metod odredjivanja prostornog polozaja tacaka predavanje4

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    4.4.

    . , !."#..

    $##%& #'# 1

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    1. ($

    (2)

    2. $

    (1)

    3. $

    (3)

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    4.1.4.1. ($($ --

    ( , , .),

    ,

    ( ),

    ( ),

    (, , , ! .).

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    4.1. ($" #

    )&!* +, !- !"&. %/:$ ! $ # ,

    # % % & !.

    #' %-&%, !" %/# '"0 ,%: ( C D),

    .

    #' '%#-!0 !" %/# '"0 ,%:,

    ,

    ,

    ,,

    .

    ,+' / &%,!+-# !" %/# '"0 ,%: , .

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    4.1.4.1. ($($ -- %,!+-%,!+-%/%/!"!"

    '##'## ((,#!#"#,#!#"#%%11))

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    4.1.4.1. ($($ -- !"&!"&'#'#

    !"& '# -# '#2#: ,! $ , % # ! %# , # .

    #' *#' &' ( ,1997) +30-# :%, %.

    * !"& '# #! : % 1., % 2. .

    &%-# !"& '# #! :, .

    % I. , II, III IV.

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    4.1.4.1. ($($

    --!"& '#, # ##& *!

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    4.1.4.1. ($($ -- !"!"'##'##

    ' & $ % 1:5000 1:10000, %:

    % ,

    $ &,

    & & ! 0.8 mm, $ % & ! 0.5 mm,

    ) ! &! 0.5 mm) ! ( ! & ! 0.2 mm) ,

    , ,

    ( & ! 0.2 mm).

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    4.1.4.1. ($($ -- &%#&%#!"&.!"&.*!**!*

    ()

    .

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    4.1.4.1. ($($

    -- /02/0200!"&'!"&'*!0*!0 --!"&!"&*!*!0'#%0%0'#%0%+'#30+'#30*#*#%#%#%/#%/#

    :(:Xi,Yi, i=A,B,C,D

    :) -i% - dij

    (:(# :Xj,Yj,=1,2,...

    B

    1

    2 C1

    2

    A

    B

    C

    D

    p

    zdB1

    d12

    d2C

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    4.1.4.1. ($($ -- /02/0200!"&'!"&'*!0*!0 --

    !"&!"&*!*!0'#%0%0'#%0%+'#30+'#30*#*#%#%#%/#%/#

    C

    B1

    2

    C1

    2

    A

    B D

    p

    zdB1

    d12

    d2C

    f = (CD -z)f *

    z

    CD + 4viCD=2C+2180

    CC

    2C + 3vi2C =

    12+2180

    22

    12 + 2vi12 =B1+1180

    11

    B1=(B1 + vi)B1=P+B180

    PBB

    i,defii%.

    vi = f/n n = 4

    - , = sn

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    (), ( # ).

    % ! # # # # .

    ! $ , :

    # . ## 30, % 1:300 1:400.

    & %. # (!) % $ # # .

    % . %, , % .

    4.1.4.1. ($($ -- +*2#+*2#!"&"!"&"*!*!

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    4.1.4.1.

    ($($ --TO19TO19))))

    K =const.fd / d* 1/Kvyi= (fy/ d) x divXi= (fX/ d) x di

    fd =fx2 + fy

    2fy=(YC YB)-dYfx= (XC XB)- dX

    (XC)

