URMHFWHGLPDJH
5HWURUHIOHFWLYHVFUHHQ
3URMHFWLYHOHQV )
)
/&'
%HDPVSOLWWHU
$SHUWXUH
([LWSXSLO D E )LJ +HDGPRXQWHG SURMHFWLYH GLVSOD\ +03' D ,OOXVWUDWLRQ RI EDVLF LPDJLQJ FRQFHSW ZLWK D PRQRFXODU FRQILJXUDWLRQ E 3URWRW\SHLPSOHPHQWDWLRQ
Proceedings of the IEEE Virtual Reality 2003 (VR’03) 1087-8270/03 $17.00 © 2003 IEEE
&DOLEUDWLRQUHTXLUHPHQWVIRUUHJLVWUDWLRQRI YLUWXDODQGUHDOREMHFWV
ZKHUH 76 ←:3 UHIHUUHG WR DV VHQVRU WUDQVIRUPDWLRQ LV PHDVXUHG H[SOLFLWO\ E\ WKH KHDG WUDFNHU DQG 7( ← 6 UHIHUUHG WR DV H\H WUDQVIRUPDWLRQ VSHFLILHV WKH H\HSRLQW SRVLWLRQ DQG YLHZLQJ RULHQWDWLRQ LQ WKH VHQVRU FRRUGLQDWHV 7KH NH\ RI WKH +03' FDOLEUDWLRQ LV WR HVWLPDWH WKH YLHZLQJ SURMHFWLRQ PDWUL[ 0 ( WKDW LV XVHG WR VSHFLI\ WKH LPDJLQJ SURSHUWLHV RI D YLUWXDO FDPHUD DQG WKH H\H WUDQVIRUPDWLRQ 7( ← 6 WKDW LV XVHG WR GHILQH WKH SRVLWLRQ DQG RULHQWDWLRQ RI D YLUWXDO FDPHUD ZLWK UHVSHFW WR WKH VHQVRUUHIHUHQFHRIWKHKHDGWUDFNHU
)LJXUHVDDQGELOOXVWUDWHWKHPDLQFRPSRQHQWVWKH DVVRFLDWHGFRRUGLQDWHV\VWHPVDQGWKHWUDQVIRUPDWLRQVLQ WKH SK\VLFDO DQG YLUWXDO ZRUOGV UHVSHFWLYHO\ ,Q WKH YLUWXDO HQYLURQPHQW ZH GHILQH D YLUWXDO ZRUOG FRRUGLQDWHV 9:& :Y;@ 7KH ZRUOGLPDJH FRUUHVSRQGHQFHV DUH PDQXDOO\ GHWHUPLQHG SRLQW E\ SRLQW DQG WKH ZRUOG FRRUGLQDWHV RI WKH VDPSOHVDUHPHDVXUHGPDQXDOO\DVZHOO7KH0&0 PHWKRGQHHGVPRUHWKDQFRUUHVSRQGHQFHVDPSOHVWR DFKLHYH VWDEOH DQG DFFXUDWH FRQYHUJHQFH ,W LV WLPH DQG ODERUFRQVXPLQJ ,Q WKLV SDSHU ZH SUHVHQW DQ HDV\ DQG IDVW RIIOLQH FDOLEUDWLRQ PHWKRG UHIHUUHG WR DV DXWRPDWLF FRUUHVSRQGHQFHPDWFKLQJ $&0 ,QWKH$&0PHWKRG IRUHDFKDUPRIWKH+03'YLHZLQJRSWLFVDFDOLEUDWLRQ FDPHUDZKLFKLVXVHGWRPLPLFDXVHU¶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
SXUH WUDQVODWLRQ 7( :LWK UHVSHFW WR WKH VHQVRU UHIHUHQFH LQGHHG WKH URWDWLRQ 5 ( GHILQHV WKH RULHQWDWLRQ RIWKH(93UHIHUHQFHDQGWKHWUDQVODWLRQ 7( VSHFLILHVLWVORFDWLRQ 0 ( LVGHILQHGE\WKHHTXLYDOHQW SURMHFWLRQSDUDPHWHUVDQGLVJLYHQE\ ª− α I 0 ( = «« «¬
− β I
X º Y »» »¼
,W LV LPSRUWDQW WR UHDOL]H WKDW WKHVH GLVSOD\ LQWULQVLF SDUDPHWHUVPD\VOLJKWO\FKDQJHGXHWRWKHLUGHSHQGHQFH RQ H\H SRVLWLRQ ZKHQ D XVHU ZHDUV WKH GLVSOD\ 7KLV GHSHQGHQFH PDNHV WKH GLVSOD\SURMHFWLRQWUDQVIRUPDWLRQ GLIIHUHQW IURP WKDW RI D FDPHUD V\VWHP ZKLFK UHPDLQV IL[HG ,PDJH3ODQH 3URMHFWLRQOHQV FHQWHU H[LWSXSLO
