trabajo tma khevin lizano_pdf

8/13/2019 Trabajo Tma Khevin Lizano_pdf

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FJPOXXIAAI U PEDZAO@EÐC FJ

DJ@OCEPDIP JC DOVAOH

GO@ZAVOF FJ ECMJCEJXÄO[.O Ecm. Dj`ïce`i Jaå`tre`o

Vjiräo fj Dïquecos





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‑Oÿi fj ao Ecvjrseðc poro ja Fjsorriaai Xuroa y ao Pjmurefof Oaedjctoreo—

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Djòcesdi pripujsti

6. Fjsorriaai ocoaäteì fja djòcesdi

:. Fjsorriaai pir djfei fj Dotaoh

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0. DJ@OCEPDI [XI[ZJPVI> Ja djòcesdi pripujsti js quj sj dujstro jc ao Gemuro ?,ci sj pripirèicoc fotis ìdi ao festocèo I8O, festocèo OH,

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osuderïc åstis poro ja pistjreir ocïaeses fja djòcesdi.

Gemuro ?> Djòcesdi pripujsti.





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⃝ ⃝ ⃝ ⃝

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Octjs fj rjsiavjr ao Jùoèðc 6 js cj`jsorei fjgecer oamucis vj`tirjs>

⃝ Jùoèðc :> Wj`tir ferj`èðc Z?

⃝ ⃝

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⃝ ⃝ ⃝ ⃝

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[ïmeco | 5

Xjoaezocfi ais desdis posis quj sj rjoaezoric poro ao vjaièfof>

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_ujfocfi ja semuejctj sestjdo fj jùoèicjs>

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:. Fjsorriaai pir djfei fj Dotaoh>

Ja semuejctj `ðfemi rjsujavj y mrogeò aos piseèicjs, vjaièfof y o`jajroèicjs fjadjòcesdi fofi>

àisj oaa àjor2girdot slirt% 6 femetis fjèdoajsà`2%Vrohoni Bljvec Aezoci %Fotis fj jctrofo syds x y w z% voreohajs sedhðaeòs poro òaùai fj aos vjaièfofjs y o`jajroèicjs fesp('O ìctecuoèic fjhjro ecmrjsor ais fotis fj jctrjfo')I8O4ecput('Ecmrjsj ao fedjcseic jc `d fja hrozi I8OR8:`d-:;`dT4 ')2% fedjcseðc fja hrozi

precèpoa(edpuasir)

OH4ecput('Ecmrjsj ao festocèo fja pucti O oa pucti HR8:`d-:;`dT4 ')22%fedjcseðc fja pucti O aorodpo I8x4;2% pucti fj rjgjrjcèo I8y4;2% pucti fj rjgjrjcèo idjmo8(0)4ecput('Ecmrjsj ao vjaièfof ocmuaor fja hrozi I8O Rrof/sT 4 ')22%Wjaièfof fj meri oago8(0)4ecput('Ecmrjsj ao o`jajroèic ocmuaor fja hrozi I8O Rrof/sS8T 4 ')2% O`jajroèic fj meri

posi4pe/72% posi poro aos seduaoèicjstljto84ecput('Ecmrjsj ja ïcmuai tljto8 jc mrofis (8=;»-07;») 4 ')2tljto64ecput('Ecmrjsj ja ïcmuai tljto8 jc mrofis (?»-<5») 4 ')2tjto84tljto8*pe/?<;2% Ïcmuai precèpoa fja hrozi edpuasir tjto64tljto6*pe/?<;2% Ïcmuai fj ao rodpo I6y4I8O*sec(tjto8)-OH*ìs(tjto6)-RI8O*ìs(tjto8)+OH*sec(tjto6)T*toc(tjto6)2%Festocèo y fj ao rodpo

