Topografia 8 Método de Intersección Múltiple

7/31/2019 Topografia 8 Mtodo de Interseccin Mltiple

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Pbhj ? Aepbt}bmmae Hcpa~cb

H% Ijtkj} :

Pbhj ?;Hpf`f `b Aepbt}bmmae Hcpa~cb


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H% Ijtkj} 4

E@AMB

:% @B]MTA^MAE LBEBTJC%

:%: Hpf`f lbebtjc `b fd}btyjmae%

:%4 Mcj}aiamjmae `b cj} aepbt}bmmafeb} hcpa~cb}%

% ]ble ~repf} `b b}pjmae%

( @atbmpj%( Aeybt}j%( Haxpj%

% ]ble pa~f `b fd}btyjmae

% Jelrcjt%% Jelrcjt h} à}pjemaj}%

:%= Fdpbemae `b cj }fcrmae iaejc mfhf hbàj jtaphpamj f ~fe`btj`j `b cj}aepbt}bmmafeb} }ah~cb} ~f}adcb}%

:%0 Hbpf`fcflj lbebtjc `b mcmrcf ~ft heahf} mrj`tj`f}%

J! Cj} hbà`j} pf~fltiamj} q bc hf`bcf hjpbhpamf%

D! Aeptf`rmmaej cf} jkr}pb} `b cj} hbà`j} pf~fltiamj} ~ft hhmm%M! Hf`bcf} `b tbcjmafeb} `b fd}btyjmae be cj} hbà`j} pf~fltiamj}%

@! Hpf`f `b jkr}pb hhmm%B! Hjpta{ `b ~b}f}%

I! ^tbma}ae `b cj} mfft`bej`j} jkr}pj`j}%

4% CJ AEPBT]BMMAE JELRCJT HRCPA^CB%

4%: Aeptf`rmmae%

4%4 Bx~tb}ae `b cj tbcjmae `b fd}btyjmae ~ft àtbmmae jelrcjt fd}btyj`j%

4%= Tb}fcrmae `bc hpf`f `b aepbt}bmmae àtbmpj hcpa~cb ~ft heahf}mrj`tj`f}%

% Mfft`bej`j} j~tfxahj`j} `bc ~repf j `bpbthaejt%% ^cjepbjhabepf `b cj} tbcjmafeb} `b fd}btyjmae%


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H% Ijtkj} =

% Tb}fcrmae%

4%0 Tb}fcrmae `bc hpf`f `b aepbt}bmmae aeybt}j hcpa~cb ~ft heahf}

mrj`tj`f} %% Mfft`bej`j} j~tfxahj`j} `bc ~repf j `bpbthaejt%

% ^cjepbjhabepf `b cj} tbcjmafeb} `b fd}btyjmae%

% Tb}fcrmae%

4%2 Tb}fcrmae `bc hpf`f `b aepbt}bmmae haxpj hcpa~cb ~ft heahf}mrj`tj`f} %

% Mfft`bej`j} j~tfxahj`j} `bc ~repf j `bpbthaejt%


% Tb}fcrmae%

4%9 Tb}fcrmae `b cj aepbt}bmmae jelrcjt hcpa~cb mfe h} `b re ~repf j`bpbthaejt# ~ft heahf} mrj`tj`f}%

% Mfft`bej`j} j~tfxahj`j} `b cf} ~repf} j `bpbthaejt%


% Tb}fcrmae%

=% CJ AEPBT]BMMAE HCPA^CB MFE JELRCF] Q MFE @A]PJEMAJ]%

=%: Aeptf`rmmae%

=%4 Bx~tb}ae `b cj tbcjmae `b fd}btyjmae ~ft àtbmmae jelrcjt fd}btyj`j%

=%= Bx~tb}ae `b cj tbcjmae `b fd}btyjmae ~ft à}pjemaj fd}btyj`j%

=%0 Hbpf`fcflj lbebtjc `b mcmrcf ~ft heahf} mrj`tj`f}%


% ^cjepbjhabepf `b cj} tbcjmafeb} `b fd}btyjmae%( Fd}btyjmafeb} jelrcjtb}%( Fd}btyjmafeb} `b à}pjemaj%

% J}alejmae `b ~b}f}%

% Tb}fcrmae `bc }a}pbhj `b bmrjmafeb} ~ft heahf} mrj`tj`f}%( Tbcjmafeb} efthjcb}%

( ]fcrmae jc }a}pbhj `b bmrjmafeb} `b fd}btyjmae%% Mfft`bej`j} jkr}pj`j} `bc ~repf j `bpbthaejt%