    XC= X2 + dX2C

    d2C cos+ vx2= dX

    2C

    X2= X1 + dX12

    d12 cos+vx12= dX12

    X1 = XB + dXB1

    dB1 cos + vxB1= dXB1

    XB

    XX

    YC - YB

    dY

    d2C sin

    d12 sin

    dB1 sin

    dYdY

    XC - XB

    dX

    d2C cos

    d12 cos

    dB1 cos

    dXdX

    d

    d2C

    d12

    dB1

    ddijij

    CD + 4vi=z

    2C + 3vi

    12 + 2vi

    B1 + vi

    i,defi,def

    f = (CD -z)=T-If *

    (YC)z

    YC= Y2 +dY2CCD=2C+2180CC

    d2C sin + vy2C

    = dY2C

    2C =12+2180

    Y2= Y1 +dY1222

    d12 sin + vy12= dY12

    12 =B1+1180

    Y1= YB+ dYB11

    1

    dB1 sin + vyB1= dYB1

    B1=P+B180

    YBPBB

    YYiiii%%

    C

    B1

    2 C1

    2

    A

    B D

    p

    zdB1

    d12d2C

    +

    +

    =

    +

    +

    =

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    4.1.4.1. ($($ -- --

    5= 236 30 30

    4= 120 45 00485.123C

    3= 258 11 00612.1523

    z

    =106 17 302= 63 20 00359.6112

    p

    = 43 31 301= 104 00 30305.41A1

    ugaoduzinastrana

    106 17 30z

    =

    106 17 30-60106 18 30CD

    286 18 30DC

    236 30 30

    49 47 12-4849 48 003C

    229 48 00C3

    120 45 00

    109 02 24-36109 03 0023

    289 03 0032

    258 11 00

    30 51 36-2430 52 0012

    210 52 0021

    63 20 00

    147 31 48-12147 32 00A1

    104 00 30

    43 31 30p

    =

    def.dir.ugaopopravkapr.dir.ugaostrana

    p1

    2

    34

    5A

    1

    2

    3C

    B

    z D

    Date take:A,B,C,D

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    4.1.4.1.

    ($($ !

    fd/ d = 1/5182~1/5100

    fd = 0.34

    fy = 0.298fx = 0.168

    1297.839164.71treba

    1297.541164.542ima

    (5619.243)(6405.272)d = 1762.29

    5619.2436405.272C

    + 370.541313.258370.46313.21149 47 12485.12

    5248.7026092.0143

    + 578.764- 199.642578.66-199.7109 02 24612.15

    4669.9386291.6562

    + 184.520+ 308.731184.459308.69730 51 36359.61

    4485.4185982.9251

    + 164.014- 257.637163.962-257.666147 31 48305.41

    4321.4046240.562A

    YXdydxdir.ugaoduzinastanica

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    4.1.4.1. ($($ --

    =20, 45, 60

    n = n + b; c=0.05 ili 0.03

    n - ,- #!'. *#+. 0"!* 0 *!0, b # #& *!

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    4.1.4.1. ($($ -- +*4#+*4#0"!*0"!*&%02#&%02#

    #!%*#!%*#+&%#+&%!"&.!"&.*!**!*

    tanM:1 =

    nE =

    10101:20000

    20211:10000

    20281:7500

    30411:5000

    11 091:3000

    13 261:1000

    "

    " #"

    - E

    #"

    ' 1:5000

    n = 9 ,

    =309 = 90

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    4.1.4.1. ($($ -- %%.+%!#.+%!#%/&%%/&%

    *#*#!"!"'##'##

    (,1997)

    1:10 0001:20 000

    2. 1.

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    4.1.4.1. ($($ -- #5-##5-#'##2'##200

    !"&'!"&''#''#'

    < 20 km

    < 4 km ( 2.5 km)

    1:3 ( 1:5

    ) 50 m -500 m ( 50 m -250 m

    50-500 m )

    (1:2500, 1:5000, 1:10 000, ! -",

    -", 1. 0.6 mm, 2. 0.2 mm) (1:5000 1:10 000, , ,

    #$, $, " %, " ,

    , ,

    " 100 cm x 70 cm 70 cm x 50 cm)

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    4.1.4.1. ($($ --

    1 2

    2 ,

    ! ,

    :

    -" " " " #"

    --" # ,

    - #

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    4.1.4.1. ($($ -- $#6#$#6#'##2'##20"!*0"!*

    &462#&462#"#6#"#6#

    e

    1 2

    -",

    -"

    stanica

    signalsignal

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    4.1.4.1. ($($ -- !!

    # $ $

    " !

    .

    # $

    $ $ .

    %

    ! $ $

    $ .

    &

    $ $. $

    $ "$ .

    $

    $ ,

    $

    $.

    '

    % .

    ($

    # $

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    4.1.4.1. ($($

    -- "!"!!!

    s

    a

    n-1

    n

    n

    P2

    T1

    T2

    t

    )(180

    sins

    bsin

    )xx()yy(s

    )sin(

    sin

    ab

    )sin(

    sinad

    )(180

    t

    2

    2T1T

    2

    2T1T

    1

    ++++==== ++++====

    ====

    ++++====

    ++++

    ====

    ++++

    ====

    ++++====

    b

    d1

    Mereno: ,, , aDato: koordinate T1, T2Nepoznato: t

    ""!!

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    4.1.4.1. ($($

    -- "!"!!!!!--

    :

    = 68-47-58 = 48-26-44a = 76.50 m

    = 127-05-16

    :

    53c x = 59110.16 y = 37084.4025c x = 58948.42 y = 36411.43

    : t= 111-24-40

    a

    143

    25c

    53c

    144P

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    4.1.4.1. ($($ -- &%!#&%!#'#%#'#%#.+%!".+%!"

    +2+2

    ,

    + -%, , ,

    -" #.

