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jet jet jet jet jet jet
otou otou otou otou otou otou
gdkot1 gdkot1 gdkot1 gdkot1 gdkot1 gdkot1
ckkrljeot ckkrljeot ckkrljeot ckkrljeot ckkrljeot ckkrljeot
x y z x y z
lorj lorj lorj lorj lorj lorj
tjtjc tjtjc tjtjc tjtjc tjtjc tjtjc
pnrtoio pnrtoio pnrtoio cnluo cnluo cnluo
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9'(+=-& rnht(x, y, dn`or, tjeffj)3
!="=0%+%" x y dn`or tjeffj
jet jet jet jet
otou otou otou otou
gdkot1 gdkot1 gdkot1 gdkot1
ckkrljeot x lorj snfj nipot ckkrljeot y lorj snfj nipot dn`or lorj snfj nipot tjeffj lorj snfj nipot
V2&+2>N%6#B%& %#= '#$%B ]2&++*&%%&= "2N $%& %/6#B%:#
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9'(+=-& nddjpsn(x, y, dn`or, tjeffj)3
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jet jet jet jet
otou otou otou otou
gdkot1 gdkot1 gdkot1 gdkot1
ckkrljeot x lorj ndjps ckkrljeot y lorj ndjps dn`or lorj ndjps tjeffj lorj ndjps
V2&+2>N%6#B%& %#= '#$%B ]2&++*&%%&= "2N $%& %/6#B%:#
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B%&-"'8&' 7#'#B %:%6 $%,# 266#/:2 $%/%' $#*N%- $2&+%& U*&+:# 266#/:2V($2PW8 >($2 $2U%*6' $%,# 266#/:2 >($2 %$%6%- 266#/:2V($2PHDK)mKWM @%&+ >2&2&'*B%& '#'#B %:%6 266#/:2 '2,62'%B $# :#:# B#,# %'%: N%'%: B('%B @%&+ >2>N2&'*B 266#/:28 V2>%&++#6 U*&+:# 266#/:2V($2PHm)7mKoOC`Vm 266#/:2V($2PHm)7mKoOC`Vm7mKW 7mKW %B%& >2&++%>N%, N2&'*B 266#/:2 $%,# /*:%' 266#/:8 ]%,%>2'2, -%,*: $#'*6#: $2&+%& cknKnA SmI`Kc :2>*%&@% B%,2&% ],(<2::#&+ %$%6%N%-%:% <%:2 :2&:#'#L2 %'%* >2>N2$%B%& -*,*U N2:%, $%& -*,*U B2<#68
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!="=0%+%" x? y? x0 y0 x8 y8 x< y<
jet jet jet jet jet jet jet jet
otou otou otou otou otou otou otou otou
gdkot1 gdkot1 gdkot1 gdkot1 gdkot1 gdkot1 gdkot1 gdkot1
ckkrljeot ckkrljeot ckkrljeot ckkrljeot ckkrljeot ckkrljeot ckkrljeot ckkrljeot
x y x y x y x y
lorj lorj lorj lorj lorj lorj lorj lorj
tjtjc tjtjc tjtjc tjtjc tjtjc tjtjc tjtjc tjtjc
pnrtoio pnrtoio cnluo cnluo cntjfo cntjfo cnnipot cnnipot
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:#
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!="=0%+%" IKLN
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9'(+=-& jg(ncsprnsj) { pnreyotooe }
!="=0%+%" Ncsprnsj pnreyotooe
ncsprnsj vodjl yoef ocoe ljnvoduosj opocob `nrejdoj trun otou godsn sotu otou dn`jb pnreyotooe yoef ocoe ljncsncusj
]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= ndsn
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
;@
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
:H U [2&% A=0=D %2&% gkr(jet j 9 >3 j 4 :>3 j +9 >) { jg(j 4 8>) { djen( 8=, j, 2=, j )3 } ndsn { djen( 0=, j, :=, j )3 } }
gkr(jet j 9 >3 j 4 :>3 jg(j 4 8>) { djen( 8=, j, 2=, j } ndsn jg (j 4 7>) { djen( 0=, j, :=, j } ndsn { djen( =, j, ?==, j } }
j +9 >) { )3 )3 )3
