trabajo tma khevin lizano_pdf
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8/13/2019 Trabajo Tma Khevin Lizano_pdf
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | ?
VXOHONI
VJIXÄO FJ
DÏ_ZECOP
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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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | 8
‑Oÿi fj ao Ecvjrseðc poro ja Fjsorriaai Xuroa y ao Pjmurefof Oaedjctoreo—
Osemcoturo>
VJIXÄO FJ DÏ_ZECOP
[rigjsir>
Ecm. DEMZJA @OPVXI PÏC@LJ^
Vjdo>
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
Ectjmroctjs>
BLJWEC JXE@BPIC OCFXJ AE^OCI HIXXJXI
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | 0
Äcfe`j
?. Ectrifu``eðc
8. Ihnjtevis fja trohoni
0.
Dj`ocesdi pripujsti
6. Fjsorriaai ocoaäte`i fja dj`ocesdi
:. Fjsorriaai pir djfei fj Dotaoh
7. Mroge`os fj rjsuatofis
=. @ic`auseicjs
<. Ocjxis
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | :
0. DJ@OCEPDI [XI[ZJPVI> Ja dj`ocesdi pripujsti js quj sj dujstro jc ao Gemuro ?,ci sj pripir`eicoc fotis `idi ao festoc`eo I8O, festoc`eo OH,
,
,
,
2 pir ai quj sj
osuderïc åstis poro ja pistjreir ocïaeses fja dj`ocesdi.
Gemuro ?> Dj`ocesdi pripujsti.
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | 7
6. FJPOXXIAAI FJ DJ@OCEPDI
Oa ci tjcjr ais fotis sj osuderïc uci voairjs ece`eoajs>
I8O4 6<`d I6O4 67`d
46rof/s
4<rof/s
408;»
48:»
Oliro oa tjcjr jstis fotis ece`eoajs sj pri`jfjrï oa fjsorriaai fja sestjdo>
[redjri sj `oa`uaorï ao vjai`efof y ao o`jajro`eðc fja pucti O. Ja pucti O pir pjrtjcj`jr o ao horro 8 tjcfrï ao semuejctj jxprjseðc>
⃝ ⃝ ⃝
J`uo`eðc ?> Wjai`efof fja pucti O
Ficfj>
⃝ ⃝
⃝ J`uo`eðc 8> [ise`eðc fja pucti O
⃝ Xjoaezocfi ja prifu`ti vj`tireoa>
⃝ | ⃝ | ⃝
⃝
[oro ja `ïa`uai fj ao o`jajro`eðc fja pucti O. Ja pucti O pir pjrtjcj`jr o ao horro 8 tjcfrï aosemuejctj jxprjseðc>
⃝ ⃝ ⃝ ⃝
J`uo`eðc 0> O`jajro`eðc fja pucti O
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | =
Pustetuyjcfi jc ao J`uo`eðc 0>
⃝ R T | ⃝ |
⃝
⃝
Oa jstor `icj`tofi ao Horro 8 y ao Horro 0 pir ja pucti O sj pujfj fjgecer jctic`js>
⃝ ⃝
⃝ ⃝
Oliro poro ja `ïa`uai fj ao vjai`efof fja pucti H sj fjhj tjcjr jc `ujcto quj pjrtjcj`j o ao horro 6 pjri fjpjcfj fj ao Wjai`efof ohsiauto y Wjai`efof rjaotevo fja pucti O. [ir ai tocti,sj tejcj ao semuejctj jxprjseðc>
⃝ ⃝ ⃝
J`uo`eðc 6> Wjai`efof fja pucti H
Octjs fj rjsiavjr ao J`uo`eðc 6 js cj`jsorei fjgecer oamucis vj`tirjs>
⃝ J`uo`eðc :> Wj`tir ferj``eðc Z?