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H% Ijtkj} 0

% ^tbma}ae `b cj} mfft`bej`j} jkr}pj`j}%

0% TB]FCRMAE @B CJ JCPAHBPTJ%

0%: Aeptf`rmmae%

0%4 Bx~tb}ae `b cj tbcjmae `b fd}btyjmae ~ft `b}eaybc%

0%= Hbpf`fcflj lbebtjc `b mcmrcf ~ft heahf} mrj`tj`f}%

% Jcpapr`b} j~tfxahj`j} `b cf} ~repf j `bpbthaejt%


% J}alejmae `b ~b}f}%

% Tb}fcrmae `bc }a}pbhj `b bmrjmafeb} ~ft heahf} mrj`tj`f}%( Tbcjmafeb} efthjcb}%( ]fcrmae jc }a}pbhj `b bmrjmafeb} `b fd}btyjmae%

% Jcpapr` jkr}pj`j `b cf} ~repf} j `bpbthaejt%

% ^tbma}ae `b cj} jcpapr`b} jkr}pj`j}%

2% DADCAFLTJIJ MFH^CBHBEPJTAJ%


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H% Ijtkj} 2

:% @B]MTA^MAE LBEBTJC

:%: Hpf`f lbebtjc `b fd}btyjmae%

:%4 Mcj}aiamjmae `b cj} aepbt}bmmafeb} hcpa~cb}%

% ]ble ~repf} b b}pjmae%

( @atbmpj%( Aeybt}j%( Haxpj%

% ]ble pa~f `b fd}btyjmae

% Jelrcjt%% Jelrcjt h} à}pjemaj}%

:%=

Fdpbemae b cj }fcrmae iaejc mfhf hbàj jtaphpamj f ~fe`btj`j b cj} aepbt}bmmafeb}}ah~cb} ~f}adcb}%

:%0 Hbpf`fcflj lbebtjc `b mcmrcf ~ft heahf} mrj`tj`f}%

J! Cj} hbà`j} pf~fltiamj} q bc hf`bcf hjpbhpamf%

D! Aeptf`rmmaej cf} jkr}pb} b cj} hbà`j} pf~fltiamj} ~ft hhmm%M! Hf`bcf} b tbcjmafeb} b fd}btyjmae be cj} hbà`j} pf~fltiamj}%

B! Hpf`f b jkr}pb hhmm%B! Hjpta{ b ~b}f}%

L! ^tbma}ae b cj} mfft`bej`j} jkr}pj`j}%

:%: HPF@F LBEBTJC @B FD]BTYJMAE

Bc hpf`f `b fd}btyjmae be cj aepbt}bmmae hcpa~cb b} bc ha}hf zrb bc zrbb}pràjhf} be cj aepbt}bmmae }ah~cb; hpf`f `b yrbcpj} `b ofta{fepb% B}pbhpf`f pbebhf} zrb tbcjmafejtcf }abh~tb mfe cj fd}btyjmae jelrcjt hcpa~cb# qjzrb eremj }b tbjca{j rej fd}btyjmae ~jtj tb}fcybt re hpf`f }ah~cb% Effcya`bhf} zrb pf`j} cj} fd}btyjmafeb} `b mjh~f oje `b }bt }abh~tbtb`re`jepb}%

Tbmft`bhf} zrb bc hpf`f `b yrbcpj} `b ofta{fepb mfe}a}pb be b}pjmafejt bcae}ptrhbepf be bc ytpamb# ~ft bkbh~cf be J q be ~f}amae M%@% ya}jt j pf`j} cj}àtbmmafeb}# yfcybt j hatjt j cj ya}rjc `b ftalbe# q mfh~tfdjt }a }r cbmprtj#ccjhj`j `b mabttb# b} cj ha}hj zrb jc mfhabe{f# cf zrb ~tfdjtj zrb bcae}ptrhbepf ef oj }rita`f eaele pa~f `b hfyahabepf `rtjepb cj fd}btyjmae%

]b ~tfmb`b j }aprjt bc bzra~f be ~f}amae M%A% q }b tb~apbe cj} fd}btyjmafeb}latje`f be }bepa`f mfeptjtaf jc jepbtaft q mfh~tfdje`f alrjchbepb bc mabttb% ]a b}mfttbmpf }b àmb zrb }b oj fd}btyj`f rej }btab f yrbcpj `b ofta{fepb be mj}fmfeptjtaf }b oj `b tb~bpat pf`f `b}`b bc ~taema~af%