RULJLQRIGLVSOD\ ,
9R 8R /&'6FUHHQ
(
1RUPDOL]HG LPDJHSODQH 3Q 9R 1
)LJ
2
8R
&HQWHURI(\H RU&DOLEUDWHGFDPHUD I
7ZRVWHSSURMHFWLRQLQ+03'V\VWHP
Proceedings of the IEEE Virtual Reality 2003 (VR’03) 1087-8270/03 $17.00 © 2003 IEEE
XQWLO WKH RYHUDOO HUURU LV PLQLPL]HG :H DGRSWHG WKLV PHWKRGLQRXUH[SHULPHQW 0D[LPXPOLNHOLKRRGQRQOLQHDUVHDUFK ,IWKHOHQV GLVWRUWLRQLVH[SHFWHGWREHIDLUO\ODUJHWKHILUVWDSSURDFK PD\ QRW ZRUN ZHOO ,Q WKLV FDVH RQH PD\ FDOFXODWH GLVWRUWLRQIDFWRUXVLQJ0D[LPXP/LNHOLKRRG(VWLPDWLRQ 7KHGLVWRUWLRQLVQRWPHUHO\DOLQHDUSUREOHPWKXVDQRQ OLQHDUVHDUFKIRUJOREDOPLQLPXPKDVWREHDSSOLHG:H GLG QRW DSSO\ WKLV PHWKRG GXH WR OHQV GLVWRUWLRQ LQ RXU V\VWHPLVQHJOHFWDEOH
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
&DOLEUDWLRQSURFHGXUHVDQGUHVXOWV
7KH FDOLEUDWLRQ LPSOHPHQWDWLRQ FRQVLVWV RI WKH IROORZLQJVWHSV 0RXQW WKH +03' DQG WZR FDOLEUDWLRQ FDPHUDV RQH IRU HDFK RSWLFV RQ D IL[HG SODWIRUP UHFRUG WKH PHDVXUHPHQW RI WKH KHDG VHQVRU DQG REWDLQ WKH FRUUHVSRQGLQJ VHQVRU WUDQVIRUPDWLRQ 76 ←:3
ª 5 º 76 ← ( = 76 ←:3 7:3 ← % 7%←& « ( » ¬ ¼
(PSLULFDOO\ZKHQRQO\RQHVHQVRULVXVHGIRUERWK KHDG WUDFNLQJ DQG VW\OXV PHDVXUHPHQW WKH VHQVRU PHDVXUHPHQWVKRXOGEHUHFRUGHGDWWKHHQGRIWKH H[SHULPHQWV &DOLEUDWH WKH FDPHUDV XVLQJ VHOHFWHG FDPHUD FDOLEUDWLRQ PHWKRGV > @ DQG REWDLQ WKH LQWULQVLFDQGH[WULQVLFSDUDPHWHUVRIHDFKFDPHUD ,QH[SHULPHQWVZHXVHG=KDQJ¶VPHWKRG>@ &DSWXUH WKH LPDJH RI DQ H[WUD FDPHUD FDOLEUDWLRQ ERDUGDQGFDOFXODWHWKHDWWLWXGHRIWKHERDUGLQWKH FDPHUD UHIHUHQFH WR REWDLQ WKH WUDQVIRUPDWLRQ 7%←& IURPWKHFDOLEUDWLRQFDPHUDUHIHUHQFH&WR WKHERDUGUHIHUHQFH%0RUHH[WUDERDUGVFDQEH XVHGWRLPSURYHDFFXUDF\ 0HDVXUH VHOHFWHG SRLQWV RQ WKH H[WUD FDOLEUDWLRQ ERDUG XVLQJ WKH WUDFNLQJ VW\OXV WR REWDLQ WKH WUDQVIRUPDWLRQ 7:3 ← % IURP WKH ERDUG UHIHUHQFH
,W LV LPSRUWDQW WR QRWH WKDW WKH FKRLFH RI FDPHUD FDOLEUDWLRQPHWKRGVLVFULWLFDO7KHRUHWLFDOO\DQ\LPDJH EDVHG FDPHUD FDOLEUDWLRQ PHWKRGV FDQ EH XVHG LQ RXU PHWKRG +RZHYHU FRQVLGHULQJ WKH OLPLWHG DFFXUDF\ RI VW\OXV PHDVXUHPHQW =KDQJ¶V IDVW FDPHUD FDOLEUDWLRQ PHWKRG LV UHFRPPHQGHG ,Q =KDQJ¶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←&