⃝ ⃝
J`uo`eðc 7> Wj`tir ferj``eðc Z6
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | <
⃝ Pustetuyjcfi jc ao J`uo`eðc 6>
⃝ ⃝ RT _ujfocfi ja semuejctj sestjdo fj j`uo`eicjs>
J`uo`eðc => Pestjdo fj j`uo`eicjs poro ja `ïa`uai fj WH6 y WO60
Xjsiavejcfi sj ihtejcj>
Oliro poro ja `ïa`uai fj ao o`jajro`eðc fja pucti H sj fjhj tjcjr jc `ujcto quj pjrtjcj`j o ao horro 6 pjri fjpjcfj fj ao O`jajro eðc ohsiauto y O`jajro`eðc rjaotevo fja pucti O. [ir aitocti, sj tejcj ao semuejctj jxprjseðc>
⃝ ⃝ ⃝ ⃝
J`uo`eðc <> O`jajro`eðc fja pucti H
Octjs loy quj `icsefjror oamucos icfe`eicjs>
⃝ (⃝ ⃝ ) ⃝
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | 5
Xjoaezocfi ais desdis posis quj sj rjoaezoric poro ao vjai`efof>
⃝ ⃝
_ujfocfi ja semuejctj sestjdo fj j`uo`eicjs>
Xjsiavejcfi sj ihtejcj>
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | ?;
:. Fjsorriaai pir djfei fj Dotaoh>
Ja semuejctj `ðfemi rjsujavj y mroge`o aos pise`eicjs, vjai`efof y o`jajro`eicjs fjadj`ocesdi fofi>
`aisj oaa `ajor2girdot slirt% 6 femetis fj`edoajs`a`2%Vrohoni Bljvec Aezoci %Fotis fj jctrofo syds x y w z% voreohajs sedhðae`os poro `oa`uai fj aos vjai`efofjs y o`jajro`eicjs fesp('O `ictecuo`eic fjhjro ecmrjsor ais fotis fj jctrjfo')I8O4ecput('Ecmrjsj ao fedjcseic jc `d fja hrozi I8OR8:`d-:;`dT4 ')2% fedjcseðc fja hrozi
prec`epoa(edpuasir)
OH4ecput('Ecmrjsj ao festoc`eo fja pucti O oa pucti HR8:`d-:;`dT4 ')22%fedjcseðc fja pucti O aorodpo I8x4;2% pucti fj rjgjrjc`eo I8y4;2% pucti fj rjgjrjc`eo idjmo8(0)4ecput('Ecmrjsj ao vjai`efof ocmuaor fja hrozi I8O Rrof/sT 4 ')22%Wjai`efof fj meri oago8(0)4ecput('Ecmrjsj ao o`jajro`eic ocmuaor fja hrozi I8O Rrof/sS8T 4 ')2% O`jajro`eic fj meri
posi4pe/72% posi poro aos seduao`eicjstljto84ecput('Ecmrjsj ja ïcmuai tljto8 jc mrofis (8=;»-07;») 4 ')2tljto64ecput('Ecmrjsj ja ïcmuai tljto8 jc mrofis (?»-<5») 4 ')2tjto84tljto8*pe/?<;2% Ïcmuai prec`epoa fja hrozi edpuasir tjto64tljto6*pe/?<;2% Ïcmuai fj ao rodpo I6y4I8O*sec(tjto8)-OH*`is(tjto6)-RI8O*`is(tjto8)+OH*sec(tjto6)T*toc(tjto6)2%Festoc`eo y fj ao rodpo
I6x4;2%Festo`eo x fj ao rodpo N4?2O@4(ohs(I8O*sec(tjto8))+?.?*I8O)/`is(tjto6)2% Aicmetuf fja pucti H oa gecoa fja hroziedpuazofi [gx4I6x+0*I8O*`is(tjto6)2% pucti gecoa fj ao rodpo [gy4I6y+0*I8O*sec(tjto6)2% pucti gecoa fj ao rodpo [ix4I6x-0*I8O*`is(tjto6)2% pucti ece`eoa fj ao rodpo [iy4I6y-0*I8O*sec(tjto6)2% pucti ece`eoa fj ao rodpo fh`4O@+OH2% Aicmetuf titoa fja hrozi edpuasofi %Mrïge`or pise`eðc gir tjt84tjto8>posi>tjto8+6*pe2Ox4I8O*`is(tjt8)2%@iirfjco x fja pucti O Oy4I8O*sec(tjt8)2%@iirfjco y fja pucti O
hx4I8O*`is(tjt8)-I8O*`is(tjto6+pe/8)2 % Dïxedo `iirfjco x fja pucti H
hy4I8O*sec(tjt8)-I8O*sec(tjto6+pe/8)2% Dïxedo `iirfjco y fja pucti H r8O(N,>)4ROx Oy ;T2% Wj`tir pise`eic fja pucti O u?4R`is(tjto6),sec(tjto6),;T2% Wj`tir ferj``eic u? u64R`is(tjto6+pe/8),sec(tjto6+pe/8),;T2% Wj`tir ferj``eic u6 R[x,[yT 4 aecaec( Ox,Oy,hx,hy,[ix,[iy,[gx,[gy)2%guc`eic poro jc`ictro @([x,[y) ficfj A?(Ox,Oy,hx,hy) y A8 ([ix,[iy,[gx,[gy) foh4(Ox-[x)/`is(tjto6+pe/8)2% Festoc`eo fja pucti O oa pucti H fo`4fh`-foh2% Festoc`eo fja pucti O oa pucti @ @x4Ox+fo`*`is(tjto6+pe/8)2%@iirfjco x fja pucti @
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | ??
