Ps22Pdf

Transcription

1

2

3 ,,,,,,,,,

4 1,, ( ),,,,,, 3S( GPS RS GIS),,,,,,,,,,,, 2002,,,,,,,,,,,,,,,,,,

5 2,?,,

6 1,,,,,,,,,,, :,,,,,,,,,,!!,,,,

7

8 ( GPS)

9

10 1 1. 1,,,,, : 1.,,,,,, : 2.,,, : ; ;, 3.,,,,,, ( GIS),, 21

11 2 4.,, : 5.,,, 20 80,, 80,,,,,,,,,,,,,,,,,,,,, ( GIS),

12 3,, ( GPS) ( RS) ( GIS),, ;, ;,,, 1. 2,,,,,,,, GPS-RTK,,,, :, ; ( ),,, ( DTM),, ( GIS) : ; ;,,, 20 50, 20 70,,, :,,

13 4, 20 80,,, 20 70, ,,,,,,,,,,,, ;,, 20 90, RTK( Real Time Kinematic), ( ) GPS GPS,, GPS,,, 20 km,, RTK RTK GPS, GPS 1. 3,,,,, ;,,,,,

14 5,,, :,,,,,,,,,,,,,,

15 6 2. 1,, m, m,,, 71%, 29%, : ;,,, ( 2-1 ),,, ( ), 2-1,,,,,, ( 2-2),,,,

16 7 2-2 ( 2-3 ) ;,,,, a f : f = a - b a,, a / m f IUGG IUGG 17 WGS ( DMA) : IUGG( International Union of Geodesy and Geophysics),,, :

17 8 R = 1 ( a + a + b) 6 371km ,, ( ), ( ), ( ) ( ), 1. ( B, L, H), 2-4, P,, L,, ;, P, B,, 090 ;, 0 90 P H,,,, P P, P ( ) L B,

18 9 2. O, X, X Y, Z, O-XYZ,, P OP x y z , : : e e 2 = a2 - b 2 a N = 1 - e 2 sin 2 B, : x P y P z P = ( N + H) cosbcosl = ( N + H) cosbsinl ( 2-1) = [ N( 1 - e 2 ) + H] sinb a 2 L = arctan y x B = arctan z + Ne2 sinb x 2 + y 2 ( 2-2) H = x 2 + y 2 cosb - N ( 2-2) B, tanb 1 = x 2 z, B 2 + y B 1 N 1 sinb 1, ( 2-2), B 3. WGS-84 WGS-84 ( GPS), WGS-

19 ( 2-1), WGS-84 ; Z BIH ( CIP) ; X BIH CIP ; Y X Z, X Y Z 4.,, :, X,, ; Y,, ; ( 2-6), X Y, 2-6, -, ( 100km 2 ),,,,, x y,,,,,, 2-7, xoy, AOB, ( x O, y O ) O, A P ( A P, B P ), ( x P, y P ) :

20 11 x P = x O + A P cos- B P sin y P = y O + A P sin+ B P cos, x O y O ( 2-3), P ( x P, y P ), ( A P, B P ) : A P = ( x P - x O ) cos+ ( y P - y O ) sin B P = - ( x P - x O ) sin+ ( y P - y O ) cos ( 2-4), 2-7, 2-8, P, P P, P, P,, : ; ; 2-8,,,,,,, 1949,, , ( 2-1), 1942, ,, ,, 1980

21 12, 60km, ( 2-1 ),,, 1980, 1954, ,,,,,,,,,, ( ), : x = F 1 ( L, B) y = F 2 ( L, B) ( 2-5), L B, x y, ( 2-5),,,,,,,,,,,,, 2.,,, 1 ),

22 13,, , ( ),,,,,,,,,,,, 2 ), ( ),,,,,,,,, :

23 14,,,, -( Gauss-kr ger),, ( UTM), 3.,, ( ), :, ;,,,,,,,,, ( ),,,,,, 1. -,, , 1912,,, ,, ( ),,,, : 2.,, ( 1 ),,, ( 2 ),,, ( 3 ),,

24 15 3., O, X, X ; Y, Y, ( 2-11 ) ,,,,,, 63, 6 3( 2-12 ) : 0, 6, 1, 2, 3,, 60,, 11 6, N L 0 : L 0 = 6N - 3 ( 2-6) 3 : , 3, 1, 2, 3,, , 24

25 16 45 n l 0 : l 0 = 3n ( 2-7) 5.,, X, Y Y, X 500km, Y 500km( 2-13),, 2-13, P X P = m; Y P = m, 19, P : x P = m, y P = m 6.,, S,, R, = S + y2 m 2R 2 S ( 2-8) ( 2-8), S y m ( ), S, : S = - S = y2 m 2R 2 S ( 2-9) ( 2-9),, ( 2-9) : y m S S = y 2 m 2R 2 ( 2-10) km, 2-2, , ( )

26 y m / km S/ S 1 / / / / / / / / ( a) AB, Q A B ABB 1 A 1 : ABB 1 A 1 : : P ; R 360 = P R 2 ( 2-11),,, 2-14 ( b), a b,, AB, 2-14,, a b a b, ( ), 1 2, = 1, 2 + 2, 1 = 1 ( 2-12) 2 2 P aa 1 b 1 b, : ( 2-12) : P = 1 2 ( y 1 + y 2 ) ( x 2 - x 1 ) = y m ( x 2 - x 1 ) ( 2-13) = y m ( x 2R x 1 ) ( 2-14) ( 2-14), AB