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hx4I8O*ìs(tjt8)-I8O*ìs(tjto6+pe/8)2 % Dïxedo ìirfjco x fja pucti H

hy4I8O*sec(tjt8)-I8O*sec(tjto6+pe/8)2% Dïxedo ìirfjco y fja pucti H r8O(N,>)4ROx Oy ;T2% Wj`tir piseèic fja pucti O u?4Rìs(tjto6),sec(tjto6),;T2% Wj`tir ferj`èic u? u64Rìs(tjto6+pe/8),sec(tjto6+pe/8),;T2% Wj`tir ferj`èic u6 R[x,[yT 4 aecaec( Ox,Oy,hx,hy,[ix,[iy,[gx,[gy)2%gucèic poro jcìctro @([x,[y) ficfj A?(Ox,Oy,hx,hy) y A8 ([ix,[iy,[gx,[gy) foh4(Ox-[x)/ìs(tjto6+pe/8)2% Festocèo fja pucti O oa pucti H fo`4fh`-foh2% Festocèo fja pucti O oa pucti @ @x4Ox+fo`*ìs(tjto6+pe/8)2%@iirfjco x fja pucti @





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@y4Oy+fo`*sec(tjto6+pe/8)2%@iirfjco x fja pucti @ %Wjaièfofjs ocma(N)4tjt82 % OcmuaiWo8(N,>)4;.;?*`riss(idjmo8,r8O(N,>))2% Wj`tir Wjaièfof fja pucti O

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pait(RI8x,OxT,RI8y,OyT,'hi-')2 liaf ic pait(ROx,[xT,ROy,[yT,'ri-')2

pait(ROx,@xT,ROy,@yT,'mi-')2 pait(R[gx,[ixT,R[gy,[iyT,'f-')2tetaj('Mrogeì fj piseèic fja djòcesdi')xaohja('Festocèo x R`dT')yaohja('Festocèo y R`dT')tjxt(?.;:*I8x,?.;:*I8y,'IY{8}')2%?.;: poro quj sj pujfo vesuoaezortjxt(?.;:*I6x,?.;:*I6y,'IY{6}')2%?.;: poro quj sj pujfo vesuoaezortjxt(?.;:*Ox,?.;:*Oy,'O')2%?.;: poro quj sj pujfo vesuoaezortjxt(?.;:*[x,?.;:*[y,'H')2%?.;: poro quj sj pujfo vesuoaezortjxt(?.;:*@x,?.;:*@y,'@')2%?.;: poro quj sj pujfo vesuoaezormrefoxes(R-8;; 8;; -8;; 8;;T)2gemurj(8)

suhpait(0,?,?)ocmuai(N)4ocma(N)*?<;/pe2 pait(ocmuai,WO8)tetaj('Wjaièfof ohsiauto fja pucti O')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('Wjaièfof Rd/sT')mrefsuhpait(0,?,8)

pait(ocmuai,WO6Y0)tetaj('Wjaièfof rjaotevo fja pucti O ìc rjspj`ti oa pucti H')





[ïmeco | ?8

xaohja('Ocmuai QtljtoY{8}R»T')yaohja('Wjaièfof Rd/sT')mrefsuhpait(0,?,0)

mref pait(ocmuai,WO6)tetaj('Wjaièfof ohsiauto fja pucti H')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('Wjaièfof Rd/sT')mrefgemurj(0)suhpait(0,?,?)

pait(ocmuai,OO8)tetaj('O`jajroèðc ohsiauto fja pucti O')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('O`jajroèðc Rd/sS{8}T')mrefsuhpait(0,?,8)

pait(ocmuai,OO6)tetaj('O`jajroèðc rjaotevo fja pucti O ìc rjspj`ti oa pucti H')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('O`jajroèðc Rd/sS{8}T')mrefsuhpait(0,?,0)mref

pait(ocmuai,OO6Y0)tetaj('O`jajroèðc ohsiauto fja pucti H')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('O`jajroèðc Rd/sS{8}T')mrefN4N+?2

jcf

Ja semuejctj `ðfemi rjsujavj y mrogeò aos piseèicjs fja djòcesdi fofi>

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[ïmeco | 88

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jùoèicjs poro ja òaùai fj aos vjaièfofjs7:. Rx?,y?T4siavj(jqW6(N,?),jqW6(N,8))2% Xjsiauèic fja sestjdos

fj jùoèicjs77. WO6(N)4jvoa(x?)2% [osocfi ao voreohaj fj òro`tjr o rjoa 7=. WO6Y0(N)4jvoa(y?)2% [osocfi ao voreohaj fj òro`tjr o rjoa