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H% Ijtkj} 9

Ef `bdbhf} fcya`jt pjh~fmf bc hpf`f `b ~jtb} }fdtb rej tbibtbemaj% Mfe}a}pbbe bcblat rej àtbmmae `b tbibtbemaj T# zrb b}pb dabe `biaea`j# q zrb ~rb`b }bt fef jclrej `b cj} àtbmmafeb} j fd}btyjt% ]b ojmbe cj} cbmprtj} mfttb}~feàbepb}}fdtb T q D mfhf }a }b ptjpj}b `b rej yrbcpj `b ofta{fepb mfh~rb}pj ej`j h}zrb ~ft àmof~jt`b àtbmmafeb}% J mfepaerjmae }b ya}je `b alrjc hf`f j T q M#zrb mfe}paprate bc }blre`f ~jt# q j}# }rmb}ayjhbepb oj}pj ojdbt mfhdaej`f mfeT pf`j} cj} àtbmmafeb}% Mfhf cj fd}btyjmae `b mj`j ~jt }b ojmb be hrq ~fmfpabh~f }b byapje ~f}adcb} hfyahabepf} `bc bzra~f%

]a bc erhbtf `b àtbmmafeb} b} ltje`b# }b pjt`j dj}pjepb be cj fd}btyjmae `b cj}àtbmmafeb} ~ft ~jtb} j rej tbibtbemaj# ~ft cf zrb ~jtj jdtbyajt }b ~rb`be rpaca{jtbc hpf`f haxpf zrb mfe}a}pb be àyaàt cj} àtbmmafeb} pfpjcb} be yjtaj} `b pjchjebtj zrb }b ya}b j cj tbibtbemaj q j rej} àtbmmafeb} q crblf }b yrbcpj j ya}jt jcj tbibtbemaj q jc tb}pf `b cj} àtbmmafeb}% ^jtj tbireàt cj} yrbcpj} `b ofta{fepb berej }fcj }b à}~febe `b à}paepj} cbmprtj} j cj tbibtbemaj T be mj`j rej `b bccj}%

:%4 MCJ]AIAMJMAE @B CJ] AEPBT]BMMAFEB] HCPA^CB]%

% ]ble ~repf} b b}pjmae%( @atbmpj%( Aeybt}j%( Haxpj%

% ]ble pa~f `b fd}btyjmae% Jelrcjt%% Jelrcjt h} à}pjemaj}%

J! ]BLE BC ^REPF @B B]PJMAE

Cj} aepbt}bmmafeb} ~f`bhf} mcj}aiamjtcj} jpbeàbe`f j `f} mtapbtaf}% Bc~tahbtf `b bccf} à}paelrb }a bc ~repf `b b}pjmae# `b}`b bc zrb }b fdpabebecj} fd}btyjmafeb} b} f ef mfefma`f `b jepbhjef% Bc jeca}a} `b b}pj


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H% Ijtkj} # QJ> # OJ>

^jthbptf} j~tfxahj`f} zrb }b aeptf`rmbe be bc }blre`f mcmrcf# be cj~tahbtj apbtjmae;

_J: # QJ

: # OJ:

^jthbptf} j~tfxahj`f} zrb }b aeptf`rmbe be bc pbtmbt mcmrcf# be cj}blre`j apbtjmae;

_J4 # QJ4 # OJ4

Q j} }rmb}ayjhbepb%

Bc hpf`f `b hhmm b} bc zrb }% ]b ptjpj `b rej obttjhabepj `b mcmrcf zrbtb}rbcyb }a}pbhj} caebjcb} tb`re`jepb}# }a}pbhj} mfe h} bmrjmafeb} zrbaemleapj}%

Tbmr~btje`f erb}ptj rdamjmae be cj} hbpf`fcflj} pf~fltiamj}# ef} ~cjepbjhf}zrb ~jtj tb}fcybt cj} aepbt}bmmafeb} hcpa~cb} yjhf} j tbmrttat j re hpf`f be bczrb;

( j ~jtpat `b cf} `jpf} `b mjh~f#( mtbjhf} re }a}pbhj `b bmrjmafeb}#( zrb tb}fcybtbhf} ~ft jkr}pb hhmm#