27 18, y m = 280km, x 2 - x 1 = 5km, R 6 371km, = 4, 2-15 : = + 1, 2-1, 3 ( 2-15),, ( ) ( ),, 2-15 ( UTM ),,,,,,, ( Universal Transverse Mercator Projection), UTM 1938, 1945, UTM ( 2-16 ) ,,,, m 0 = UTM , B = 0, l = (, 180km 1 40) ; ; ; UTM 60, 6, 180W 174 W 1, 1, 2, 3,, : y = y ( ), x = x ( ) y = y( ), x = x ( )

28 UTM,,, UTM 2. 4,,,, H,,,,, 2-17,,,, 2-17,,,,,,,,

29 ,,,, , 1956, , , m, m,,,, 2-18, H A H B A B, H A H B, h AB A B,, h AB = H B - H A = H B - H A ,,,,,, R = 6 371km 2-19, AB, S,, R A AC, t A, AC

30 AB, S: : S = AC - AB = t - s S = R AC = t = Rtan AB = S = R ,, = S, : R S = 1 3 S 3 R 2 S S = 1 3 S 2 R 2 ( 2-16) S = 10km, S S = , : 10km,,,, : = P ( 2-17) R 2, P, R, 1, = / P = 100 km 2, = 0. 51, 100 km 2,, 2-19, BC BC = h,

31 22 ( R + h) 2 = R 2 + t 2 t 2 h = 2R + h S t, h 2R, : h = S2 2R ( 2-18), h S = 1km, h = 8cm,,,, 100 km 2,,,, 2. 6,, 1.,,, 2. ( X ), X 3., 1., :, ;, ( 2-20 ), L C P : P = ( L P - L C ) sinb P = LsinB ( 2-19), L P B P P ( 2-19 ), L,,, = L;,, = 0 2.,,

32 23, :, ;,,,,,,,, :, A 2. :, 3. :, A m,, 2-21, A A m :,, A = A m + ( 2-20) A = + ( 2-21) = A m + - ( 2-22), 2-22, P 1 P 2 P 1 P 2, 12 P 1 P 2, 2 1 P 2 P , 21

33 24, 180, 12 = ( 2-23) ,,,,,, , ;,,, 2-24,,, :, ;, ;, 1.,

34

35 26 : ( 1 ) 1 d, D, : d D = 1 M ( 2-24), M M, ; M, : ; ; ( 2 ),, , 2cm 2-25,,,, 1 /10, 1 /100, ( ),, / ,,,,, 0. 1mm,

36 27,,, 0. 1mm 0. 1mm / m , : ( 1 ),, ( 2 ),,, , , ( GB/ T ) a. b. 4 a. 15 a. b. b

37 a. b : 1., ,,,,,, 3.

38 29,,, 1.,,,, 10cm 5mm, 10cm, ,,,,,,,,, 2.,, ,, , , 36 00,,,, 1,, km( ), 89 90, 39, 19321, 19, 321, km ( 321km km = - 179km),,,, ( 2-29 ) ( ) ( 2-30 )

39 30

40 , : ;

41 32 ( ), 1100,,, ( ),,, ;, ( ) , 1100, , , A, B, C, D J-51-A [ 1], [ 2],, [ 16] J-51-[ 2] , 2,, 144 J A, B, C, D J-51-5-B ( 1), ( 2),, ( 64) J-51-5-( 24) , 2, 3, 4 J-51-5-B a, b, c, d J-51-5-( 24) -b 1 ) , 60 76, , , 1100, 4, 88 22, ( ) A, B, C,, V 180, 6, 60, ( ) 1, 2, 3,, 60, 88Z

42 , 1100, 4 6, N S, N , , , 1100 J-51,, NP-47, 48; NP-49, 50, 51, ) 150, 125,

43 , ; A B C D 150 J-51-A, , 125, , , [ 1 ], [ 2 ],, [ 16] 125 J-51-[ 2 ], , , l, 2, 3,, J-51-5, 2-33

44 35 3 ) 15, 12. 5, , , 125, , A B C D 110, 15 J-5l-5-B , l , J-5l-5-B , 64 11, ( 1 ), ( 2), ( 3),, ( 64) ; 2 30, 3 45, 110. J ( 24) 4 ) ( 2-35) 1 15, l a b c d J-5l-5-( 24) -b

45 , 1992 ( GB/ T ), ( 1 ) , 1100,, ( ) ( ), 1100 J , 1100,, 1100,, B C D E F G H

46

47 ( 2-38) J50B ( 2-39) J50C ( 2-40) 45J50D

48 ( 2-40) 135 J50 E ( 2-40) J50F ( 2-40) J50G ( 2-40 ) J50H ( 2 ), 1100 : a = [ /4 ] + 1 b = [ /6 ] + 31 : [ ] ; a 1100 ; b 1100 ; ; , , a = [ /4 ] + 1 = 10 ( J) b = [ /6] + 31 = J50, 1100 : c = 4 / - [ ( /4 ) / ] d = [ ( /6 ) / ] + 1 : ( ) ; [ ] ; c 1100 ; d 1100 ; ; ; ; , , J50G = 30 2, = 3 45 c = 4 / [ ( /4 ) /2 30 ] = 015 d = [ ( /6 ) /3 45 ] + 1 = ,