@y4Oy+fo`*sec(tjto6+pe/8)2%@iirfjco x fja pucti @ %Wjai`efofjs ocma(N)4tjt82 % OcmuaiWo8(N,>)4;.;?*`riss(idjmo8,r8O(N,>))2% Wj`tir Wjai`efof fja pucti O
WO8(N)4cird(Wo8(N,>))2% Xopefjz fja pucti O vo6(N,>)4x*u?2% Wj`tir Wjai`efof WH6 jc sedhiae`ivo6Y0(N,>)4y*u62% Wj`tir Wjai`efof WO6Y0 jc sedhiae`ijqW6(N,>)4vo6Y0(N,>)+Wo8(N,>)-vo6(N,>)2% Pestjdos fj j`uo`eicjs poro ja `oa`uai fj aos vjai`efofjsRx?,y?T4siavj(jqW6(N,?),jqW6(N,8))2% Xjsiau`eic fja sestjdos fj j`uo`eicjsWO6(N)4jvoa(x?)2% [osocfi ao voreohaj fj `oro`tjr o rjoa WO6Y0(N)4jvoa(y?)2% [osocfi ao voreohaj fj `oro`tjr o rjoa WO6v(N,>)4WO6(N)*u?2% Wj`tir Wjai`efof WH6 WO6Y0v(N,>)4WO6Y0(N)*u62% Wj`tir Wjai`efof WO6Y0 %O`jajro`eicjs Oo8(N,>)4;.;?*R`riss(oago8,r8O(N,>))-Ridjmo8(0)S8*r8O(N,>)TT2% Wj`tir O`jajro`eic fja pucti O OO8(N)4cird(Oo8(N,>))2% O`jajro`eic fja pucti O Oo6(N,>)4w*u?2% Wj`tir O`jajro`eic OH6 jc sedhiae`iOo6Y0(N,>)4z*u62% Wj`tir O`jajro`eic OO6Y0 jc sedhiae`i jquO6(N,>)4Oo8(N,>)+Oo6Y0(N,>)-Oo6(N,>)2% Pestjdos fj j`uo`eicjs poro ja `oa`uai fj aos O`jajro`eicjs Rw?,z?T4siavj(jquO6(N,?),jquO6(N,8))2% Xjsiau`eic fja sestjdos fj j`uo`eicjsOO6(N)4jvoa(w?)2% [osocfi ao voreohaj fj `oro`tjr o rjoa OO6Y0(N)4jvoa(z?)2% [osocfi ao voreohaj fj `oro`tjr o rjoa OO6Y0v(N,>)4OO6Y0(N)*u62% Wj`tir O`jajro`eic OH6 OO6v(N,>)4OO6(N)*u?2% Wj`tir O`jajro`eic OO6Y0%paitji fj gemurosgemurj(?)2liaf igg
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('Mroge`i fj pise`eic fja dj`ocesdi')xaohja('Festoc`eo x R`dT')yaohja('Festoc`eo 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('Wjai`efof ohsiauto fja pucti O')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('Wjai`efof Rd/sT')mrefsuhpait(0,?,8)
pait(ocmuai,WO6Y0)tetaj('Wjai`efof rjaotevo fja pucti O `ic rjspj`ti oa pucti H')
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
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[ïmeco | ?8
xaohja('Ocmuai QtljtoY{8}R»T')yaohja('Wjai`efof Rd/sT')mrefsuhpait(0,?,0)
mref pait(ocmuai,WO6)tetaj('Wjai`efof ohsiauto fja pucti H')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('Wjai`efof Rd/sT')mrefgemurj(0)suhpait(0,?,?)