B%&-"'8&' V2>/2,6*%: :',*B'*, #UPW >2>N*%' /,(+,%> >2>#6#- %&'%,% $*% %'%* 62N#- N6(B B($28 V2&2&'*B%& :2N*%- N6(B B($2 $#2B:2B*:# N#6% #UPW N2,%# U%6:28
9'(+=-& jg(ncsprnsj) { pnreyotooe } ndsn { pnreyotooe } jg(ncsprnsj) { pnreyotooe } ndsn jg(ncsprnsj) { pnreyotooe } ndsn { pnreyotooe }
!="=0%+%" ncsprnsj godsn stotninets
ncsprnsj vodjl yoef ocoe ljnvoduosj opocob `nrejdoj trun otou sotu otou dn`jb pnreyotooe yoef ocoe ljncsncusj
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!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= jg()
X 1=+';=( lo\\Ilo\3 W "h33 h*&%B%& >2'-($ #UPW *&'*B >2>N*%' $*% /(6% @%&+ N2,N2$% $# $%6%> /,(+,%> @%&+ :%>% "h34 h*&%B%& >2'-($ #UPW $%& 26:2PW *&'*B >2>N*%' '#+% /(6% @%&+ N2,N2$% $# $%6%> /,(+,%> @%&+ :%>%
o%"=- 3 O%0M=+=&' 2=N=" H%,% >2>N%'%:# 6%@%, $%/%' $#6#-%' /%$% /('(&+%& /,(+,%> N2,#B*'= jg(x 4 =) { x 9 ?3 } jg(x 5 wjltb) { x 9 wjltb-?3 } jg(y 4 =) { y 9 ?3 } jg(y 5 bnjfbt) { y 9 bnjfbt-?3 }
O%(),M=; ="=; H%,% >2&+*N%- %,%- $%/%' $#6#-%' /%$% /('(&+%& /,(+,%> N2,#B*'= // ^plotn pksjsj lorj rout vkjl fnroc() { xpks +9 ( xspnnl * x[orob )3 ypks +9 ( yspnnl * y[orob )3 // Inefntns opocob rout indn`jbj `otos doyor // @jdo indn`jbj, `odjccoe orobeyo lnefoe inefodjcoe orobeyo lnefoe -? jg (xpks 4 =) { x[orob *9 -?3 } jg (xpks 5 wjltb-sjzn) { x[orob *9 -?3 } jg (ypks 4 =) { y[orob *9 -?3 } jg (ypks 5 bnjfbt-sjzn) { y[orob *9 -?3 } }
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
;L
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
X 1=+';=( lo\YIlo\Z W "h31 h2,%BB%& :2N*%- 262>2& L#:*%6 $# 6%@%,8 F2'#B% >2&+-#6%&+ $# *g*&+ 6%@%,M +2,%BB%& B2>N%6# B2 $%6%> N#&+B%# "h3; h2,%BB%& :2N*%- 262>2& L#:*%6 $# 6%@%,8 F2'#B% >2&@2&'*- *g*&+ 6%@%,M N%6#BB%& N%6#BB%& %,%-&@% "h3R nN%- B2<2/%'%& $%,# +2,%B :2N*%- N2&'*B B2'#B% N2&'*B '2,:2N*' '2,:2N*' >2>%:*B# 0#6%@%- @%&+ N2,N2$% $# 6%@%,
?=2-,2=&' 3 B%"=C=+ U 5=/'=( A=0=D /%)"%%&EP gdkot rol 9 ]J/<3 gdkot lnf 9 lnfrnns(rol)3 prjetde(rol + " roljoe soio lnefoe " + lnf + " lnroaot")3
B%&-"'8&' V2&+*N%- %# ,%$#%& B2 %# @%&+ :%>% $%6%> $2,%g%'8 K%$#%& $%& :*$*' %$%6%- $*% <%,% >2&+-#'*&+ :2:*%'* @%&+ :%>%8 72,$%/%' ;E3 $2,%g%' $%6%> :2N*%- 6#&+B%,%& $%& g*+% 1q]C ,%$#%& $%6%> :2N*%- 6#&+B%,%&8 H(&'(-M _3r e ]C?1 e 48J535_ER8 I2>*% >2'-($ ',#+(&(>2',# $%6%> ],(<2::#&+ >2&+-%,*:B%& :2>*% /%,%>2'2, $#-#'*&+ $%6%> ,%$#%&8
9'(+=-& lnfrnns(sulut)3
!="=0%+%" sulut
jet otou gdkot
V2&+2>N%6#B%& %#= U6(%' ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= roljoes()
A=0=D "=/'=(&EP gdkot lnf 9 <>.=3 gdkot rol 9 roljoes(lnf)3 prjetde(lnf + " lnroaot soio lnefoe " + rol + " roljoe")3
B%&-"'8&' V2&+*N%- %# $2,%g%' B2 %# @%&+ :%>% $%6%> ,%$#%&8 K%$#%& $%& :*$*' %$%6%- $*% <%,% >2&+-#'*&+ :2:*%'* @%&+ :%>%8 72,$%/%' ;E3 $2,%g%' $%6%> :2N*%- 6#&+B%,%& $%& g*+% 1q]C ,%$#%& $%6%> :2N*%- 6#&+B%,%&8 H(&'(-M _3r e ]C?1 e 48J535_ER8 I2>*% >2'-($ ',#+(&(>2',# $%6%> ],(<2::#&+ >2&+-%,*:B%& :2>*% /%,%>2'2, $#-#'*&+ $%6%> ,%$#%&8