49 40 ( GB/ T ),, , 2-37, ,, ( ) 40cm40cm 40cm50cm 50cm50cm cm 2 /km : 1., x, y, km ; km; km x = m y = m, ,,, 2-41( a), 15 3., 2-41 ( b), A , , 2-41 ( c ) ,, 2-41( d),

50

51 ,,,,,,,,,,, : 1.,,,, 1mm, 2.,,, 3,,,, 3.,,,,,,,,,,

52 43 1.,,,,, 30m m, m,,,,, 2.,,,, ( ),,,,,,,,,,, 3., 4.,,,,,,,,,,,,,,,,, ( ),,, ( ) ;, ( ),,,,, X, n, l 1, l 2,, l n, ( ) 1, 2,, n,

53 44 i = X - l i, i = 1, 2,, n ( 3-1),,,,,,, 358, ( 180 ),, ( 3-1) ( ),, d= 3 k, k/ n( n = 358 ), k /n 3-1, 3-1 ( 3-1), ( k / n) ( d ),,, d k k /n k k/ n k k/ n , : ( 1 ), ; ( 2 ), ; ( 3 ) ; ( 4 ),, : 1 + lim n n, [ ] n = lim n [ ] = 0 ( 3-2) n

54 ,,,, ( n ), d, 3-1, P n,, : f( ) = 1 e ( 3-3), = , e = ,, 2 :, : n [ 2 ] = n lim = lim n n n = lim n [ 2 ] n = lim n [ ] n ( 3-4) ( 3-5) ( 3-5),,,, ( 3-3),,, 3. 2,,,

55 46, 2,,,,,,, m, 3-1 m = n n = [ ] n ( 3-6) 10, ( ),, m 1 = 2 = m = 2 = , m 2 m 1, ( - 7, + 8 ),,,,, 3-3, = 0, f( ), 1 2m

56 47 m,,,, ; m,,, ,, 200m 40m, 2cm,,,, ( ),, /200 = 1 /10 000, /40 = 1 /2 000, ( 3-1 ) :,,,,, d: P( ) = f( ) d= 1 2 m e - 2 2m2 d ( 3-7) ( 3-7), k, : P ( < km) = + km - km 1 2m e - 2 2m2 d ( 3-8) k = 1, k = 2, k = 3 ( 3-8 ), 2 3 : P( m) = = %

57 48 P ( 2m) = = 95. 4% P ( 3m) = = 99. 7%, 2 5 %, %, 2,, 2,,, 2 = 2m ( 3-9) 3. 3, n, l 1, l 2,, l n x,, : x = l 1 + l l n n = [ l] n ( 3-10), : X, l 1, l 2,, l n, 1, 2,, n,, n, : 1 = X - l 1 2 = X - l 2 n = X - l n [ ] = X - [ l] n n ( 4 ),, [ ], n lim n [ ] = 0 n ( 3-11) ( 3-12),,,,,, ( v) : v 1 = x - l 1 v 2 = x - l 2 ( 3-13) v n = x - l n

58 49, ( 3-10), [ v] = nx - [ l] [ v] = n [ l] n - [ l] = 0 ( 3-14),, ( 3-5),,, m, ( 3-6) X i,, ( 180 ), X, i,, ( 3-6), x, v i ; x X, x X, v i i ( 3-6), ( ) : m = [ vv] n - 1 ( 3-15) ( 3-15) ( 3-6), [ vv] [ ], ( n-1) n :, n ;,, ( n - 1), n ( n - 1 ) ( 3-15) ( 3-1) ( 3-13 ) :, 1 = X - l 1, v 1 = x - l 1 2 = X - l 2, v 2 = x - l 2 n = X - l n, v n = x - l n 1 = v 1 + ( X - x) 2 = v 2 + ( X - x) n = v n + ( X - x), [ v] = 0, [ ] = n( X - x) X - x = [ ] n

59 50, [ v] = 0 : ( X - x) 2 = [ ] 2 n 2 [ ] = [ vv] + n( X - x) 2 = n + n 2 2( n 2 n - 1 n ), i j ( ji), ( 4 ), lim n n n - 1 n n,, n,, ( X - x) 2 = [ ] n 2 [ ] = [ vv] + [ ] n [ ] = [ vv] n n - 1, ( 3-6) ( 3-15) ( 3-15) 3-2, 6,, 3-3,, l 0, l i, : = 0 l i = l 0 + l i ( 3-16) x = l 0 + [ l] n ( 3-17) 3-3 l / m l / cm v/ cm vv/ mm x, m x = l 0 + [ l] n = m m = [ vv] n - 1 = 3. 0cm ( l 0 = )

60 ( ),,,,,, ( ),,, : 1., D n, d 1, d 2,, d n, D = d 1 + d d n, D d 1, d 2,, d n, : Z = x 1 + x x n 2., d, D = 1 000d, D d : Z = mx 3., :, l i x = 1 n ( l 1 + l l n ) = 1 n l n l n l n ( ),,, : 4. Z = k 1 x 1 + k 2 x k n x n, c, a b, a = c sin, b = ccos : Z = f( x 1, x 2,, x n ) ( 3-18),,, 3-3, a b, P,