7<. WO6v(N,>)4WO6(N)*u?2% Wj`tir Wjaièfof WH6 75. WO6Y0v(N,>)4WO6Y0(N)*u62% Wj`tir Wjaièfof WO6Y0 =;. %O`jajroèicjs =?. Oo8(N,>)4;.;?*R`riss(oago8,r8O(N,>))-

Ridjmo8(0)S8*r8O(N,>)TT2% Wj`tir O`jajroèic fja pucti O =8. OO8(N)4cird(Oo8(N,>))2% O`jajroèic fja pucti O =0. Oo6(N,>)4w*u?2% Wj`tir O`jajroèic OH6 jc sedhiaeì=6. Oo6Y0(N,>)4z*u62% Wj`tir O`jajroèic OO6Y0 jc sedhiaeì =:. jquO6(N,>)4Oo8(N,>)+Oo6Y0(N,>)-Oo6(N,>)2 =7. % Pestjdos fj jùoèicjs poro ja òaùai fj aos O`jajroèicjs ==. Rw?,z?T4siavj(jquO6(N,?),jquO6(N,8))2 =<. % Xjsiauèic fja sestjdos fj jùoèicjs

=5. OO6(N)4jvoa(w?)2% [osocfi ao voreohaj fj òro`tjr o rjoa <;. OO6Y0(N)4jvoa(z?)2% [osocfi ao voreohaj fj òro`tjr o rjoa <?. OO6Y0v(N,>)4OO6Y0(N)*u62% Wj`tir O`jajroèic OH6 <8. OO6v(N,>)4OO6(N)*u?2% Wj`tir O`jajroèic OO6Y0<0. %paitji fj gemuros<6. %horro/haiquj6 <:. Gd6(N,>)4-OO6v(N,>)*d62 <7. G`m4-Gòrmo*u?2





[ïmeco | 80

<=. Gedp6(N,>)4-(Gd6(N,>)+G`m)2 <<. %ìrrjfiro0 <5. Gpedp(N,>)4-Gedp6(N,>)2 5;. Gd0(N,>)4-Oo8(N,>)*d02 5?. X0(N,>)4-(Gpedp(N,>)+Gd0(N,>))2 58. %horro8 50. A4(I8O)/?;;2 56. E4(?/?8)*d8*(AS8)2 5:. Vd8(N,>)4-E*oago82 57. r`m(N,>)4RA*ìs(tjt8),A*sec(tjt8),;T*;.:2 5=. O`m8(N,>)4R`riss(oago8,r`m(N,>))-R(idjmo8(0)S8)*r`m(N,>)TT2 5<. Gd8(N,>)4-d8*O`m8(N,>)2 55. Gr0(N,>)4-X0(N,>)2 ?;;. Gr8(N,>)4-(Gd8(N,>)+Gr0(N,>))2 ?;?. Vr8(N,>)4`riss(-r`m(N,>),Gr8(N,>))2

?;8.

Vr0(N,>)4`riss(r`m(N,>),Gr0(N,>))2 ?;0. Vditv(N,>)4-(Vr8(N,>)+Vr0(N,>)+Vd8(N,>))2 ?;6. Vdit(N,>)4cird(Vditv(N,>))2 ?;:. gemurj(?)2 ?;7. liaf igg ?;=. pait(RI8x,OxT,RI8y,OyT,'hi-')2 liaf ic ?;<. pait(ROx,[xT,ROy,[yT,'ri-')2 ?;5. pait(ROx,@xT,ROy,@yT,'mi-')2 ??;. pait(R[gx,[ixT,R[gy,[iyT,'f-')2 ???. tetaj('Mrogeì fj piseèic fja djòcesdi') ??8. xaohja('Festocèo x R`dT') ??0. yaohja('Festocèo y R`dT')