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
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!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
9'(+=-& roljoes(sulut)
!="=0%+%" sulut
jet otou gdkot
V2&+2>N%6#B%& %#= U6(%' ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= $2+,22:PW
9'(,& =(/ ?#&'(,& A=0=D &'(EP gdkot o 9 =.=3 gdkot jeh 9 \VK[]J/0>.=3 gkr(jet j9=3 j4?==3 j9j+<) { djen(j, >=, j, >=+sje(o)*<=.=)3 o 9 o + jeh3 }
B%&-"'8&' V2&+-#'*&+ :#&*: $%,# :*%'* :*$*'8 A*&+:# :#&PW >2&2,#>% %# /%,%>2'2, :*$*' $%6%> ,%$#%& P%# %&'%,% 3 $%& E81GW8 )#6%# $#B2>N%6#B%& $%6%> ,2&'%&+ $%,# 94 :%>/%# $2&+%& 48
9'(+=-& sje(rol)3
!="=0%+%" rol
gdkot1 sulut ljbjtuef lodoi roljoe (]J s/l -]J)
V2&+2>N%6#B%& %#= U6(%' ]2&++*&%%&= "2N $%& %6#B%:# ]2,#&'%- '2,B%#'= hks() toe() otoe0() roljoes()
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
;G
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
A=0=D $#&EP gdkot o 9 =.=3 gdkot jeh 9 \VK[]J/0>.=3 gkr(jet j9=3 j4?==3 j9j+<) { djen(j, >=, j, >=+hks(o)*<=.=)3 o 9 o + jeh3 }
B%&-"'8&' V2&+-#'*&+ <(:#&*: $%,# :*%'* :*$*'8 A*&+:# <(:PW >2&2,#>% %# /%,%>2'2, :*$*' $%6%> ,%$#%& P%# %&'%,% 3 $%& E81GW8 )#6%# $#B2>N%6#B%& $%6%> ,2&'%&+ $%,# 94 :%>/%# $2&+%& 48
9'(+=-& hks(rol hks(rol)3 )3
!="=0%+%" rol
gdkot1 sulut ljbjtuef lodoi roljoe (]J s/l -]J)
V2&+2>N%6#B%& %#= U6(%' ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= sje() toe() otoe0() roljoes()
X 1=+';=( lo\hIlo\Q W "h3J S*%'6%- :2N*%- %&#>%:# $#&%>#: >2&++*&%B%& >2'-($ >2'-($ <(:PW :2N%+%# /2&+-%:#6 +2,%B%& "h3E S*%'6%- :2N*%- %&#>%:# $#&%>#: >2&++*&%B%& >2'-($ >2'-($ :#&PW $%& <(:PW :2N%+%# /2&+-%:#6 +2,%B%&
R"=(&H#"0=&' 3 R"=(&2=+% A=0=D +"=(&2=+%EP troesdotn(8=, 0=)3 rnht(=, =, >>, >>)3
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
MB
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
troesdotn(8=, 0=, ->=)3 rnht(=, =, >>, >>)3
troesdotn(8=, 0=)3 rnht(=, =, >>, >>)3 troesdotn(?<, ?<)3 rnht(=, =, >>, >>)3
B%&-"'8&' V2&2&'*B%& g%,%B *&'*B >2>#&$%-B%& (Ng2B $# $%6%> ,*%&+8 ]%,%>2'2, f >2&2&'*B%& ',%&:6%:# B%&%&?B#,#M /%,%>2'2, @ >2&2&'*B%& ',%&:6%:# &%#B?'*,*&M $%& /%,%>2'2, i >2&2&'*B%& ',%&:6%:# >%g*?>*&$*, $%,# 6%@%,8 I2<%,% '2B&#:M ',%&:6%'2PW >2&+%6#B%& >%',#B: ',%&:U(,>%:# /%$% :%%' #&# $2&+%& >%',#B: ',%&:6%:#8
9'(+=-& troesdotn(x, y)3 troesdotn(x, y, z)3
!="=0%+%" x y z
jet otou gdkot1 troesdosj coeoe/cjrj jet otou gdkot1 troesdosj otos/`owob jet otou gdkot1 troesdosj ioau/iuelur
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= rktotn() rktotnR() rktotnZ() rktotnQ() shodn() pusb() pkp()
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
MF
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