61 52 P = a b ( 3-19) 3-3 a b a b a b, P,,, ( 3-19) a b : dp = P a da + P b db dp = bda + a db ( 3-20) : ( 3-20) P = b a + a b ( 3-21) ( 3-21) 3-3, : b a a b, P, a b, a b n, : : n: [ P P ] P 1 P 2 = b+ a a 1 b1 = b+ a a 2 b2 P n = b a n + a bn = b 2 [ a a ] + a 2 [ b b ] + 2 ab[ a b ] ( 3-22) [ P P ] [ = b 2 a a ] [ + a 2 b b ] + 2a b [ a b ] n n n n ( 3-23), ( 4 ), lim n [ a b ] = 0 n

62 53, ( 3-23) : [ P P ] n, ( 3-24) : P : [ = b 2 a a ] [ + a 2 b b ] n n m 2 P = b 2 m 2 a + a 2 m 2 b ( 3-24) :, x 1, x 2,, x n m n, Z x i m P = b 2 m 2 a + a 2 m 2 b ( 3-25) Z = f( x 1, x 2,, x n ) ( 3-26) ( ), m 1, m 2,, i, Z Z, ( 3-26), d,, Z = f x1 + f x2 + + f xn x 1 x 2 x n f x i ( i = 1, 2,, n),, m Z = f x 1 2 m f x 2 2 m f x n 2 m 2 n ( 3-27) ( 3-27),, 3-3, : Z = k 1 x 1 + k 2 x k n x n ( 3-28), k 1, k 2,, k n, x 1, x 2,, x n, m 1, m 2,, m n, : f f f = k 1, = k 2,, = k n x 1 x 2 x n m Z = k 2 1 m k 2 2m k 2 nm 2 n ( 3-29) n, ( 3-18) ( 3-29), m x = 1 n 2 m n 2 m n 2 m 2 n,, m 1 = m 2 = = m n = m, m : m x = m n = [ vv] n( n - 1) ( 3-30)

63 54, 1, n, 3-3,, : m x = m n = 3. 0 = 1. 2 ( cm) ( 3-31) 6, cm, : = cm, : = ( 3-32) ( 3-33) ( ) D x y, A B D m m D, m x m y :,, : x = Dcos y = Dsin d x = cos dd - Dsin d d y = sindd + Dcos d, : ( 3-34) ( 3-35) m 2 m x = cos 2 m 2 D + ( Dsin ) 2 2 ( 3-36) m 2 m y = sin 2 m 2 D + ( Dcos ) 2 2 A B : M AB = m 2 x + m 2 y = m 2 D + D m 2 ( 3-37),,,, A B : ( 3-36) ( 3-37 ), : m x D = m m, = = mm, m y = mm, M AB = mm

64 , n ( ),,,,,,,,,, ( m ),, P, : P i = C m 2 i ( 3-38), C 1, m 0 ( 0 ), : : P i = m2 0 m 2 i ( 3-39) m i = m 0 1 P i ( 3-40) m 0, m, N : ( 3-39), N : m ( N ) = m N ( 3-41) P m 2 ( N ) = Nm2 = N ( 3-42), 1km m 0, L k m : m H = m 0 L ( 3-43) ( 3-39), L k m : P H = m2 0 m 2 0 L = 1 L ( 3-44), L 1, L 2,, L n, m 1, m 2,, m n,

65 56 ( 3-38) P 1, P 2,, P n, : : x = P 1 L 1 + P 2 L P n L n = [ PL] P 1 + P P n [ P],, : ( 3-45) L i = L 0 + L i ( 3-46) x = L 0 + [ PL] [ P] ( 3-47) n, x, v 1 = x - L 1 v 2 = x - L 2 ( 3-48) v n = x - L n : x,, : [ Pvv] = [ P( x - L) 2 ] = min ( 3-49) d[ Pvv] dx = 2 [ P( x - L) ] = 0 [ P] x - [ PL] = 0 x = [ PL] [ P] ( 3-45), : ( 3-50) [ P v] = [ P ( x - L) ] = [ P ] x - [ P L] = 0 ( 3-51) ( 3-50) :, : x = P 1 [ P ] L 1 + P 2 [ P ] L P n [ P ] L n m x = P 1 [ P] 2 m P 2 [ P] 2 m P n [ P ] 2 m 2 n ( 3-39), m 2 i = m2 0 P i ( m 0 ), m x = m 0 P 1 [ P] 2 + P 2 [ P] P n [ P] 2 m x = m 0 [ P ] ( 3-39), : ( 3-52) P x = [ P] ( 3-53)

66 57, ( 3-39) m 2 0 = P i m 2 i ( 3-54) n, m 2 0 = P 1 m 2 1 m 2 0 = P 2 m 2 2, m 2 0 m 2 0 = [ Pm2 ] n = P n m 2 n = [ Pmm] n i m i, : v i m 0 = [ P ] n ( 3-55), x X, i, ( 3-15), : 3-5 m 0 = [ P vv] n - 1 ( 3-56) 3, 2 4 6, ( 3-4 ), 3-4 L L( ) P PL( ) v( ) Pv( ) L 0 = x = = [ Pvv] = 60, m 0 = = 5. 5 P x = 12, m x = = 1. 6

67 , ( ) 3-4, A H A, L 1 L 2 L 3 L 4 L 5, B C D,,,,,,,, 3-4 t x 1, x 2,, x t, n L 1, L 2,, L n, p 1, p 2,, p n, L 1 + v 1 = a 1 x 1 + b 1 x t 1 x t + d 1 L 2 + v 2 = a 2 x 1 + b 2 x t 2 x t + d 2 ( 3-57) L n + v n = a n x 1 + b n x t n x t + d n, d i L i, l i = d i - L i ( 3-58) : v 1 = a 1 x 1 + b 1 x t 1 x t + l 1 v 2 = a 2 x 1 + b 2 x t 2 x t + l 2 ( 3-59), a i, b i, c i, l i v n = a n x 1 + b n x t n x t + l n [ pvv] = min x 1, x 2,, x t,,