pait(ocmuai,OO8)tetaj('O`jajro`eðc ohsiauto fja pucti O')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('O`jajro`eðc Rd/sS{8}T')mrefsuhpait(0,?,8)
pait(ocmuai,OO6)tetaj('O`jajro`eðc rjaotevo fja pucti O `ic rjspj`ti oa pucti H')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('O`jajro`eðc Rd/sS{8}T')mrefsuhpait(0,?,0)mref
pait(ocmuai,OO6Y0)tetaj('O`jajro`eðc ohsiauto fja pucti H')xaohja('Ocmuai QtljtoY{8}R»T')yaohja('O`jajro`eðc Rd/sS{8}T')mrefN4N+?2
jcf
Ja semuejctj `ðfemi rjsujavj y mroge`o aos pise`eicjs fja dj`ocesdi fofi>
`aisj oaa `ajor2girdot slirt `a`2%Vrohoni Bljvec Aezoci fesp('O `ictecuo`eic fjhjro ecmrjsor ais fotis fj jctrjfo')I8O4ecput('Ecmrjsj ao fedjcseic jc `d fja hrozi I8OR8:`d-:;`dT4 ')2OH4ecput('Ecmrjsj ao festoc`eo fja pucti O oa pucti HR8:`d-:;`dT4 ')2I8x4;2I8y4;2
posi4pe/8;2tljto84ecput('Ecmrjsj ja ïcmuai tljto8 jc mrofis (8=;»-07;») 4 ')2tljto64ecput('Ecmrjsj ja ïcmuai tljto8 jc mrofis (?»-<5») 4 ')2tjto84tljto8*pe/?<;2tjto64tljto6*pe/?<;2I6y4I8O*sec(tjto8)-OH*`is(tjto6)-RI8O*`is(tjto8)+OH*sec(tjto6)T*toc(tjto6)2I6x4;2O@4(ohs(I8O*sec(tjto8))+?.8*I8O)/`is(tjto6)2
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | ?0
[gx4I6x+0*I8O*`is(tjto6)2[gy4I6y+0*I8O*sec(tjto6)2[ix4I6x-0*I8O*`is(tjto6)2[iy4I6y-0*I8O*sec(tjto6)2
posi4pe/<;2fh`4O@+OH2gir tjt84tjto8>posi>tjto8+6*pe2Ox4I8O*`is(tjt8)2Oy4I8O*sec(tjt8)2Hrx4I8O*`is(tjt8)-OH*`is(tjto6+pe/8)2Hry4I8O*sec(tjt8)-OH*sec(tjto6+pe/8)2
hx4I8O*`is(tjt8)-I8O*`is(tjto6+pe/8)2 hy4I8O*sec(tjt8)-I8O*sec(tjto6+pe/8)2R[x,[yT 4 aecaec( Ox,Oy,hx,hy,[ix,[iy,[gx,[gy)2foh4(Ox-[x)/`is(tjto6+pe/8)2fo`4fh`-foh2@x4Ox+fo`*`is(tjto6+pe/8)2@y4Oy+fo`*sec(tjto6+pe/8)2gemurj(?)2liaf igg
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('Mroge`i fj pise`eic fja dj`ocesdi')xaohja('Festoc`eo x R`dT')yaohja('Festoc`eo 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 vesuoaezor
tjxt(?.;:*@x,?.;:*@y,'@')2%?.;: poro quj sj pujfo vesuoaezormrefoxes(R-8;; 8;; -8;; 8;;T)2jcf
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | ?6
7. Mrïge`is fj rjsuatofis>
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | ?:
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | ?7
=. @ÏA@ZAI FJ GZJX^OP>
[oro `oa`uaor aos gujrzos, tirqujs prjsjctjs jc ais jsaohicodejctis sj uteaezorï ja prec`epei fj
f ' Oajdhjrt ja `uïa paoctjo ais semuejctjs oportofis>
∟
∟
VDIVIX
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | ?=
