Vaishig Poits Two ways Itsctio of tasfomd lis Tasfomatio of oits at ifiity Y Y VP z X VP x X Z
Pla Gomtic Pojctios Paalll Pscti Othogahic Axoomtic Obliq Sigl Poit Timtic Dimtic Isomtic Caali Cabit Two Poit Th Poit
Imlmtatio Isss Mo fom Itfac oit of iw Y V U Ey N X Z Wold Coodiat Systm (WCS) Viwig Coodiat Systm (VCS)
Viw Coodiat Systm (VCS) Viwig coodiat systm Positio ad oitatio of th iw la Extt of th iw la (widow) Positio of th y Viw Pla Viw Rfc Poit (VRP): th oigi of VCS scifid as ( x, y, z ) i WCS: ct of th sc Nomal to th iw la ( x, y, z )
Viw Coodiat Systm (VCS) Viw Pla Nomal Dictio (Viw Pla Nomal VPN) ( x, y, z ) Us may oid omalizd cto.g. x si φ cos θ y si φ si θ z cos φ X Z φ θ Y
Viw Coodiat Systm (VCS) Viw Pla Dictio is a it cto ititily cosodig to cto cto is scifid by th s i WCS (.) / Dictio x ( Lft Hadd)
Widow ad Ey Viw Coodiat Systm (VCS) Widow : lft, ight, bottom,to (w l,w,w b,w t ) gally is ctd at VRP (oigi) w w t Ey : (,, ) Tyically (,,-E) w l w b
Tasfomatio fom WCS to VCS Y O (x, y) ( x y ) ( a ( a b) + b) M + O X
Tasfomatio fom WCS to VCS Poit objct is std as (a,b,c) i VCS (x,y,z) i WCS z y x z y x z y x M
[ ] [ ] [ ] T M M c b a M c b a z y x ) ( ) ( + Tasfomatio fom WCS to VCS Cosio fom o coodiat systm to aoth Thfo a(-)., b(-)., c(-).
Tasfomatio fom WCS to VCS I Homogos Coodiats (a,b,c,) (x,y,z,) A w A w? M? T?
[ ] taslatio T T T M M M c b a ) ( I Homogos Coodiats -M T (-.,-.,-.) ( x, y, z ) xyz A w ' ' ' ' ' ' z y x z z z y y y x x x z y x T w M A Tasfomatio fom WCS to VCS
Tasfomatio fom VCS to Viw Pla (,, ) t *(*,*) * t tt Paamtically (t) (-t)+.t
Tasfomatio fom VCS to Viw Pla O - la, (t) t t t + * * ' ' ' ) ( ) (
M Wh y is o -axis * /( - ), * /( - ) Matix fom (*) Pscti Tasfomatio Tasfomatio fom VCS to Viw Pla
Usig Pscti Tasfomatio M Tasfomatio fom VCS to Viw Pla (sdo dth),),, ( ),, ( * * * * * * * M
s M *(,,,)M s M q : i WCS mas to *qa w M s M Tasfomatio fom VCS to Viw Pla If y is off -axis w ha aoth matix
Viw Volm Ey Viw Pla, Fot Pla F Back Pla B
Viw Volm w t w t F w b B w b F/(-F/ ) B/(-B/ )
Volm Nomalizatio Tasfomatio V t V b V l V
Volm Nomalizatio Tasfomatio F/(-F/ ) B/(-B/ ) o t Fo ) ( ) ( ) ( ) )( ( 2 B F B F F B B F F F B B F F o o t + Scalig s Taslatio
s s s N ) ( ))/ )( (( ) )/( ( ) )/( ( 2 F B F B s w w s w w s b t b t l l Volm Nomalizatio Tasfomatio wh ) ( )/ ( ) )/( ( ) )/( ( B F B F w w w w w w w w b t b t t b l l l Total Tasfomatio: A w M s M N
Pili Assigmt 3D It Sc i WCS Sc with las/olygos Wold Coodiat Systm (WCS)
Pili Assigmt V U Ey VRP i WCS N Ey ad Widow xtds i VCS Viwig Coodiat Systm (VCS)
Pili Assigmt Ey Viw Pla, Fot Pla F Back Pla B Fot ad Back la i VCS Ey alog N-axis
Pili Assigmt w t w t F w b B w b F/(-F/ ) B/(-B/ )
Pili Assigmt V t V b V l V
Pili Assigmt Dislay of ocss of iwig tasfomatio sig OGL Th sc i wold Th sc (withot cliig) aft tasfomatio to VCS with iw fstm Th sc aft scti tasfomatio Th sc aft omalizatio Th sc aft ojctio ad cliig o th iwig la Chag of it aamts
Pili Assigmt Th sc i wold
Pili Assigmt Th sc aft tasfomatio to VCS with iw fstm
Pili Assigmt Th sc aft scti/omalizatio tasfomatio
Pili Assigmt Th sc aft ojctio ad cliig o th iwig la
Pili Assigmt