WRWKHZRUOGUHIHUHQFH7KHPHWKRGVXVHGWRIRUP 7:3 ← % FDQ EH IRXQG LQ RXU SUHYLRXV FDOLEUDWLRQ
DQG 7: ← % 7KUHH /&' LPDJHVDUHFDSWXUHGXVLQJWKH
)LJ
FDOLEUDWLRQFDPHUDIRUHDFKH\H7KHGLVSOD\FDOLEUDWLRQ SDWWHUQ XVHG WR FDOFXODWH WKH DWWLWXGH RI QRUPDOL]HG LPDJHSODQHKDVWRWDO[SRLQWVZLWKLQWKH)29RIWKH FDOLEUDWLRQFDPHUD7KHHVWLPDWHGLQWULQVLFDQGH[WULQVLF SDUDPHWHUVDUHOLVWHGLQ7DEOH,FRUUHVSRQGLQJWRWKHOHIW DQGULJKWH\HVUHVSHFWLYHO\ ª − − º « − » » >76 ← ( @ /HIW = « «− − − » » « ¼ ¬
'LVSOD\WRLPDJHFRUUHVSRQGHQFHPDWFKLQJ
Proceedings of the IEEE Virtual Reality 2003 (VR’03) 1087-8270/03 $17.00 © 2003 IEEE
$VN WKH VXEMHFW WR DOLJQ D YLUWXDO FURVV ZLWK HDFK RI WKH JULG LQWHUVHFWLRQV RQ WKH WDUJHW DQG UHFRUG WKHFRUUHVSRQGLQJSL[HOFRRUGLQDWHV 4LN M X Y
ª − − º « »» >76 ← ( @5LJKW = « «− − − » « » ¼ ¬ 7DEOH,,QWULQVLFDQGH[WULQVLFSDUDPHWHUVRIWKH +03' 3DUDPHWHUV /HIW 5LJKW )RFDOOHQJWK PP )29 GHJUHHV + + 9 9 'LVSOD\RIIVHWV SL[HO + + 9 9
&RPSXWH WKH GLIIHUHQFH EHWZHHQ WKH FRPSXWHG DQG WKH JURXQGWUXWK SURMHFWLRQV HLN M X Y = 4LN M X Y − 4LN M X Y &KDQJH WKH WDUJHW DWWLWXGH DQG UHSHDW WKH VWHSV WKURXJK (YDOXDWH WKH PHDQV DQG VWDQGDUG GHYLDWLRQV 67'V RIWKHVDPSOHVDWDOOGLIIHUHQWDWWLWXGHV
5HVXOWVDQGGLVFXVVLRQ
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¶VH\HWRWKHFDOLEUDWHGH\HSRLQWLVOHVV WKDQPP7KLVXSSHUERXQGZLOOOHDGWRDURXQGSL[HO HUURU LQ WKH GLVSOD\ VSDFH ZKLFK LV DFWXDOO\ LV VPDOOHU WKDQWKHHUURUFDXVHGE\WKHFXUUHQWKHDGWUDFNHU:KHQD
(YDOXDWLRQH[SHULPHQWVDQGUHVXOWV
,QWKLVVHFWLRQZHZLOOGHVFULEHWKHH[SHULPHQWDOVHWXS DQG PHWKRG XVHG WR HYDOXDWH WKH $&0 FDOLEUDWLRQ PHWKRG (YDOXDWLRQ GDWD DUH FROOHFWHG E\ D KXPDQ VXEMHFW ZKR PDQXDOO\ SHUIRUPV WKH ZRUOGWRLPDJH FRUUHVSRQGHQFH PDWFKLQJ DW WKH +03' H[LW SXSLO 7KH H[SHULPHQWLVDSSOLHGRQOHIWH\HRQO\
([SHULPHQWDOVHWXSDQGSURFHGXUHV
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← % 7UDQVIHU WKH JULG FRRUGLQDWHV IURP ZRUOG FRRUGLQDWHVWRH\HFRRUGLQDWHXVLQJWKHPDWUL[VHW REWDLQHG LQ FDOLEUDWLRQ SURFHVV L H WKH H\H −
WUDQVIRUPDWLRQ
ª 5( º − − « » 7% →& 7: ← % 3OHDVH ¬ ¼
QRWHWKDWWKHIRRWPDUN%KHUHLVUHIHUUHGDVWRWKH H[WUDFDOLEUDWLRQERDUG 3URMHFW WKH JULG FRRUGLQDWHV IURP H\H FRRUGLQDWHV WR WKH QRUPDOL]HG SODQH XVLQJ WKH SURMHFWLRQ PDWUL[ IRUPHG E\ WKH LQWULQVLF SDUDPHWHUV ZH REWDLQHG LQ WKH FDOLEUDWLRQ SURFHVV :H H[SUHVV