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FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
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FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
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VXOHONI FJVJIXÄO FJDÏ_ZECOP
FJPOXXIAAI U PEDZAO@EÐC FJ DJ@OCEPDIP JC DOVAOH
[ïmeco | 88
6=. hx4I8O*`is(tjt8)-I8O*`is(tjto6+pe/8)2 % Dïxedo `iirfjco x fjapucti H
6<. hy4I8O*sec(tjt8)-I8O*sec(tjto6+pe/8)2% Dïxedo `iirfjco y fjapucti H
65. r8O(N,>)4ROx Oy ;T2% Wj`tir pise`eic fja pucti O :;. u?4R`is(tjto6),sec(tjto6),;T2% Wj`tir ferj``eic u? :?. u64R`is(tjto6+pe/8),sec(tjto6+pe/8),;T2% Wj`tir ferj``eic u6 :8. R[x,[yT 4 aecaec( Ox,Oy,hx,hy,[ix,[iy,[gx,[gy)2 :0. %guc`eic poro jc`ictro @([x,[y) ficfj A?(Ox,Oy,hx,hy) y A8
([ix,[iy,[gx,[gy) :6. foh4(Ox-[x)/`is(tjto6+pe/8)2% Festoc`eo fja pucti O oa pucti
H ::. fo`4fh`-foh2% Festoc`eo fja pucti O oa pucti @ :7. @x4Ox+fo`*`is(tjto6+pe/8)2%@iirfjco x fja pucti @ :=. @y4Oy+fo`*sec(tjto6+pe/8)2%@iirfjco x fja pucti @ :<. %Wjai`efofjs
:5. ocma(N)4tjt82 % Ocmuai7;. Wo8(N,>)4;.;?*`riss(idjmo8,r8O(N,>))2% Wj`tir Wjai`efof fja
pucti O 7?. WO8(N)4cird(Wo8(N,>))2% Xopefjz fja pucti O 78. vo6(N,>)4x*u?2% Wj`tir Wjai`efof WH6 jc sedhiae`i70. vo6Y0(N,>)4y*u62% Wj`tir Wjai`efof WO6Y0 jc sedhiae`i76. jqW6(N,>)4vo6Y0(N,>)+Wo8(N,>)-vo6(N,>)2% Pestjdos fj
j`uo`eicjs poro ja `oa`uai fj aos vjai`efofjs7:. Rx?,y?T4siavj(jqW6(N,?),jqW6(N,8))2% Xjsiau`eic fja sestjdos
fj j`uo`eicjs77. WO6(N)4jvoa(x?)2% [osocfi ao voreohaj fj `oro`tjr o rjoa 7=. WO6Y0(N)4jvoa(y?)2% [osocfi ao voreohaj fj `oro`tjr o rjoa
7<. WO6v(N,>)4WO6(N)*u?2% Wj`tir Wjai`efof WH6 75. WO6Y0v(N,>)4WO6Y0(N)*u62% Wj`tir Wjai`efof WO6Y0 =;. %O`jajro`eicjs =?. Oo8(N,>)4;.;?*R`riss(oago8,r8O(N,>))-
Ridjmo8(0)S8*r8O(N,>)TT2% Wj`tir O`jajro`eic fja pucti O =8. OO8(N)4cird(Oo8(N,>))2% O`jajro`eic fja pucti O =0. Oo6(N,>)4w*u?2% Wj`tir O`jajro`eic OH6 jc sedhiae`i=6. Oo6Y0(N,>)4z*u62% Wj`tir O`jajro`eic OO6Y0 jc sedhiae`i =:. jquO6(N,>)4Oo8(N,>)+Oo6Y0(N,>)-Oo6(N,>)2 =7. % Pestjdos fj j`uo`eicjs poro ja `oa`uai fj aos O`jajro`eicjs ==. Rw?,z?T4siavj(jquO6(N,?),jquO6(N,8))2 =<. % Xjsiau`eic fja sestjdos fj j`uo`eicjs
=5. OO6(N)4jvoa(w?)2% [osocfi ao voreohaj fj `oro`tjr o rjoa <;. OO6Y0(N)4jvoa(z?)2% [osocfi ao voreohaj fj `oro`tjr o rjoa <?. OO6Y0v(N,>)4OO6Y0(N)*u62% Wj`tir O`jajro`eic OH6 <8. OO6v(N,>)4OO6(N)*u?2% Wj`tir O`jajro`eic OO6Y0<0. %paitji fj gemuros<6. %horro/haiquj6 <:. Gd6(N,>)4-OO6v(N,>)*d62 <7. G`m4-G`ormo*u?2