??6. tjxt(?.;:*I8x,?.;:*I8y,'IY{8}')2%?.;: poro quj sj pujfovesuoaezor??:. tjxt(?.;:*I6x,?.;:*I6y,'IY{6}')2%?.;: poro quj sj pujfo

vesuoaezor??7. tjxt(?.;:*Ox,?.;:*Oy,'O')2%?.;: poro quj sj pujfo vesuoaezor??=. tjxt(?.;:*[x,?.;:*[y,'H')2%?.;: poro quj sj pujfo vesuoaezor??<. tjxt(?.;:*@x,?.;:*@y,'@')2%?.;: poro quj sj pujfo vesuoaezor??5. mref ?8;. oxes(R-8;; 8;; -8;; 8;;T)2 ?8?. gemurj(8) ?88. suhpait(0,?,?) ?80. ocmuai(N)4ocma(N)*?<;/pe2

?86. oxes(Rtljto8 Ocmgecoa*(?<;/pe) ?.5 8T)2 ?8:. pait(ocmuai,WO8) ?87. tetaj('Wjaièfof ohsiauto fja pucti O') ?8=. xaohja('Ocmuai QtljtoY{8}R»T') ?8<. yaohja('Wjaièfof Rd/sT') ?85. mref ?0;. suhpait(0,?,8) ?0?. oxes(Rtljto8 Ocmgecoa*(?<;/pe) -6 6T)2 ?08. pait(ocmuai,WO6Y0)





[ïmeco | 86

?00. tetaj('Wjaièfof rjaotevo fja pucti O ìc rjspj`ti oa puctiH')

?06. xaohja('Ocmuai QtljtoY{8}R»T') ?0:. yaohja('Wjaièfof Rd/sT')

?07. mref ?0=. suhpait(0,?,0) ?0<. mref ?05. oxes(Rtljto8 Ocmgecoa*(?<;/pe) -6 6T)2 ?6;. pait(ocmuai,WO6) ?6?. tetaj('Wjaièfof ohsiauto fja pucti H') ?68. xaohja('Ocmuai QtljtoY{8}R»T') ?60. yaohja('Wjaièfof Rd/sT') ?66. mref ?6:. gemurj(0) ?67. suhpait(0,?,?) ?6=. oxes(Rtljto8 Ocmgecoa*(?<;/pe) 7 ?;T)2 ?6<. pait(ocmuai,OO8) ?65. tetaj('O`jajroèðc ohsiauto fja pucti O') ?:;. xaohja('Ocmuai QtljtoY{8}R»T') ?:?. yaohja('O`jajroèðc Rd/sS{8}T') ?:8. mref ?:0. suhpait(0,?,8) ?:6. oxes(Rtljto8 Ocmgecoa*(?<;/pe) -?: ?:T)2 ?::. pait(ocmuai,OO6) ?:7. tetaj('O`jajroèðc rjaotevo fja pucti O ìc rjspj`ti oa pucti

H') ?:=. xaohja('Ocmuai QtljtoY{8}R»T')

?:<.

yaohja('O`jajroèðc Rd/sS{8}T') ?:5. mref ?7;. suhpait(0,?,0) ?7?. mref ?78. oxes(Rtljto8 Ocmgecoa*(?<;/pe) -?: ?:T)2 ?70. pait(ocmuai,OO6Y0) ?76. tetaj('O`jajroèðc ohsiauto fja pucti H') ?7:. xaohja('Ocmuai QtljtoY{8}R»T') ?77. yaohja('O`jajroèðc Rd/sS{8}T') ?7=. mref ?7<. N4N+?2 ?75. gemurj(6)

?=;. mref?=?. oxes(Rtljto8 Ocmgecoa*(?<;/pe) ?; ?;;;T)2 ?=8. pait(ocmuai,Vdit) ?=0. mref ?=6. jcf ?=:. Vdit ?=7. Vdox4dox(Vdit) ?==.