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    4.1.4.1. ($($

    -- #3*2##3*2#!-!-#+%.#+%.%/%/##'##' -- &*0&*00#0##"#"0"!0"!

    ( )[ ]

    AC

    ACC

    A

    2

    AC

    2

    AC

    XX

    YYarctan

    )XX(YYb

    =

    +=

    )(180 +=

    B

    AA'B

    B

    AA'B

    coscXX

    sincYY

    +=

    +=

    B

    CC"B

    B

    CC"B

    cosaXXsinaYY

    +=+=

    1

    2

    3

    4

    5

    sin

    sinbc

    sin

    sinba

    =

    =

    2

    )XX(X

    2

    )YY(Y

    ''B'B

    B

    ''B'BB

    def

    def

    +=

    +=

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    4.1.4.1. ($($

    -- /02#/02#%%#+%##+%#%/#%/###'##'#'#'**&&*#*#%#%#%/#%/# ((%#%#,+#,+#))

    ( ) )cos()sin(

    sinbXcossinsinbXcosaXX ACC

    A

    CC

    B

    CCB

    +

    ++=++=+=

    b

    XXcos

    ,b

    YYsin

    CAA

    C

    CAA

    C

    =

    =

    sinb

    YYcos

    b

    XX)cos( CACAAC

    =+

    BACAC

    CACAC

    CACACB

    Xctgctg

    ctgXctgX)YY(

    ctgctg

    )YY(

    ctgctg

    ctg)XX(X

    )sin(

    sinsin)YY(

    )sin(

    cossin)XX(XX

    =+

    ++=

    =+

    +

    +=

    +

    +

    +=

    ctgctg

    ctgYctgY)XX(Y ACCAB +

    ++=

    1

    2

    3

    4

    5

    sincoscossin)sin( =

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    4.1.4.1. ($($-- /02#/02#%%#+%##+%#%/#%/###'##'

    ##50-#50-#%"#&%"#&

    0XctgYctgYX

    ctg)YY(XX

    C

    B

    CC

    B

    CBB

    B

    CCBCB

    =+

    =

    0XctgYctgYX

    ctg)YY(XX

    A

    B

    AA

    B

    ABB

    B

    AABAB

    =+

    =

    B

    C

    B

    A

    B

    AA

    B

    CCACB

    ctgctg

    ctgYctgY)XX(Y

    +=

    B

    AABA"B

    B

    CCBC'B

    ctg)YY(XX

    ctg)YY(XX

    +=

    +=

    1

    2

    3

    4

    -

    =

    )

    B

    C

    XB - XA

    XB - XC

    YB - YCYB - YA

    X

    Y

    AB

    CB

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    4.1.4.1. ($($-- #3*2##3*2#!-!-#+%.#+%.%/%/00+'#30+'#30

    *#*#%#%#%/#%/#0*-0*-

    )YY(d

    dYY

    )XX(d

    dXX

    AB

    AB

    AiAi

    AB

    AB

    AiAi

    +=

    +=

    AB

    AB

    iABAB

    AD

    A

    B

    AiDi

    AB

    ABiAB

    AB

    ADA

    BAiDi

    d

    )XX(

    d)YY(d

    d

    Y

    cosdYY

    d

    )YY(d)XX(

    d

    dX

    sindXX

    +

    +=

    =+=

    +

    ==

    AB

    ABiAB

    AB

    ADA

    BAiDi

    AB

    ABiAB

    AB

    ADA

    B

    AiDi

    d

    )XX(d)YY(

    d

    dY

    cosdYY

    d

    )YY(d)XX(

    d

    dX

    sindXX

    +=

    ==

    +

    +

    =+=

    1

    2

    3

    didAD

    B (YB,XB)

    A (YA,XA)

    YB YA

    XB XA

    Y

    X

    i

    dAi

    B (ZB,XB)

    A (YA,XA)

    i (Yi,Xi)

    YB YA

    XB XA

    Y

    X

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    4.1.4.1. ($($-- /02#/02#%%!-!-#+%##+%#%/#%/#

    &*0&*0'##2'##200

    AB

    ABB

    AXX

    YYarctan

    =

    2

    AB

    2

    ABAB )XX()YY(d +=

    APAB

    2

    BP

    2

    AP

    2

    AB

    dd2

    dddcos

    +

    =

    += BAP

    A

    P

    AAPA'P

    P

    AAPA'P

    sindXX

    sindYY

    +=

    +=

    BPAB

    2

    AP

    2

    BP

    2

    AB

    dd2

    dddcos

    +=

    = ABP

    B

    P

    BBPB"P

    PBBPB"P

    sindXX

    sindYY

    +=

    +=

    2

    XXX

    2

    YYY

    "P'PP

    "P'PP

    +=

    +=

    ABBPAP dcosdcosd =+

    sindsind BPAP =

    1

    2

    3

    4

    5

    6

    7

    8

    9

    dCP

    dBPdAP

    AB

    P

    C

    1

    2

    2-3 cm

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    4.2. $&-

    ) - . % %

    . % % . $ #

    . .