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[ïmeco | 80
<=. Gedp6(N,>)4-(Gd6(N,>)+G`m)2 <<. %`irrjfiro0 <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*`is(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('Mroge`i fj pise`eic fja dj`ocesdi') ??8. xaohja('Festoc`eo x R`dT') ??0. yaohja('Festoc`eo 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('Wjai`efof ohsiauto fja pucti O') ?8=. xaohja('Ocmuai QtljtoY{8}R»T') ?8<. yaohja('Wjai`efof Rd/sT') ?85. mref ?0;. suhpait(0,?,8) ?0?. oxes(Rtljto8 Ocmgecoa*(?<;/pe) -6 6T)2 ?08. pait(ocmuai,WO6Y0)
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[ïmeco | 86
?00. tetaj('Wjai`efof rjaotevo fja pucti O `ic rjspj`ti oa puctiH')
?06. xaohja('Ocmuai QtljtoY{8}R»T') ?0:. yaohja('Wjai`efof Rd/sT')
?07. mref ?0=. suhpait(0,?,0) ?0<. mref ?05. oxes(Rtljto8 Ocmgecoa*(?<;/pe) -6 6T)2 ?6;. pait(ocmuai,WO6) ?6?. tetaj('Wjai`efof ohsiauto fja pucti H') ?68. xaohja('Ocmuai QtljtoY{8}R»T') ?60. yaohja('Wjai`efof 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`jajro`eðc ohsiauto fja pucti O') ?:;. xaohja('Ocmuai QtljtoY{8}R»T') ?:?. yaohja('O`jajro`eðc Rd/sS{8}T') ?:8. mref ?:0. suhpait(0,?,8) ?:6. oxes(Rtljto8 Ocmgecoa*(?<;/pe) -?: ?:T)2 ?::. pait(ocmuai,OO6) ?:7. tetaj('O`jajro`eðc rjaotevo fja pucti O `ic rjspj`ti oa pucti
H') ?:=. xaohja('Ocmuai QtljtoY{8}R»T')
?:<.
yaohja('O`jajro`eðc 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`jajro`eðc ohsiauto fja pucti H') ?7:. xaohja('Ocmuai QtljtoY{8}R»T') ?77. yaohja('O`jajro`eðc 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) ?==.
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[ïmeco | 8:
?=<. @IC@AZPEICJP
Pj pujfj ihsjrvor quj jc aos mroge`os ci sj `udpajc aos semuejctjs jxprjseicjs>
⃝ ⃝ ⃝
⃝ ⃝ ⃝ ⃝ Jsti sj fjhj yo quj aos j`uo`eicjs octjreirjs sic j`uo`eicjs vj`tireoajs y ai quj sjmroge`o sic ja difuai (y ja sjctefi) fj `ofo vj`tir fj ao rjspj`tevo j`uo`eðc. [oro`idprihor se sj `udpaj ao j`uo`eic sj sustetuyjric ais vj`tirjs fj `ofo j`uo`eic y jc
jsj didjcti jgj`tevodjctj `udpaäo `ic ja rjsuatofi Ao seduao`eðc quj sj rjoaezi js jgj`tevo poro uc `ejrti rocmi fj fotis fj
jctrofo(festoc`eo I8O, festoc`eo OH, , , , ) yo quj jstis sj osudejric, sj pifräo ihtedezor ja foti pjri jsto setuo`eic sjrï paoctjofo jc ja semuejctj ecgirdj.