[ïmeco | 8:

?=<. @IC@AZPEICJP

Pj pujfj ihsjrvor quj jc aos mrogeòs ci sj ùdpajc aos semuejctjs jxprjseicjs>

⃝ ⃝ ⃝

⃝ ⃝ ⃝ ⃝ Jsti sj fjhj yo quj aos jùoèicjs octjreirjs sic jùoèicjs vj`tireoajs y ai quj sjmrogeò sic ja difuai (y ja sjctefi) fj òfo vj`tir fj ao rjspj`tevo jùoèðc. [oroìdprihor se sj ùdpaj ao jùoèic sj sustetuyjric ais vj`tirjs fj òfo jùoèic y jc

jsj didjcti jgj`tevodjctj ùdpaäo ìc ja rjsuatofi Ao seduaoèðc quj sj rjoaezi js jgj`tevo poro uc èjrti rocmi fj fotis fj

jctrofo(festocèo I8O, festocèo OH, , , , ) yo quj jstis sj osudejric, sj pifräo ihtedezor ja foti pjri jsto setuoèic sjrï paoctjofo jc ja semuejctj ecgirdj.





[ïmeco | 87

OCJ\IP





[ïmeco | 8=

Ja `ðfemi poro ectjrsj`èðc fj fis rj`tos sj prjsjcto o ìctecuoèðc>

% [rimorodo poro òaùaor ja pucti fj ectjrsj`èðc fj fis aäcjos % FOVIP FJ ECMXJPI % [uctis fj ao predjro aäcjo (Ox,Oy) y (Hx,Hy) % [uctis fj ao sjmucfo aäcjo (@x,@y) y (Fx,Fy) % POAEFO % Fjvujavj ja pucti fj ectjrsj`èðc ([x,[y) guc`teic R [x,[y T 4 aecaec( Ox,Oy,Hx,Hy,@x,@y,Fx,Fy)

% òaùaor se ao predjro i sjmucfo rj`to sic vjrteòajs eg (Hx-Ox44;) rj`WjrtO4?2 jasj rj`WjrtO4;2 jcf eg (Fx-@x44;) rj`WjrtH4?2 jasj rj`WjrtH4;2 jcf eg (rj`WjrtO 44? && rj`WjrtH44?)

jrrir('Aos rj`tos sic porjajos')2 jcf

eg (rj`WjrtO 44? && rj`WjrtH44;) %predjro rj`to vjrteòa d84((Fy-@y)/(Fx-@x))2 [x4Ox2 [y4d8*([x-Fx)+Fy2

jasjeg (rj`WjrtO 44; && rj`WjrtH44?)%sjmucfo rj`to vjrteòa d?4((Hy-Oy)/(Hx-Ox))2 [x4@x2 [y4d?*([x-Hx)+Hy2

jasj %Xj`tos jc uoaquejr piseèðc d?4((Hy-Oy)/(Hx-Ox))2 d84((Fy-@y)/(Fx-@x))2 %Wjreòr cujvodjctj se aos rjòtos ci sic poroajaos eg (d? 44 d8)

jrrir('Aos rj`tos sic porjajos')2 jcf [x4(d?*Ox-d8*Fx+Fy-Oy)/(d?-d8)2 [y4d?*([x-Ox)+ Oy2

jcf jcf





[ïmeco | 8<

Ja `ðfemi poro ectjrsj`èðc fj uco rj`to ìc uco èrùcgjrjcèo sj prjsjcto o ìctecuoèðc>

% [rimorodo poro òaùaor ja pucti fj ectjrsj`èðc fj fis aäcjos % FOVIP FJ ECMXJPI % [uctis fj ao predjro aäcjo (Ox,Oy) y (Hx,Hy) % [uctis fja fjctri fja èrùai (@x,@y) y Xofei X % POAEFO % Fjvujavj ais puctis fj ectjrsj`èðc ([x,[y) y (_x,_y) guc`teic R [x,[y,_x,_y T 4 aecèr( Ox,Oy,Hx,Hy,@x,@y,X)