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H% Ijtkj} :>

( ~jtj fdpbebt rej eamj }fcrmae%

D! AEPTF@RMMAFE J CF] JKR]PB] @B CJ] HB@A@J] PF^FLTJIAMJ] ^FT

HHMM%

Cf} jkr}pb} heahf mrj`tpamf} be Pf~fltjij b}pe hrq dabe ptjpj`f}# be bcmj~prcf :0 ]rtybq Hbj}rtbhbep J`kr}phbep} dq Cbj}p ]zrjtb} `b Tjrc T% \fci#`bc cadtf Pob ]rtybqael Oje`dffg `b Tr}}bcc Dtaegbt q Tjq Haeeamg# zrb }b ojaeàmj`f mfhf tbibtbemaj be cj dadcafltjij mfh~cbhbepjtaj% Cf} mfepbea`f} zrb}alrbe j mfepaerjmae }fe cj ptj`rmmae jc b}~jfc `b b}pb mj~prcf%

Be b}pb cadtf `b tbibtbemaj }b `b}mtadbe cj} mfeàmafeb} ire`jhbepjcb} zrbmfeifthje bc jkr}pb ~ft heahf} mrj`tj`f}# q }b fitbmbe bkbh~cf} bcbhbepjcb}7}b bx~camje cf} ~tfmbàhabepf} }a}pbhpamf} zrb `bdbe }blrat}b ~jtj ifthjt qtb}fcybt cj} bmrjmafeb} be bc hpf`f `b HHMM# aemcrqbe`f cf} hpf`f}

hjptamajcb}7 iaejchbepb }b bx~camje cf} ~tfmbàhabepf} b}~bmiamf} `b jkr}pb `btb`b} `b eaybcjmae# ptacjpbtjmae# ptajelrcjmae q ~fcalfejmae# q }b bx~camjebkbh~cf} `b ~tfdcbhj}%

^jtj mfhbe{jt bc jeca}a} `b cf} jkr}pb} be cj} hbà`j} be bc pbhj zrb ef} fmr~j#`bdbhf} tbmft`jt zrb be Pf~fltjij# }alrabe`f cj pbthaefcflj mc}amj# }b `biaebe`f} mcj}b} `b bttftb}; }a}pbhpamf} q jmma`bepjcb}% Cf} bttftb} }a}pbhpamf} }alrbecbqb} i}amj}# q }a }b ha`be cj} mjr}j} zrb cf ~tf`rmbe# }b ~rb`be mrjepaiamjt qj~camjt cj} mfttbmmafeb} zrb cf} bcahaeje% Cf} bttftb} jmma`bepjcb} bxa}pbe }abh~tbbe cf} yjcftb} fd}btyj`f}%

Bx~btahbepjchbepb }b oj `bhf}ptj`f zrb cf} bttftb} jmma`bepjcb} be Pf~fltjij}alrbe cbqb} hjpbhpamj} `b ~tfdjdaca`j`# q zrb rej }btab `b hbà`j} mfepabebebttftb} jmma`bepjcb} zrb tb}~fe`be j cj à}ptadrmae efthjc% Tb}~bmpf j cj ha}hj#

}b j~tbmaj zrb cf} bttftb} jmma`bepjcb} pabebe cj} }alrabepb} mjtjmpbt}pamj};:%Cf} bttftb} ~bzrbf} }b `je mfe h} itbmrbemaj zrb cf} ltje`b}%4%Cf} bttftb} ~f}apayf} q ebljpayf} `bc ha}hf yjcft# }b `je mfe alrjc

itbmrbemaj%

=%Cf} bttftb} ltje`b} tjtj yb{ j~jtbmbe%@bdbhf} pbebt be mrbepj zrb cj} bzrayfmjmafeb} ef }fe bttftb} q ef ~rb`be }btmfe}a`btj`j} mfhf pjcb}% @bdb byapjt}b mfhbpbt bzrayfmjmafeb} pbeabe`f mra`j`fq pfhje`f cj ~tbmjrmae `b mfeptj}pjt pf`f} cf} yjcftb} hbà`f}%

Be cf} ptjdjkf} pf~fltiamf}# ptj} bcahaejt bzrayfmjmafeb} q ojmbt cj} mfttbmmafeb}`b cf} bttftb} }a}pbhpamf}# }b ojmb bya`bepb cj ~tb}bemaj `b cf} bttftb}jmma`bepjcb}# zrb }fe cf} zrb ef} }atybe `b tbibtbemaj ~jtj mrjepaiamjt cj}aembtpa`rhdtb} iaejcb}%