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[ïmeco | 87
OCJ\IP
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[ïmeco | 8=
Ja `ðfemi poro ectjrsj``eðc fj fis rj`tos sj prjsjcto o `ictecuo`eðc>
% [rimorodo poro `oa`uaor ja pucti fj ectjrsj``eðc 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``eðc ([x,[y) guc`teic R [x,[y T 4 aecaec( Ox,Oy,Hx,Hy,@x,@y,Fx,Fy)
% `oa`uaor se ao predjro i sjmucfo rj`to sic vjrte`oajs 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 vjrte`oa d84((Fy-@y)/(Fx-@x))2 [x4Ox2 [y4d8*([x-Fx)+Fy2
jasjeg (rj`WjrtO 44; && rj`WjrtH44?)%sjmucfo rj`to vjrte`oa d?4((Hy-Oy)/(Hx-Ox))2 [x4@x2 [y4d?*([x-Hx)+Hy2
jasj %Xj`tos jc uoaquejr pise`eðc d?4((Hy-Oy)/(Hx-Ox))2 d84((Fy-@y)/(Fx-@x))2 %Wjre`or cujvodjctj se aos rj`otos 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
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[ïmeco | 8<
Ja `ðfemi poro ectjrsj``eðc fj uco rj`to `ic uco `er`ucgjrjc`eo sj prjsjcto o `ictecuo`eðc>
% [rimorodo poro `oa`uaor ja pucti fj ectjrsj``eðc fj fis aäcjos % FOVIP FJ ECMXJPI % [uctis fj ao predjro aäcjo (Ox,Oy) y (Hx,Hy) % [uctis fja fjctri fja `er`uai (@x,@y) y Xofei X % POAEFO % Fjvujavj ais puctis fj ectjrsj``eðc ([x,[y) y (_x,_y) guc`teic R [x,[y,_x,_y T 4 aec`er( Ox,Oy,Hx,Hy,@x,@y,X)
% Wjrege`or se ao rj`to js vjrte`oa i ci eg (Hx-Ox44;) % Ao rj`to js vjrte`oa
%vjrege`or quj jxesto ectjrsj``eðc tdp4XS8-(Ox-@x)S82
eg (tdp1;) jrrir('Ci jxestj ectjrsj``eðc jctrj aäcjo y `är`uai')2 jcf [x4Ox2 _x4Ox2 [y4@y + tdpS;.:2 _y4@y - tdpS;.:2
jasj % Ao rj`to ci js vjrte`oa d4(Hy-Oy)/(Hx-Ox)2
h4Oy-d*Ox2 %vjrege`or quj jxesto ectjrsj``eðc 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``eðc jctrj aäcjo y `är`uai')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
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[ïmeco | 85
Ja `ðfemi poro ao ectjrsj``eðc fj fis `er`ucgjrjc`eos sj prjsjcto o `ictecuo`eðc>
% [rimorodo poro `oa`uaor ja pucti fj ectjrsj``eðc fj fis aäcjos % FOVIP FJ ECMXJPI % [uctis fja `jctri fja `er`uai ? (Ox,Oy) y Xofei X? % [uctis fja fjctri fja `er`uai 8 (Hx,Hy) y Xofei X8 % POAEFO % Fjvujavj ais puctis fj ectjrsj``eðc ([x,[y) y (_x,_y) guc`teic R [x,[y,_x,_y T 4 `er`er( Ox,Oy,X?,Hx,Hy,X8)
% Wjrege`or se loy ectjrsj``eðc fest 4 ((Hx-Ox)S8+(Hy-Oy)S8)S82 eg (fest3X?+X8)
jrrir('Ci jxestj ectjrsj``eðc jctrj ais `är`uais')2
jcf % oa`uaor ao ectjrsj``eðc
[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 -
8/13/2019 Trabajo Tma Khevin Lizano_pdf
http://slidepdf.com/reader/full/trabajo-tma-khevin-lizanopdf 30/30
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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
jcf