% Wjregeòr se ao rj`to js vjrteòa i ci eg (Hx-Ox44;) % Ao rj`to js vjrteòa

%vjregeòr quj jxesto ectjrsj`èðc tdp4XS8-(Ox-@x)S82

eg (tdp1;) jrrir('Ci jxestj ectjrsj`èðc jctrj aäcjo y `ärùai')2 jcf [x4Ox2 _x4Ox2 [y4@y + tdpS;.:2 _y4@y - tdpS;.:2

jasj % Ao rj`to ci js vjrteòa d4(Hy-Oy)/(Hx-Ox)2

h4Oy-d*Ox2 %vjregeòr quj jxesto ectjrsj`èðc tdp4- @xS8*dS8 + 8*@x*@y*d - 8*@x*h*d - @yS8 + 8*@y*h + XS8*dS8 + XS8 - hS82 eg (tdp1;)

jrrir('Ci jxestj ectjrsj`èðc jctrj aäcjo y `ärùai')2 jcf [x4(@x - (tdp)S(?/8) + @y*d - h*d)/(dS8 + ?)2 _x4(@x + (tdp)S(?/8) + @y*d - h*d)/(dS8 + ?)2 [y4d*[x+h2 _y4d*[y+h2

jcf jcf





[ïmeco | 85

Ja `ðfemi poro ao ectjrsj`èðc fj fis èrùcgjrjcèos sj prjsjcto o ìctecuoèðc>

% [rimorodo poro òaùaor ja pucti fj ectjrsj`èðc fj fis aäcjos % FOVIP FJ ECMXJPI % [uctis fja `jctri fja èrùai ? (Ox,Oy) y Xofei X? % [uctis fja fjctri fja èrùai 8 (Hx,Hy) y Xofei X8 % POAEFO % Fjvujavj ais puctis fj ectjrsj`èðc ([x,[y) y (_x,_y) guc`teic R [x,[y,_x,_y T 4 èrèr( Ox,Oy,X?,Hx,Hy,X8)

% Wjregeòr se loy ectjrsj`èðc fest 4 ((Hx-Ox)S8+(Hy-Oy)S8)S82 eg (fest3X?+X8)

jrrir('Ci jxestj ectjrsj`èðc jctrj ais `ärùais')2

jcf % oaùaor ao ectjrsj`èðc

[x4Ox/8 + Hx/8 - (Ox*X?S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) +(Ox*X8S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) + (Hx*X?S8)/(8*OxS8 -6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) - (Hx*X8S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 -6*Oy*Hy + 8*HxS8 + 8*HyS8) + (Oy*(- OxS6 + 6*OxS0*Hx - 8*OxS8*OyS8 + 6*OxS8*Oy*Hy -7*OxS8*HxS8 - 8*OxS8*HyS8 + 8*OxS8*X?S8 + 8*OxS8*X8S8 + 6*Ox*OyS8*Hx - <*Ox*Oy*Hx*Hy +6*Ox*HxS0 + 6*Ox*Hx*HyS8 - 6*Ox*Hx*X?S8 - 6*Ox*Hx*X8S8 - OyS6 + 6*OyS0*Hy - 8*OyS8*HxS8 -7*OyS8*HyS8 + 8*OyS8*X?S8 + 8*OyS8*X8S8 + 6*Oy*HxS8*Hy + 6*Oy*HyS0 - 6*Oy*Hy*X?S8 -6*Oy*Hy*X8S8 - HxS6 - 8*HxS8*HyS8 + 8*HxS8*X?S8 + 8*HxS8*X8S8 - HyS6 + 8*HyS8*X?S8 +8*HyS8*X8S8 - X?S6 + 8*X?S8*X8S8 - X8S6)S(?/8))/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 +8*HyS8) - (Hy*(- OxS6 + 6*OxS0*Hx - 8*OxS8*OyS8 + 6*OxS8*Oy*Hy - 7*OxS8*HxS8 - 8*OxS8*HyS8 +

8*OxS8*X?S8 + 8*OxS8*X8S8 + 6*Ox*OyS8*Hx - <*Ox*Oy*Hx*Hy + 6*Ox*HxS0 + 6*Ox*Hx*HyS8 -6*Ox*Hx*X?S8 - 6*Ox*Hx*X8S8 - OyS6 + 6*OyS0*Hy - 8*OyS8*HxS8 - 7*OyS8*HyS8 + 8*OyS8*X?S8 +8*OyS8*X8S8 + 6*Oy*HxS8*Hy + 6*Oy*HyS0 - 6*Oy*Hy*X?S8 - 6*Oy*Hy*X8S8 - HxS6 - 8*HxS8*HyS8+ 8*HxS8*X?S8 + 8*HxS8*X8S8 - HyS6 + 8*HyS8*X?S8 + 8*HyS8*X8S8 - X?S6 + 8*X?S8*X8S8 -X8S6)S(?/8))/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8)2