^ft bkbh~cf# be eaybcjmae }b mabttj be ~repf} `b jcpapr` mfefma`j% Cf} bttftb} `bmabttb `b cj cebj ~rb`be mjcmrcjt}b# fitbmabe`f re aeàmj`ft `b cf} bttftb}jmma`bepjcb} tbhjebepb}% @b alrjc hf`f# be cj hbà`j `b elrcf}# cj }rhj `b cf}elrcf} hbà`f} be rej yrbcpj `b ofta{fepb `bdb }bt `b =9># q be Pf~fltjij~cjej cj }rhj `b cf} elrcf} `b rej ~fcalfejc `bdb }bt hcpa~cf `b 4>>l %

Cj} à}mtb~jemaj} bxa}pbepb} mfe tb}~bmpf j b}j} mfeàmafeb} aeàmje cj ~tb}bemaj`b bttftb} jmma`bepjcb} be cf} yjcftb} hbà`f}%

Be Pf~fltjij# cf} jkr}pb} }b j~camje ~jtj `bpbthaejt cf} yjcftb} zrb à}ptadrqbe

cf} bttftb} `b mabttb q zrb ~bthapbe zrb }b mrh~cje cj} mfeàmafeb} lbfhptamj}hjpbhpamj}% ]b r}je àybt}f} ~tfmbàhabepf}% Bc ~tahbtf `b bccf} ~f`tj }bt`bpbthaejt cj} mfttbmmafeb} }ah~cb}# `b alrjc yjcft ~jtj pf`f} cf} yjcftb}


11/60


H% Ijtkj} ::

hbà`f}# zrb }b fdpbe`tj àyaàbe`f bc bttft `b mabttb pfpjc ~ft bc ehbtf `bhbà`j}% Fptj ifthj mfe}a}patj be aeptf`rmat mfttbmmafeb} `b à}paepf yjcft }blebc ftalbe `bc bttft `bpbmpj`f%

Be Pf~fltjij cf} bttftb} tb}~fe`be j cj à}ptadrmae efthjc q b}pe mfeifthb}

mfe cj} cbqb} hjpbhpamj} `b ~tfdjdaca`j`% ^jtj j~camjt ~tfmbàhabepf} `b jkr}pbh} talrtf}f} zrb cf} hbemafej`f}# ojq zrb pbebt be mrbepj b}pj pbftj `bà}ptadrmae% Bc hpf`f `b jkr}pb ~ft heahf} mrj`tj`f} }b j~fqj be cj} cbqb} `b~tfdjdaca`j`%

M! HF@BCF] @B TBCJMAFEB] @B FD]BTYJMAE BE CJ] HB@A@J]PF^FLTIAMJ]%

Mfhf obhf} aeàmj`f jepbtafthbepb# be pf~fltjij pbebhf} ptb} pa~f} `bfd}btyjmafeb};

( àtbmmafeb} jelrcjtb}%( à}pjemaj}%( `b}eaybcb}%

Pbe`tbhf} ptb} hf`bcf} `b bmrjmafeb}% J mj`j pa~f `b fd}btyjmae `b mjh~f cbmfttb}~fe`b re hf`bcf `b bmrjmae% @bdbt }bt ~f}adcb ojdcjt `b;

( Tbcjmae `b fd}btyjmae ~ft àtbmmae jelrcjt%( Tbcjmae `b fd}btyjmae `b à}pjemaj}%( Tbcjmae `b fd}btyjmae `b `b}eaybc%

Q pjc mfhf obhf} ~cjepbj`f# ~jtj mj`j `jpf `b mjh~f }b mfe}ptrat rej eamj

bmrjmae%

m%:! B_^TB]AE @B CJ TBCJMAE @B FD]BTYJMAE ^FT @ATBMMAEJELRCJT FD]BTYJ@J%

]b ptjpj `b fdpbebt bmrjmafeb} j ~jtpat `b cf} `jpf} `b mjh~f% ^jtj cj}fd}btyjmafeb} `b àtbmmae /hbà`j} jelrcjtb} jmahrpjcb}! fdpbebhf} bchf`bcf `b bmrjmae j ~jtpat `b cj bx~tb}ae `bc jmahrp%

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12/60


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13/60


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16/60


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H% Ijtkj} 42

Bc pb}p `b Djjt`j b} rej pmeamj zrb mfhdaej cj `bpbmmae `b tb}a`rf}jefthjchbepb ltje`b} djkf re mabtpf mtapbtaf b}pj`}pamf# cj cfmjca{jmae `bc bttftltf}btf q }r `bpbthaejmae%

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26/60


H% Ijtkj} 49

4% CJ AEPBT]BMMAE JELRCJT HRCPA^CB%

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27/60


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28/60


H% Ijtkj} 4?

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H% Ijtkj} 41

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36/60


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Topografia 8 Método de Intersección Múltiple