5#+=+% A=0=D "#+=+%EP troesdotn(wjltb/0, bnjfbt/0)3 rktotn(]J/8.=)3 rnht(-07, -07, >0, >0)3
B%&-"'8&' V2>*'%, (Ng2B :2N%&@%B @%&+ $#'2&'*B%& (62- /%,%>2'2, :*$*'8 DNg2B :26%6* $#,('%:# $# :2B#'%, /(:#:# ,26%'#U&@% B2 '#'#B %0%68 S#6%&+%& /(:#'#U >2>*'%, (Ng2B N2,6%0%&%& %,%g%,*> g%>8 I2<%,% '2B&#:M ,('%'2PW >2&+%6#B%& >%',#B: ',%&:U(,>%:# $2&+%& >%',#B: /2,B%6#%&8
9'(+=-& rktotn(sulut)3
!="=0%+%" sulut
gdkot1 sulut rktosj otou putoroe ljtnetucoe lodoi roljoe
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= rktotnR() rktotnZ() rktotnQ() troesdotn() shodn() pusb() pkp()
9$=2% A=0=D &$=2%EP rnht(8=, 0=, >=, >=)3 shodn(=.>)3 rnht(8=, 0=, >=, >=)3
rnht(8=, 0=, >=, >=)3 shodn(=.>, ?.8)3
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
M;
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
rnht(8=, 0=, >=, >=)3
B%&-"'8&' V2&%>N%- $%& >2&+*,%&+# *B*,%& $%,# (Ng2B $2&+%& >2>/2,N2:%, $%& >2&+2,*'B%& L2,'2B:8 )#6%# :<%62 $#'2&'*B%& (62- /2,:2&'%:2 $2:#>%68 V2>%&++#6 U*&+:# :<%62P183W %B%& >2&%>N%- N2:%, *B*,%& :*%'* N2&'*B :2N2:%, $*% ,%'*: /2,:2&8 DNg2B :26%6* $#:B%6%B%& $%,# %:%6 ,26%'#U&@% B2 :#:'2> B((,$#&%'8
9'(+=-& shodn(ucuroe)3 shodn(x, y)3 shodn(x, y, z)3
!="=0%+%" ucuroe x y z
gdkot1 gdkot1 gdkot1 gdkot1
pnrsnetosn pnrsnetosn pnrsnetosn pnrsnetosn
uetuc uetuc uetuc uetuc
inescodocoe inescodocoe inescodocoe inescodocoe
k`anc k`anc lodoi sui`u "x" k`anc lodoi sui`u "y" k`anc lodoi sui`u "z"
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= troesdotn() rktotn() rktotnR() rktotnZ() rktotnQ() shodn() pusb() pkp()
!,&; U !#8 A=0=D 8,&;EP rnht(=, =, >=, >=)3 //Xnfj nipot putjb pusb()3 troesdotn(8=, 0=)3 gjdd(=)3 rnht(=, =, >=, >=)3 //Xnfj nipot bjtoi pkp()3 gjdd(?=0)3 rnht(?>, ?=, >=, >=)3 //Xnfj nipot o`u-o`u
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
MM
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
B%&-"'8&' ]*:- %$%6%- >2&$(,(&+ ',%&:U(,>%:# >%',#B: B2 %'%: '*>/*B%& >%',#B: P>%',#f :'%%-%># /*:-PW $%& /(/PW >2>2,6*B%&/2>%-%>%& >2>2,6*B%&/2>%-%>%& %B%& B(&:2/ >%',#f :'%2&@#>/%& :#:'2> B((,$#&%' :%%' #&# B2 $%6%> '*>/*B%& $%& /(/PW >2&+2>N%6#B%& B2 :2>*6% :#:'2> B((,$#&%' :2N26*>&@%8 /*:-PW $%& /(/PW $#+*&%B%& $%6%> B%#'%& $2&+%& >2'($2 ',%&:U(,>%:# 6%#&&@% $%& N#:% $#62B%'B%& *&'*B >2&+(&',(6 g%&+B%*%& $%,# ',%&:U(,>%:#8
9'(+=-& pusb()3
V2&+2>N%6#B%& %#= ]2&++*&%%&= ]2,#&'%- '2,B%#'= pkp() troesdotn() rktotn() rktotnR() rktotnZ() rktotnQ()
A=0=D 8#8EP rnht(=, =, >=, >=)3 //Vbjtn rnhtoefdn pusb()3 troesdotn(8=, 0=)3 gjdd(=)3 rnht(=, =, >=, >=)3 //@dohc rnhtoefdn pkp()3 gjdd(?=0)3 rnht(?>, ?=, >=, >=)3 //Froy rnhtoefdn
B%&-"'8&' ](/: %$%6%- >2>*&<*6B%& ',%&:U(,>%:# >%',#B: B26*%, $%,# '*>/*B%& >%',#B: P>%',#f :'%%-%># /*:-PW $%& /(/PW >2>2,6*B%&/2>%-%>%& %B%& B(&:2/ >%',#f :'%2&@#>/%& :#:'2> B((,$#&%' :%%' #&# B2 $%6%> '*>/*B%& $%& /(/PW >2&+2>N%6#B%& B2 :2>*6% :#:'2> B((,$#&%' :2N26*>&@%8 /*:-PW $%& /(/PW $#+*&%B%& $%6%> B%#'%& $2&+%& >2'($2 ',%&:U(,>%:# 6%#&&@% $%& N#:% $#62B%'B%& *&'*B >2&+(&',(6 g%&+B%*%& $%,# ',%&:U(,>%:#8