Ö X Y WKHVH'SRLQWVDV 4 L M N
Proceedings of the IEEE Virtual Reality 2003 (VR’03) 1087-8270/03 $17.00 © 2003 IEEE
PRUH SUHFLVH UHJLVWUDWLRQ LV GHPDQGHG DQ RQOLQH FDOLEUDWLRQLVQHFHVVDU\DIWHUWKHRIIOLQHFDOLEUDWLRQ
UHIOHFWLYH ILOP 7KLV SDSHU LV EDVHG RQ ZRUN VXSSRUWHG E\1DWLRQDO6FLHQFH)RXQGDWLRQ*UDQW,,6,75 DQG%HFNPDQ,QVWLWXWH(TXLSPHQW$OORFDWLRQV
&RQFOXVLRQ
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
5HIHUHQFHV
:HZRXOGOLNHWRVSHFLDOO\WKDQNRXUFROODERUDWRUV'U -DQQLFN 5ROODQG RI WKH 2'$/DE DW WKH 8QLYHUVLW\ RI &HQWUDO)ORULGDIRUKHUVWLPXODWLQJGLVFXVVLRQ:HZRXOG DOVR OLNH WR DFNQRZOHGJH 0 ,QF IRU VXSSO\LQJ UHWUR
>@
>@
@ >@ > @ >@
>@ >@
>@
>@
>@
>@
>@
>@
'HIDQWL ³6XUURXQG VFUHHQ SURMHFWLRQEDVHG 9LUWXDO 5HDOLW\ WKHGHVLJQDQGLPSOHPHQWDWLRQRIWKH&$9(´,Q 3URFHHGLQJV RI 6,**5$3+ $QDKHLP &$ $XJ 0LFKDHO 'HHULQJ +LJK UHVROXWLRQ YLUWXDO UHDOLW\ &RPSXWHU *UDSKLFV 3URI 6,**5$3+¶ &RQI -XO\ - )HUJDVRQ ³2SWLFDO V\VWHP IRU KHDG PRXQWHG GLVSOD\ XVLQJUHWURUHIOHFWRUDQGPHWKRGRIGLVSOD\LQJDQLPDJH´ 86SDWHQW$SULO 6)HLQHU%0DF,QW\UHDQG'6HOLJPDQQ³.QRZOHGJH EDVHG DXJPHQWHG UHDOLW\´ &RPP $&0 -XO\ :(/*ULPVRQ*-(WWLQJHU6-:KLWH7/R]DQR SHUH] : 0 :HOOV DQG 5 .LNLQLV ³ $Q DXWRPDWLF UHJLVWUDWLRQ PHWKRG IRU IUDPHOHVV VWHUHUWD[\ LPDJH JXLGHG VXUJHU\ DQG HQKDQFHG UHDOLW\ YLVXDOL]DWLRQ´ ,(((7UDQV2Q0HGLFDO,PDJLQJ $SULO +RQJ+XD$*LUDUGRW&KXQ\X*DRDQG-35ROODQG ³(QJLQHHULQJ RI KHDGPRXQWHG SURMHFWLYH GLVSOD\V´ $SSOLHG2SWLFV +RQJ +XD &KXQ\X *DR )UDQN %LRFFD DQG -DQQLFN 3 5ROODQG $Q 8OWUDOLJKW DQG &RPSDFW 'HVLJQ DQG ,PSOHPHQWDWLRQ RI +HDG0RXQWHG 3URMHFWLYH 'LVSOD\V 3URFHHGLQJVRI,(((95S0DUFK @ 0LKUDQ 7XFHU\DQ HW DO ³&DOLEUDWLRQ UHTXLUHPHQWV DQG SURFHGXUHV IRU D PRQLWRUEDVHG DXJPHQWHG UHDOLW\ V\VWHP´ ,((( 7UDQV 9LVXDOL]DWLRQ DQG &RPSXWHU *UDSKLFV 6HS >@ 0LKUDQ 7XFHU\DQ 1DVVLU 1DYDE ³6LQJOH SRLQW DFWLYH DOLJQPHQW PHWKRG 63$$0 IRU RSWLFDO VHHWKURXJK +0' FDOLEUDWLRQ $5´ ,Q 3URFHHGLQJV RI ,((( ,QWHUQDWLRQDO 6\PSRVLXP RQ $XJPHQWHG 5HDOLW\ SS >@ = =KDQJ $ IOH[LEOH QHZ WHFKQLTXH IRU FDPHUD FDOLEUDWLRQ,(((7UDQVDFWLRQVRQ3DWWHUQ$QDO\VLV
DQG 0DFKLQH ,QWHOOLJHQFH
> @ &DPHUDFDOLEUDWLRQWRROER[IRUPDWODE KWWS ZZZYLVLRQFDOWHFKHGXERXJXHWMFDOLEBGRF