    # # #

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    4.2. $ -)*

    : #

    & (, )

    +: # # !$ #

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    4.2. $ -'-'""##!"##!"*#!'*#!'

    #

    .

    +

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    4.2. $&* #!#'#% "#'#%-&"

    *#!'

    RR11

    22

    RR22

    22

    RR11

    RR22RR33

    .%.%

    ++

    RR1212

    RR11RR22

    ""

    RR1212

    RR11

    RR22

    RR33

    RR44

    ''

    $

    7

    *##" '2#'++%%1.1.

    2.2.

    3.3.

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    4.2. $

    #! &*# %#&%#"#'#%-&" *#!'

    11258 mm+

    2225 755 mm+

    /2475 2502 mm+

    /2 7 8 km250 km1 mm+

    +

    -

    +

    $

    &

    +

    -3 m100 - 130 220 - 40+

    0.32 3 m60 8020 -3015 20+

    0.31 2 m50 6025 3610 15+

    0.51 m35 40 (65)35 405 -10+

    0.6 0.71 m25 -35 (50) m40 5 10 +

    -

    %

    )

    !

    +

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    4.2. $ -#%-#%,, 0'#-0'#-%/%/&%,!+-&%,!+-%/%/00"#'#%-&'"#'#%-&'*#!'0*#!'0

    + 1:5000 - , - & - - %

    0

    +: + - , + % , + + +("

    % +8 ( , , %, , , , , , ! , ( , , &

    4040 140140

    3030

    30305050

    1.21.21.81.8

    6060

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    4.2. $ -%##%##*&*&+!#+!#*#!'*#!'&%#&%#

    ( )

    ( )

    )obostrano...S2

    kili(,

    S

    kpili

    ojednostran...

    S2

    1p

    obostrano...S

    1p

    km1Sza,1pkm1Sza

    S

    sKKp

    3...

    s

    S

    12

    2...s

    SnnsS

    )1(...n

    ...

    ...

    s...ss

    hh...hhhH

    H

    i

    H

    i

    H

    H

    2

    h

    2

    H

    H

    2

    h

    2

    H

    2

    h

    2

    H

    hhhh

    2

    h

    2

    h

    2

    h

    2

    H

    n21

    n

    1i

    in321AB

    n21

    n21

    =

    =

    =

    ==

    ==

    =

    ==

    =

    ===

    ++=

    =++++= =

    HHABAB

    ss11

    ss22

    sszz sspp

    ssnn

    hh11

    hh22

    hhnn

    ss

    *4 %## #*4 %##

    ( )

    ( )

    ( )3...kp

    2...1

    p

    1...n

    k

    n

    Kp

    2

    H

    H

    2H

    2

    h

    H

    =

    =

    =

    =

    ++

    ++2H

    2

    H

    2

    H

    2

    H

    S06.0S40

    S04.0S25

    S06.0S32

    S04.0S20

    +=

    +=

    +=

    +=

    ++++

    !!

    +!+!

    +*4# &%02# #-

    +

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    4.2. $ -%##%##*&*&+!#+!#*#!'&"*#!'&"*!*!

    ( )

    ( )2...k

    P

    1...S

    1P

    SS

    SS...SSp

    1

    p

    p1...

    p1

    p1

    p1

    p

    1

    1P

    H...HHHH

    2

    i

    H

    H

    i

    n21

    i

    n21

    n321

    =

    =

    =+++=

    +++=

    =

    ++++=

    %

    %

    % e

    11.04[1/p]=

    3.620.275936242.02

    1.890.528018941.11

    2.100.477320951.22

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    1/piPi =1000/i2i

    2Si (km)

    P=1/P=1/ [1/p]=1/11.04=0.09

    !

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    4.2. $ -+*2#+*2#0'#%0%"0'#%0%"*#!'&"*#!'&"*!*!

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    4.2. $ -###&+&+&11

    3.019

    5.2098.228400

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    h = Z - P8itanjena letvi

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    5.209

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    4.2. $ -

    +*2#+*2#*!*!0'#%0%"0'#%0%"+'#30+'#30**%%#### 33

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    95.920R2

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    98.933R1

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    96.312N2.8RA1

    Primedba

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    4.2. $ -

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    4.2. $ -

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