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
MO
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
9'(+=-& pkp()3
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= pusb()
X 1=+';=( lo33Ilo3Y W "h44 h*&%B%& >2'-($ ,('%'2PW ,('%'2PW *&'*B >2&+2B:/,2:#B%& #$2 bB2:2#>N%&+%&j "h41 h*&%B%& >2'-($ :<%62PW *&'*B >2&+2B:/,2:#B%& >2&+2B:/,2:#B%& #$2 bB2:2#>N%&+%&j
!"%&%(+=&'D !%2=(+'() C&:',*B'*, %B%& >2>/,2:2&'%:#B%& /,(+,%> @%&+ >2&$2>(&:',%:#B%& /26%&'#&+ %'%* /%&'*6%&8
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
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!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
o%"=- /=( 5%&8#(
O=&,-=( 3 0#,&%K4 0#,&%] A=0=D 0#,&%K vkjl lrow() { djen(ikusnR, 0=, ikusnR, 2=)3 }
B%&-"'8&' Y%,#%N26 :#:'2> >(*:2X :26%6* >2>*%' B((,$#&%' -(,#i(&'%6 $%,# >(*:28
9'(+=-& ikusnR
]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= ikusnZ pikusnR pikusnZ ikusn]rnssnl ikusn]rnssnl() ikusnPndnosnl() ikusnIkvnl() ikusnLroffnl()
A=0=D 0#,&%] vkjl lrow() { djen(0=, ikusnZ, 2=, ikusnZ)3 }
B%&-"'8&' Y%,#%N26 :#:'2> >(*:2\ :26%6* >2>*%' B((,$#&%' L2,'#B%6 $%,# >(*:28
9'(+=-& ikusnZ
]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'=
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
MH
!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
ikusnR pikusnR pikusnZ ikusn]rnssnl ikusn]rnssnl() ikusnPndnosnl() ikusnIkvnl() ikusnLroffnl()
0#,&%!"%&&%/ A=0=D 0#,&%!"%&&%/ // Cdjc polo foi`or uetuc inefu`ob // woreo lorj cktoc vkjl lrow() { jg (ikusn]rnssnl 99 trun) { gjdd(=)3 } ndsn { gjdd(0>>)3 } rnht(0>, 0>, >=, >=)3 }
B%&-"'8&' ],(<2::#&+ :2<%,% ('(>%'#: >2>%&'%* %/%B%- '(>N(6 >(*:2 $#'2B%& %'%* '#$%B P>2>%&'%* '(>N(6 B#,# >(*:2 /%$% >(*:2 $2&+%& '(>N(6 62N- $%,# :%'*W8 )#6%# $%,# L%,#%N62 :#:'2> >(*:2],2::2$ %$%6%- ',*2 N#6% '(>N(6 $#'2B%& P/,2::2$W $%& U%6:2 N#6% '(>N(6 '#$%B $#'2B%&8 ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= ikusnR ikusnZ pikusnR pikusnZ ikusn]rnssnl() ikusnPndnosnl() ikusnIkvnl() ikusnLroffnl()
X 1=+';=( o5\\Io5\Y W hK33 h%>N%,6%- :2N*%:2N*%- 262>2& 262>2& L#:*%6 @%&+ N2,+2,%B N2,-*N*&+%& N2,-*N*&+%& $2&+%& $2&+%& >(*:2 hK34 h%>N%,6%- $*% 262>2& 262>2& L#:*%6 @%&+ >%:#&+9>%:#&+ N2,+2,%B N2,-*N*&+%& N2,-*N*&+%& $2&+%& >(*:2 $2&+%& <%,% @%&+ N2,N2$% hK31 h%>N%,6%- :2N*%:2N*%- 262>2& 262>2& L#:*%6 @%&+ N2,+2,%B N2,-*N*&+%& N2,-*N*&+%& $2&+%& $2&+%& >(*:2M '2'%/# $2&+%& -*N*&+%& @%&+ N2,N2$% B2'#B% >(*:2 $#B6#B
6*'*$(70 2-+?0%0 : %771"334*'*$(70(-+?0%0950=
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!"#$%&&'()" #$%$&$ '$( )*(+,-(+$( ./=?0+?$=$( 8?$<*& >(7/?$,7*<