_x4Ox/8 + Hx/8 - (Ox*X?S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) +(Ox*X8S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) + (Hx*X?S8)/(8*OxS8 -6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) - (Hx*X8S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 -6*Oy*Hy + 8*HxS8 + 8*HyS8) - (Oy*(- OxS6 + 6*OxS0*Hx - 8*OxS8*OyS8 + 6*OxS8*Oy*Hy -7*OxS8*HxS8 - 8*OxS8*HyS8 + 8*OxS8*X?S8 + 8*OxS8*X8S8 + 6*Ox*OyS8*Hx - <*Ox*Oy*Hx*Hy +6*Ox*HxS0 + 6*Ox*Hx*HyS8 - 6*Ox*Hx*X?S8 - 6*Ox*Hx*X8S8 - OyS6 + 6*OyS0*Hy - 8*OyS8*HxS8 -7*OyS8*HyS8 + 8*OyS8*X?S8 + 8*OyS8*X8S8 + 6*Oy*HxS8*Hy + 6*Oy*HyS0 - 6*Oy*Hy*X?S8 -6*Oy*Hy*X8S8 - HxS6 - 8*HxS8*HyS8 + 8*HxS8*X?S8 + 8*HxS8*X8S8 - HyS6 + 8*HyS8*X?S8 +8*HyS8*X8S8 - X?S6 + 8*X?S8*X8S8 - X8S6)S(?/8))/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 +8*HyS8) + (Hy*(- OxS6 + 6*OxS0*Hx - 8*OxS8*OyS8 + 6*OxS8*Oy*Hy - 7*OxS8*HxS8 - 8*OxS8*HyS8 +8*OxS8*X?S8 + 8*OxS8*X8S8 + 6*Ox*OyS8*Hx - <*Ox*Oy*Hx*Hy + 6*Ox*HxS0 + 6*Ox*Hx*HyS8 -6*Ox*Hx*X?S8 - 6*Ox*Hx*X8S8 - OyS6 + 6*OyS0*Hy - 8*OyS8*HxS8 - 7*OyS8*HyS8 + 8*OyS8*X?S8 +8*OyS8*X8S8 + 6*Oy*HxS8*Hy + 6*Oy*HyS0 - 6*Oy*Hy*X?S8 - 6*Oy*Hy*X8S8 - HxS6 - 8*HxS8*HyS8+ 8*HxS8*X?S8 + 8*HxS8*X8S8 - HyS6 + 8*HyS8*X?S8 + 8*HyS8*X8S8 - X?S6 + 8*X?S8*X8S8 -X8S6)S(?/8))/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8)2

[y4Oy/8 + Hy/8 - (Oy*X?S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) +(Oy*X8S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) + (Hy*X?S8)/(8*OxS8 -





6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) - (Hy*X8S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 -6*Oy*Hy + 8*HxS8 + 8*HyS8) - (Ox*(- OxS6 + 6*OxS0*Hx - 8*OxS8*OyS8 + 6*OxS8*Oy*Hy -7*OxS8*HxS8 - 8*OxS8*HyS8 + 8*OxS8*X?S8 + 8*OxS8*X8S8 + 6*Ox*OyS8*Hx - <*Ox*Oy*Hx*Hy +6*Ox*HxS0 + 6*Ox*Hx*HyS8 - 6*Ox*Hx*X?S8 - 6*Ox*Hx*X8S8 - OyS6 + 6*OyS0*Hy - 8*OyS8*HxS8 -