68 59 [ pvv] x 1, x 2,, x t,, x 1, x 2,, x t [ pvv] x 1, x 2,, x t : [ pvv] v 1 v 2 v n = 2p 1 v p 2 v p n v n x 1 x 1 x 1 x 1 [ pvv] x 2 = 2p 1 v 1 v 1 x p 2 v 2 v 2 x p n v n v n x 2 ( 3-60) [ pvv] x t = 2p 1 v 1 v 1 x t + 2 p 2 v 2 v 2 x t + + 2p n v n v n x t ( 3-59) v i x 1 = a i, v i x 2 = b i,, v i x t = t i ( i = 1, 2,, n) ( 3-60),, 2 : p 1 a 1 v 1 + p 2 a 2 v p n a n v n = [ pa v] = 0 p 1 b 1 v 1 + p 2 b 2 v p n b n v n = [ pbv] = 0 p 1 t 1 v 1 + p 2 t 2 v p n t n v n = [ ptv] = 0 ( 3-61) t, ( 3-59) n, n v t x n + t, ( 3-59) ( 3-61), : [ pa a ] x 1 + [ pab] x [ pa t] x t + [ pa l] = 0 [ pa b] x 1 + [ pbb] x [ pbt] x t + [ pbl] = 0 ( 3-62) [ pa t] x 1 + [ pbt] x [ ptt] x t + [ ptl] = 0,, ( 3-59) v, v [ pvv] = min v, : m = [ pvv] n - t ( 3-63) 3-4, H A = m, B C D X 1 X 2 X 3, : L 1 = m, S 1 = 3. 5km L 2 = m, S 2 = 2. 7km L 3 = m, S 3 = 4. 0km

69 60 L 4 = m, S 4 = 3. 0km L 5 = m, S 5 = 2. 5km : L 1 + v 1 = X 1 - H A L 2 + v 2 = - X 1 + X 2 L 3 + v 3 = X 2 - H A L 4 + v 4 = X 2 - X 3 L 5 + v 5 = X 3 - H A, : v 1 = X 1 - ( H A + L 1 ) v 2 = - X 1 + X L 2 v 3 = X 2 - ( H A + L 3 ) v 4 = X 2 - X 3 - L 4 v 5 = X 3 - ( H A + L 5 ),, X 0 1 = H A + L 1 X 1 = X x 1 X 0 2 = H A + L 3 X 2 = X x 2 X 0 3 = H A + L 5 X 3 = X x 3 v 1 = x 1 v 2 = - x 1 + x v 3 = + x 2 v 4 = x 2 - x 3-14 v 5 = + x 3 10km, p i = 10 S i, : p 1 = 2. 9, p 2 = 3. 7, p 3 = 2. 5, p 4 = 3. 3 p 5 = 4. 0: 6. 6x x = x x x = x x = 0 x 1 = mm, X 1 = m x 2 = mm, X 2 = m x 3 = mm, X 3 = m x 1 x 2 x 3 : v 1 = 11. 8mm, v 2 = 9. 2 mm, v 3 = mm v 4 = mm v 5 = mm

70 61, : ( 3-63) : m = y 1 = L 1 + v 1 = m y 2 = L 2 + v 2 = m y 3 = L 3 + v 3 = m y 4 = L 4 + v 4 = m y 5 = L 5 + v 5 = m = 13. 4mm

71 ,, 4-1, A H A, B H B A B h AB, B H B : B H B = H A + h AB 4-1 h AB : A B, A B, A B, A, a, ; B, b, A B : B H B : h AB = a - b ( 4-1)

72 63 H B = H A + ( a - b) h AB, a b, h AB, B A ; a b, h AB, B A, h AB h, h AB A B ; h B A B A, h AB = - h BA 4-1, B H i ( ) : H i = H A + a H B = H A + ( a - b) = H i - b ( 4-2),,,, 4-1 A B,,,,,, 4-2, A B h AB,, A1 h A1 12 h 12, nb h nb, 4-2, 1, 2, 3,, n h AB : h AB = h A1 + h h nb, h A1 = a 1 - b 1 h 12 = a 2 - b 2 h n B = a n b n + 1 1, 2,, n n h AB = ( a 1 - b 1 ) + ( a 2 - b 2 ) + + ( a n b n + 1 )

73 64 n + 1 = 1 n + 1 ( a - b) = 1 n + 1 a - 1 b ( 4-3), h AB ( 4-3), h AB,, ( ) A B,,,,, IN IM ( 4-3 ) 4-3, 4-3, A B : h AB = EA - FB, IM IN, MA NB, EA FB ME NF p 1 p 2 ( ) ME NF : h AB = ( MA - p 1 ) - ( NB - p 2 ),, IMIN,, f 1 f 2 ( ) MM NN, 1. h AB = ( a + f 1 - p 1 ) - ( b + f 2 - p 2 ) ( 4-4) 4-4, I R, S, t, p 2-12 p = S2 2R ( 4-5)