O=&,-=( Y 0#,&%!"%&&%/EP A=0=D 0#,&%!"%&&%/EP // Cdjc polo foi`or uetuc inefu`ob // woreo lorj cktoc jet vodun 9 =3 vkjl lrow() { gjdd(vodun)3 rnht(0>, 0>, >=, >=)3 } vkjl ikusn]rnssnl() { jg(vodun 99 =) { vodun 9 0>>3 } ndsn { vodun 9 =3 } }
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9'(+=-& ikusn]rnssnl()
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= ikusnR ikusnZ pikusnR pikusnZ ikusn]rnssnl ikusnPndnosnl() ikusnIkvnl() ikusnLroffnl()
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0#,&%5%2%=&%/EP A=0=D 0#,&%5%2%=&%/EP // Cdjc polo foi`or uetuc inefu`ob // woreo lorj cktoc jet vodun 9 =3 vkjl lrow() { gjdd(vodun)3 rnht(0>, 0>, >=, >=)3 } vkjl ikusnPndnosnl() { jg(vodun 99 =) { vodun 9 0>>3 } ndsn { vodun 9 =3 } }
B%&-"'8&' A*&+:# >(*:2K262%:2$PW $#/%&++#6 '#%/ B%6# '(>N(6 >(*:2 $#62/%:B%& %'%* '#$%B $#'2B%&8 F2'#B% >2&++*&%B%& >(*:2 $2&+%& '(>N(6 62N#- $%,# :%'*M -%&@% '(>N(6 B#,# @%&+ '2,$2'2B:#8
9'(+=-& ikusnPndnosnl()
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= ikusnR ikusnZ pikusnR pikusnZ ikusn]rnssnl ikusn]rnssnl() ikusnIkvnl() ikusnLroffnl()
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0#,&%O#>%/EP A=0=D 0#,&%O#>%/EP // Cdjc polo foi`or uetuc inefu`ob // woreo lorj cktoc jet vodun 9 =3 vkjl lrow() { gjdd(vodun)3 rnht(0>, 0>, >=, >=)3 } vkjl ikusnIkvnl() { vodun 9 vodun + >3 jg (vodun 5 0>>) { vodun 9 =3 } }
B%&-"'8&' A*&+:# >(*:2V(L2$PW $#/%&++#6 '#%/ B%6# >(*:2 N2,+2,%B $%& '(>N(6 >(*:2 '#$%B $#'2B%&8
9'(+=-& ikusnIkvnl()
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= ikusnR ikusnZ pikusnR pikusnZ ikusn]rnssnl ikusn]rnssnl() ikusnPndnosnl() ikusnLroffnl()
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0#,&%B"=))%/EP A=0=D 0#,&%B"=))%/EP // \orjc (cdjc loe toboe) ikusn oelo indoduj foi`or // uetuc inefu`ob woreo lorj cktoc jet vodun 9 =3 vkjl lrow() { gjdd(vodun)3 rnht(0>, 0>, >=, >=)3 } vkjl ikusnLroffnl() { vodun 9 vodun + >3 jg (vodun 5 0>>) { vodun 9 =3 } }
B%&-"'8&' O#/%&++#6 '#%/ B%6# >(*:2 N2,+2,%B $%& '(>N(6 $#'2B%&8 F2'#B% >2&++*&%B%& >(*:2 $2&+%& '(>N(6 62N#- %$,# :%'*M -%&@% '(>N(6 B#,# @%&+ '2,$2'2B:#8
9'(+=-& ikusnLroffnl()
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= ikusnR ikusnZ pikusnR pikusnZ ikusn]rnssnl ikusn]rnssnl() ikusnPndnosnl() ikusnIkvnl()
X 1=+';=( o5\hIo5\Q W hK3J S*%' :2N*%- 2L2&' @%&+ $#>*6%# $#>*6%# B2'#B% >(*:2 >(*:2 $#B6#B $%& N2,%B-#, B2'#B% B6#B >(*:2 $#62/%: hK3E S*%'6%- :2N*%:2N*%- +%>N%, ,2:/(&:#U @%&+ N2,B26%B*%& N2,B26%B*%& N2,N2$% N2,N2$% B2'#B% >(*:2 N2,+2,%B $%& >(*:2 $#'%,#B
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oG: 3 5#22#>%" H(&'(- N2,#B*' #&# >2&$2>(&:',%:#B%& ,(66(L2,8 "%,&% %B%& N2,*N%- N#6% >(*:2 >26%6*# (N@2B8 // Pkddkvnr // `y PNOX 4bttp1//www.frkuph.ent5 // Pkdd kvnr tbn hkdkrnl squorns je tbn hnetnr kg tbn jiofn // tk hboefn tbn hkdkr kg tbn kutsjln rnhtoefdn // ^plotnl =: Gn`ruory 0==8 // Hrnotnl 0? Oufust 0==0 jet jet jet jet