7*OyS8*HyS8 + 8*OyS8*X?S8 + 8*OyS8*X8S8 + 6*Oy*HxS8*Hy + 6*Oy*HyS0 - 6*Oy*Hy*X?S8 -6*Oy*Hy*X8S8 - HxS6 - 8*HxS8*HyS8 + 8*HxS8*X?S8 + 8*HxS8*X8S8 - HyS6 + 8*HyS8*X?S8 +8*HyS8*X8S8 - X?S6 + 8*X?S8*X8S8 - X8S6)S(?/8))/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 +8*HyS8) + (Hx*(- OxS6 + 6*OxS0*Hx - 8*OxS8*OyS8 + 6*OxS8*Oy*Hy - 7*OxS8*HxS8 - 8*OxS8*HyS8 +8*OxS8*X?S8 + 8*OxS8*X8S8 + 6*Ox*OyS8*Hx - <*Ox*Oy*Hx*Hy + 6*Ox*HxS0 + 6*Ox*Hx*HyS8 -6*Ox*Hx*X?S8 - 6*Ox*Hx*X8S8 - OyS6 + 6*OyS0*Hy - 8*OyS8*HxS8 - 7*OyS8*HyS8 + 8*OyS8*X?S8 +8*OyS8*X8S8 + 6*Oy*HxS8*Hy + 6*Oy*HyS0 - 6*Oy*Hy*X?S8 - 6*Oy*Hy*X8S8 - HxS6 - 8*HxS8*HyS8+ 8*HxS8*X?S8 + 8*HxS8*X8S8 - HyS6 + 8*HyS8*X?S8 + 8*HyS8*X8S8 - X?S6 + 8*X?S8*X8S8 -X8S6)S(?/8))/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8)2

_y4Oy/8 + Hy/8 - (Oy*X?S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) +(Oy*X8S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) + (Hy*X?S8)/(8*OxS8 -6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8) - (Hy*X8S8)/(8*OxS8 - 6*Ox*Hx + 8*OyS8 -6*Oy*Hy + 8*HxS8 + 8*HyS8) + (Ox*(- OxS6 + 6*OxS0*Hx - 8*OxS8*OyS8 + 6*OxS8*Oy*Hy -7*OxS8*HxS8 - 8*OxS8*HyS8 + 8*OxS8*X?S8 + 8*OxS8*X8S8 + 6*Ox*OyS8*Hx - <*Ox*Oy*Hx*Hy +6*Ox*HxS0 + 6*Ox*Hx*HyS8 - 6*Ox*Hx*X?S8 - 6*Ox*Hx*X8S8 - OyS6 + 6*OyS0*Hy - 8*OyS8*HxS8 -7*OyS8*HyS8 + 8*OyS8*X?S8 + 8*OyS8*X8S8 + 6*Oy*HxS8*Hy + 6*Oy*HyS0 - 6*Oy*Hy*X?S8 -6*Oy*Hy*X8S8 - HxS6 - 8*HxS8*HyS8 + 8*HxS8*X?S8 + 8*HxS8*X8S8 - HyS6 + 8*HyS8*X?S8 +8*HyS8*X8S8 - X?S6 + 8*X?S8*X8S8 - X8S6)S(?/8))/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 +8*HyS8) - (Hx*(- OxS6 + 6*OxS0*Hx - 8*OxS8*OyS8 + 6*OxS8*Oy*Hy - 7*OxS8*HxS8 - 8*OxS8*HyS8 +8*OxS8*X?S8 + 8*OxS8*X8S8 + 6*Ox*OyS8*Hx - <*Ox*Oy*Hx*Hy + 6*Ox*HxS0 + 6*Ox*Hx*HyS8 -6*Ox*Hx*X?S8 - 6*Ox*Hx*X8S8 - OyS6 + 6*OyS0*Hy - 8*OyS8*HxS8 - 7*OyS8*HyS8 + 8*OyS8*X?S8 +8*OyS8*X8S8 + 6*Oy*HxS8*Hy + 6*Oy*HyS0 - 6*Oy*Hy*X?S8 - 6*Oy*Hy*X8S8 - HxS6 - 8*HxS8*HyS8+ 8*HxS8*X?S8 + 8*HxS8*X8S8 - HyS6 + 8*HyS8*X?S8 + 8*HyS8*X8S8 - X?S6 + 8*X?S8*X8S8 -X8S6)S(?/8))/(8*OxS8 - 6*Ox*Hx + 8*OyS8 - 6*Oy*Hy + 8*HxS8 + 8*HyS8)2

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