74 R = R, K R R, K 1, K ( 4-5), f = S2 2 R K = K S2 2R ( 4-6), K,,, K = r,, K < 1, r, : ( 4-4) : r = p - f = ( 1 - K) S 2 2R ( 4-7) h = ( a - b) - ( r 1 - r 2 ) ( 4-8) K = 0. 11, S = 100m, R = 6 371km, r = 0. 7 mms 1 S 2, r 1 r 2, S 1 S 2, ( r 1 - r 2 ) 4. 2,,, 4-1 D S, D, S3 S10,, S05 S1,

75 DS05 DS1 DS3 DS mm 1mm 3mm 10mm 4-5 S3 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; S3 1 2, 3 4, 5,,,,,,,, 6, 7, 8,,,, 4-5 9, 10, ( ) 11 12,, 13,, 14 15, 4-6, CC 1,,,,,

76 67 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; , ;,,,,,, : V = 20 ( 4-9) DS3, 4-6 7,,, ( ),,,,, 4-7( a),, ( ) (, 1, 2, 3 ),, 4-7( b),,, 4-7,,, :, ;, (

77 68, ) ; ( ),, ;,,, 1., ( 4-8 ( a ) ),,,, 2mm, 4-8 ( b), O, O, LL 1,,, 4-8,, 4-9,,,, 4-9

78 69 ( 2mm), ( ), 2mm,, 4-10, R( mm), ( ) : = 2 ( ) ( 4-10) R 4-10 ( 4-10) R, R,,,, 6 30, 10 20, 10 /2mm 20 /2 mm,, 4-11, A, B C B C, A, , 4-12,,,, O, ( O ) L L 1,, 5 /2 mm 10 /

79 ,,,, 4-13 N3, 0. 3 mm 4-14 S1, 5mm, mm, S1 5mm 4-15 N3, 100, 10 mm, 0. 1 mm, 0. 01mm10, 1mm, 5mm,,,, 10mm, 5 mm;, 0mm, 5mm 4-15,, a, a , 5mm, 0,, 148, 6. 50mm,

80 71 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; N S mm - 5 mm, a : a = 148cm mm - 5mm a = cm - 5mm, ( ) 5mm,,,

81 ,,,,,,, 4-16 DSZ2, 4-17 DSZ ,,, :,, A, f = s ( 4-11),, B, 2.,, DSZ3 4-19( a),,

82 73 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; DSZ2 1. ; 2. ; 3. ; ; 6. ; 7. ; 8. ; 9. ; 10. ; DSZ B C, A, 4-19( b), ( P ),, 4-20,,, =

83 ( 1), 4-19 ( a),,, :, 4-21,,,, B ( 4-22 ),, 4-22, 4-21 ( ) ADSZ3,, = 4,,, 2 2, 2, 4, = 4,,

84 ( 2) 4-22 ( 3) 3.,, 4-23( a) P ;,,,,, ( 4-23( b) ) 4-24,,,,,,,

85 76, 3 4m,,,,,,, 1cm,,, m, ( ), ( ),, mm 4 787mm, (, 4-26 ( a) ),,,,,,, (, 4-26 ( b) ) 30cm, 2 3cm,,,,,, 10mm 5mm 10mm 4-27( a),, 0 300cm,,

86 cm,,,, 5mm 4-27 ( b ),, 5mm,,,,, m, 5mm, ,,,,,,,,,,,,,

87 78, 2., 4-28, 1 2 3,, ( ) 1 2,, 1 2, 4-28 ( a),, 4-28( b) ,,,, 4., ( ),, 5.,, ( ),,, 4-29,,,,, 4-30 N3, ( m) 4-31 S1, ( m)

88 N S1 1., ( ),,, :, Leica NA2002

89 80 NA3003 ( 4-32 ) ;, DiNi10 DiNi20 ;, DL-101C DL-102C 4-32 DNA03 NA2002, NA ,, CCD, 6. 5mm, m, 256

90 81, 3. ( ), ( ),,, ( h) ( d), ( d h), ,,,,, d,, 80 %, h 0, d 4.,, Wild Ni m / m,, ( ), 4-34, ;, 1. 35m, 4. 05m 1. 8m, 100m 4-34 ( ),,, : ; 4. 3,, :,,

91 82,,,,,,,,,,,,,,,,,, A B h H A B , 4-3,, 4-3,

92 /m /m /m /mm /mm / mm S S : 1 ), ; 2 ), ; 3 ), ; 4 ), ; ( ) ( ),, 4-4 ( 1 ) ( 8), 1. : ( 9) = ( 4 ) + K - ( 7) ( 10) = ( 3) + K - ( 8 ) ( 11) = ( 10) - ( 9) ( 10) ( 9), ( 11 ) K 4-4, 5 K = 4 787, 6 K = ( 16) = ( 3) - ( 4) ( 17) = ( 8) - ( 7) ( 16), ( 17), ( 16) ( 17) ( 4-4 ( 16 ) ( 17) 100 ), ( 11), : ( 11) = ( 16 ) ( 17) ( 12 ) = ( 1) - ( 2) ( 13 ) = ( 5) - ( 6) ( 14 ) = ( 12) - ( 13 ) ( 15 ) = ( 14) + ( 15 ) ( 12), ( 13), ( 14), ( 15) 5. 6