rnhtR, rnhtZ3 hjrhdnR, hjrhdnR, hjrhdnZ3 rnhtXjzn 9 >=3 hjrhdnXjzn 9 >83
// // // //
]ksjtjke ]ksjtjke Ljointnr Ljointnr
kg kg kg kg
squorn `uttke hjrhdn `uttke rnht hjrhdn
hkdkr rnhtHkdkr3 hkdkr hjrhdnHkdkr3 hkdkr `osnHkdkr3 `kkdnoe rnhtKvnr 9 godsn3 `kkdnoe hjrhdnKvnr 9 godsn3 vkjl sntup() { sjzn(0==, 0==)3 rnhtHkdkr 9 hkdkr(0=<, ?>8, =)3 hjrhdnHkdkr 9 hkdkr(?=0, ?>8, =)3 `osnHkdkr 9 hkdkr(?=0, ?=0, ?=0)3 hjrhdnR 9 wjltb/0+hjrhdnXjzn/0+?=3 hjrhdnZ 9 bnjfbt/03 rnhtR 9 wjltb/0-rnhtXjzn-?=3 rnhtZ 9 bnjfbt/0-rnhtXjzn/03 nddjpsnIkln(HNE\NP)3 } vkjl lrow() { uplotn(ikusnR, ikusnZ)3 ekXtrkcn()3 jg (rnhtKvnr) { `ohcfrkuel(rnhtHkdkr)3 } ndsn jg (hjrhdnKvnr) { `ohcfrkuel(hjrhdnHkdkr)3 } ndsn { `ohcfrkuel(`osnHkdkr)3 } strkcn(0>>)3 gjdd(rnhtHkdkr)3 rnht(rnhtR, rnhtZ, rnhtXjzn, rnhtXjzn)3 gjdd(hjrhdnHkdkr)3 nddjpsn(hjrhdnR, hjrhdnZ, hjrhdnXjzn, hjrhdnXjzn)3 } vkjl uplotn(jet x, jet y) { jg( kvnrHjrhdn(hjrhdnR, hjrhdnZ, hjrhdnXjzn) ) { hjrhdnKvnr 9 trun3 rnhtKvnr 9 godsn3
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} ndsn jg ( kvnrPnht(rnhtR, rnhtZ, rnhtXjzn, rnhtXjzn) ) { rnhtKvnr 9 trun3 hjrhdnKvnr 9 godsn3 } ndsn { hjrhdnKvnr 9 rnhtKvnr 9 godsn3 } } `kkdnoe kvnrPnht(jet x, jet y, jet wjltb, jet bnjfbt) { jg (ikusnR 59 x && ikusnR 49 x+wjltb && ikusnZ 59 y && ikusnZ 49 y+bnjfbt) { rnture trun3 } ndsn { rnture godsn3 } } `kkdnoe kvnrHjrhdn(jet x, jet y, jet ljointnr) { gdkot ljsR 9 x - ikusnR3 gdkot ljsZ 9 y - ikusnZ3 jg(sqrt(sq(ljsR) + sq(ljsZ)) 4 ljointnr/0 ) { rnture trun3 } ndsn { rnture godsn3 } }
*,++#( H(&'(- N2,#B*' #&# >2&$2>(&:',%:#B%& N*''(& %'%* '(>N(68 // @uttke // `y PNOX 4bttp1//www.frkuph.ent5 // Hdjhc ke ken kg tbn hkdkrnl squorns je tbn // hnetnr kg tbn jiofn tk hboefn tbn hkdkr kg // tbn kutsjln rnhtoefdn // ^plotnl =: Gn`ruory 0==8 // Hrnotnl 0? Oufust 0==0 jet rnhtR, rnhtZ3 // ]ksjtjke kg squorn `uttke jet hjrhdnR, hjrhdnR, hjrhdnZ3 // ]ksjtjke kg hjrhdn `uttke jet rnhtXjzn 9 >=3 // Ljointnr kg rnht jet hjrhdnXjzn 9 >83 // Ljointnr kg hjrhdn hkdkr rnhtHkdkr, hjrhdnHkdkr, `osnHkdkr3 hkdkr rnhtBjfbdjfbt, hjrhdnBjfbdjfbt3 hkdkr hurrnetHkdkr3 `kkdnoe rnhtKvnr 9 godsn3 `kkdnoe hjrhdnKvnr 9 godsn3 vkjl sntup() { sjzn(0==, 0==)3 rnhtHkdkr 9 hkdkr(0=<, ?>8, =)3 rnhtBjfbdjfbt 9 hkdkr(0>>, 0=<, =)3 hjrhdnHkdkr 9 hkdkr(?=0, ?>8, =)3 hjrhdnBjfbdjfbt 9 hkdkr(?>8, 0=<, =)3 `osnHkdkr 9 hkdkr(?=0, ?=0, ?=0)3 hurrnetHkdkr 9 `osnHkdkr3 hjrhdnR 9 wjltb/0+hjrhdnXjzn/0+?=3