93 ( ) : : d d K + ( 1) ( 5) ( 3) ( 8) ( 10) ( 2) ( 6) ( 4) ( 7) ( 9) ( 12) ( 13) - ( 16) ( 17) ( 11) ( 14) ( 15) : ( 3) - ( 4) = ( 16) = h {( 3) + K} - ( 8) = ( 10 ) ( 8) - ( 7) = ( 17) = h {( 4) + K} - ( 7) = ( 9)

94 85 h = 1 2 ( h + h ) h h, h : ( 15) = ( 12) - ( 13) = ( 12 ) + ( 13),,,, 1 cm ( 1 ),, ( 2), 2mm,, ( 1) ( 2), 4-5, ;,,,, ( 3), ( 3 ),,,, ( 4), ( 5) ( 6) ( 4 ),,, ( 7 ) ( 5 ),,, ( 8) 4-5 ( 1) ( 8), ( 9 ) ( 18),, : : ( 9) = ( 1) - ( 2 ) ( 10 ) = ( 5) - ( 6) ( 11 ) = ( 9) - ( 10) ( 12 ) = ( 11) + ( 12 ) ( 14) = ( 3) + K - ( 8 ) K ( N3 K = m)

95 86 ( 13) = ( 4) + K - ( 7) ( 15) = ( 3) - ( 4) ( 16) = ( 8) - ( 7) ( 17) = ( 14 ) - ( 13) = ( 15 ) - ( 16) ( 18) = 1 2 { ( 15 ) + ( 16) } 4-5 N3, S1 Ni004,,, d d + K ( ) ( ) ( ) ( 1) ( 5) ( 3) ( 8) ( 14) ( 2) ( 6) ( 4) ( 7) ( 13) ( 9) ( 10) - ( 15) ( 16) ( 17) ( 11) ( 12) h - ( 18) h h h h

96 87 d d ( ) ( ) h K ( ) cm 1cm / m / m / m / m / mm / mm / mm / mm / mm S K S K S05 60, : ( 1 ) : ; ( 2 ) : ;,, : ( 1 ), ; ; ( 2 ),, ( 3), 3

97 88 ( 4 ),, ( 5 ),,, 2, ( 6 ),, 2,, 2, ,, i, i, 4-35 A B, S A S B, x A x B, B A : h AB = ( a - x A ) - ( b - x B ) = ( a - b) - ( x A - x B ) x = Stani h AB = ( a - b) - ( S A - S B ) tani = ( a - b) - ( S A - S B ) h = ( a - b) - i ( S A - S B ) i ( 4-12) 4-35 i x A = x B, S A = S B,,,,, i i,, i

98 89,, 2.,,,,, 1., = 20 /2mm, 100m, 0. 5, 5mm,,,,, 2.,, i, 3.,,,, 4.,,,,,,,,,,, 1.,,,,,,, :, ;,,, : ;, ;, 2.,,

99 90, 0. 3m, 3.,, 4. 5,,,,,, : ;,,,,,

100 91 2. : ;,,,,,, : 1. ( 1 ),,, 4-37 V, L,,, L, V, 4-37 ( a) 180 ( 4-37( b) ), V, V,,,, L 4-37 ( b) L 2,,,

101 92 ( 2 ), 180,, ;,, ( 3 ),, 4-38,,,, l V, 4-39 ( a), V, 4-39( b),,,, 180,,,,, ( 1 )

102 93,,,,,,,,,, ;,, ( 2 ), 4-40 ( a) A,, A A, ; A, 4-40 ( b),, ( 3 ),,, 4-40 ( b) A,, A,,, ,, i,, i i = 0,,, ( 1 ) i i, : A B, A B h AB h AB i, ( 4-12) h AB i = h AB - ( S A - S B )

103 94 h AB i = h AB - ( S A - S B ) i h AB - ( S i A - S B ) = h AB - ( S A - S B ) i = h AB - h AB ( 4-13) ( S A - S B ) - ( S A - S B ), S A = S B, h AB i h AB, ( 4-13) : S A - S B = - ( S A - S B ), ( 2 ) i = i = h AB - h AB ( 4-14) S A - S B h AB - h AB ( 4-15) 2( S A - S B ) A B,, A B,, 4-41( a) h AB,, B, 4-41( b), 4-41 i h AB i, ( 4-13) i = h AB - h AB ( 4-16) S A - S B, i 15 ; i 20, A, i i : x A x A = i S A,, B, A a 2 : a 2 = a 2 - x A a 2,,

104 95, ( ) ( 4-42),, ( ), a 2,, 4-42 ( 3 ) 4-43( a) AB A, A B h AB AB B, 4-46( b), A B h AB ;, S AB h AB = a 2 - b 2 = S A - S B = - ( S A - S B ) 4-43 i ( 4-15) i: i = h AB - h AB ( 4-17) 2S AB,, B, A : x A = i S A : A, B : a 2 = a 2 - x A

105 96 x B = i S B : b 1 = b 1 - x B B, A : A, B : a 2 b 1 = a 2 - x A = b 1 - x B, B, A a 2, A, B b 1, ( 4 ),,,, i i, i i 4-44, P, V, R ; P V R AB P, V, AC P, AB AC, AB AC, AC AC 1, AC 1 V AE AB i, i,, 4-47, i 4-44 i

106 97 C 1 C 2 BC, C 1 EBE, : i, tani = BE AB BE = C 1 C 2 BC 1 = BC 1 sin = ABtan tani = ABtan sin = tan sin AB i = i = ( 4-18) 8,, = 4 i < 1, ( 4-18) : = i 14, i, i, i + ( 4-44, ) ;, i - ( ), : i, i = - i, h AB = i S - i S h AB = i ( S + S ),,,,, i +, -, i,, ( ),,,,,,, :