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hjrhdnZ 9 bnjfbt/03 rnhtR 9 wjltb/0-rnhtXjzn-?=3 rnhtZ 9 bnjfbt/0-rnhtXjzn/03 nddjpsnIkln(HNE\NP[LJOIN\NP)3 } vkjl lrow() { uplotn(ikusnR, ikusnZ)3 `ohcfrkuel(hurrnetHkdkr)3 strkcn(0>>)3 jg(rnhtKvnr) { gjdd(rnhtBjfbdjfbt)3 } ndsn { gjdd(rnhtHkdkr)3 } rnht(rnhtR, rnhtZ, rnhtXjzn, rnhtXjzn)3 jg(hjrhdnKvnr) { gjdd(hjrhdnBjfbdjfbt)3 } ndsn { gjdd(hjrhdnHkdkr)3 } nddjpsn(hjrhdnR, hjrhdnZ, hjrhdnXjzn, hjrhdnXjzn)3 } vkjl uplotn(jet x, jet y) { jg( kvnrHjrhdn(hjrhdnR, hjrhdnZ, hjrhdnXjzn) ) { hjrhdnKvnr 9 trun3 rnhtKvnr 9 godsn3 } ndsn jg ( kvnrPnht(rnhtR, rnhtZ, rnhtXjzn, rnhtXjzn) ) { rnhtKvnr 9 trun3 hjrhdnKvnr 9 godsn3 } ndsn { hjrhdnKvnr 9 rnhtKvnr 9 godsn3 } } vkjl ikusn]rnssnl() { jg(hjrhdnKvnr) { hurrnetHkdkr 9 hjrhdnHkdkr3 } jg(rnhtKvnr) { hurrnetHkdkr 9 rnhtHkdkr3 } } `kkdnoe kvnrPnht(jet x, jet y, jet wjltb, jet bnjfbt) { jg (ikusnR 59 x && ikusnR 49 x+wjltb && ikusnZ 59 y && ikusnZ 49 y+bnjfbt) { rnture trun3 } ndsn { rnture godsn3 } } `kkdnoe kvnrHjrhdn(jet x, jet y, jet ljointnr) { gdkot ljsR 9 x - ikusnR3 gdkot ljsZ 9 y - ikusnZ3 jg(sqrt(sq(ljsR) + sq(ljsZ)) 4 ljointnr/0 ) { rnture trun3 } ndsn {
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O=&,-=( ^ -%N!"%&&%/ A=0=D -%N!"%&&%/ // Cdjc polo foi`or uetuc ini`nrj gkcus // loe tncoe sni`oroef cuehj vkjl lrow() { jg (cny]rnssnl 99 trun) { gjdd(=)3 } ndsn { gjdd(0>>)3 } rnht(0>, 0>, >=, >=)3 }
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9'(+=-& cny]rnssnl
]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= cny cnyHkln cny]rnssnl() cnyPndnosnl()
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-%N A=0=D -%N // Cdjc polo wjelkw uetuc ini`nrj gkcus // loe tncoe cuehj '@' polo cny`korl vkjl lrow() { jg(cny]rnssnl) { jg (cny 99 '`' || cny 99 '@') { gjdd(=)3 } } ndsn { gjdd(0>>)3 } rnht(0>, 0>, >=, >=)3 }
B%&-"'8&' Y%,#%N26 :#:'2> B2@ :26%6* >2>*%' %# $%,# B*&<# @%&+ :%%' #&# $#'2B%& /%$% B2@N(%,$8
9'(+=-& cny
]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= cny]rnssnl cnyHkln cny]rnssnl() cnyPndnosnl()
-%N!"%&&%/EP A=0=D // cdjc polo foi`or uetuc ini`nrj gkcus, // loe tncoe sni`oroef cuehj jet vodun 9 =3 vkjl lrow() { gjdd(vodun)3 rnht(0>, 0>, >=, >=)3 } vkjl cny]rnssnl() { jg(vodun 99 =) { vodun 9 0>>3 } ndsn { vodun 9 =3 } }
B%&-"'8&' A*&+:# B2@],2::2$PW $#/%&++#6 '#%/ B%6# :2>N%,%&+ B*&<# $#'2B%&8 I2N%+%# %'*,%& *>*>M '#$%B %$% @%&+ $#+%>N%, $# $%6%> N6(B B2@],2::2$PW8
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9'(+=-& vkjl cny]rnssnl() { pnreyotooe }
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= cny]rnssnl cny cnyHkln cnyPndnosnl()
-%N5%2%=&%/EP A=0=D -%N5%2%=&%/EP // Cdjc polo foi`or uetuc ini`nrj gkcus, // loe tncoe sni`oroef cuehj jet vodun 9 =3 vkjl lrow() { gjdd(vodun)3 rnht(0>, 0>, >=, >=)3 } vkjl cnyPndnosnl() { jg(vodun 99 =) { vodun 9 0>>3 } ndsn { vodun 9 =3 } }
B%&-"'8&' A*&+:# B2@K262%:2$PW $#/%&++#6 '#%/ B%6# :2N*%- B*&<# $#62/%:B%&8 I2N%+%# %'*,%& *>*>M '#$%B %$% @%&+ $#+%>N%, $# $%6%> N6(B B2@K262%:2$PW8
9'(+=-& vkjl cnyPndnosnl() { pnreyotooe }
V2&+2>N%6#B%& %#= 7#$%B ]2&++*&%%&= "2N $%& %/6#B%:# ]2,#&'%- '2,B%#'= cny]rnssnl cny cnyHkln cny]rnssnl()
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