107 98,,,,, :, i,,, ;, i, i, 4-45,,,,,, 4-45 ( 1), :, i, 4-46( a),,,, ;, i, 4-46 ( b),,,, 4-46 ( 2),, 4-47,, A B,,,,,,, A B,,,,, 4-48

108 ;, 4-48( c) ( d) ( e), ( 4-48( d) ), i > : ( 4-51( e) ), i = 0, 0; ( 4-48 ( c) ), i <,, 2mm,,,, i,,, i,, i : ( ),

109 100,, A B,,,,, ( ) ( ), A B ;,,, 2. A B, AB 100 m, A B ( ), AB, ( 1 2 ) AB, A B h AB, ; 3, ( ), A B h AB ; 3, ( ), A B h AB ; 3, ; 1, ( ), A B h AB ; 1, ( ), A B h AB,,, h AB h AB h AB h AB h AB,, 5mm,,,, 1.,, 4-49, a < 8 mm, a,,, ,,,,,

110 101, 50 m,,, 90,, 3. : ; ; ; : ( 1 ),, 0. 5 mm,, 4-50, 103cm, 0. 2 mm,,, 4-50 ( 2 ), 1. 0 mm,,, ( 3 ) mm 4 787mm,, :, 20m, ( ), ( )

111 102,, 180, K ( 4 ),,,,, :,, 1m, A 1, A 2, z : 4-51 z = A 2 - A

112 ,,,, , AOC OA OC, AOC, A 1 B 1 C 1, AOC 5-1, A 1 B 1 C 1 OA OC OB 1 OB 1 O ( ), OB 1, OA a, OC b, b a, A 1 B 1 C 1 = b - a ( 5-1) 5-1

113 104,,,, 0 90 ( ),, Z, 0 180,, ,, ( ),,, 90, ,,,,, ( ) ( 5-3),,,,,,,,,,

114 ,, D, J, DJ07DJ1 DJ2 DJ6 DJ15 DJ6 6, J6, 5-4 J6 5-5 J2 5-6 T3, ( 1 ),, ( 2 ), ( ) ( 3 ),,, J6 1, J2 20,

115 ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; J6 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; 22. ; 23. ; 24. ; J2

116 ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; WildT3, T3 4 ( 8 ) J6,,,,, ( ),,,,,,,,,,,, ,, 0 ( 5-8( a) ) 90 ( 5-9( a) ) 2., 5-10

117 ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; ( ) 5-9 ( ) J6 : ( 1 ) J6, 1 1, , ( H), ( V), 60, 1, 10, 10, 1, 0. 1, 6 0,

118 ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; 22. ; J6

119 110, J ( 2 ) J2, ( ) 180,,,,,, T2 5-12( a) ( b) T2, ( a) , ( b) T2 ( 3 ),, ( 5-13),

120 111,,,,, ( 5-13 ) ; 1 2,,,,,,,,,,, JGJ JGJ2, ( a ) , ( b) JGJ2, 20 60,, DT5, 5-16 ET-02

121 ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. BDC21; 20. ; 21. ; 22. ; 23. ; 24. ; 25. ; 26. ; 27. ; 28. ; 29. ; 30. ; 31. ; 32. ; 33. ; DT5 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; 22. ; ET-02

122 , ( ), 5-17 ( ) ( ), ( ) 0, ( ) 1, 5-1,, ,,,,, 0,, s, s n, : s = 2 n = 360 s ( 5-2), ,,,

123 , ( a),,, a, 5-19 ( b),,,,,, ( ) 5-19 d, w,, : w = dcot ( 5-3) ( 5-2),, 5-19( a),,

124 115,,,,,,,,,, 5. 3 ;, 1.,,,,,,,,,,,,,,,,,,,, ;,,,,, 90,, 3mm 2.,,, 5-20, 1mm :,,, (, ),, (, ),,

125 ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; , ( ),,,,,, ,,,, ;,,, 2,

126 , B, BA BC, B, : ( 1 ) C, c ( 2 ), A, a, : ( 3 ), A, a ( 4 ) C, c, : = a - c ( 5-4) = a - c ( 5-5) 5-22,,, DJ6, 40, : 5-2 = 1 2 ( + ) ( 5-6) 5-2 C A B C A

127 O, O A B C D, : 5-23 : 0 00 ( ), ( ) A, B C D, 3, A,,, A D C B A,, 5-3 J6,, ( 3 5 ) , , 6, A ( 12 ),,,, J2,,,,, J2, 2C ( J6 ), : 2C = L - ( R 180 ) ( 5-7)

128 J6 J A B C D A A B C D A , L, R,

129 120 2 C, 2C, 2C ( ) 2C,, 1 2 ( L + R 180 ),,,, ,,, ( ) 2C DJ DJ DJ , 1. ( ),,,,,,, 90,,,,, : ( 1 ),, = - ; ( 2 ),, = - J6 ( ), 5-24,, L ; R,

130 : = 90- L = R - 270, : ( 5-8) = 1 2 ( + ) = 1 2 [ ( R - L) ] ( 5-9) +, ; -, ,, 90, x, x, x, x ;,, x, x ,, 90, 90 + x;, L x, :, : : = 90 - ( L - x) ( 5-10) = ( R - x) ( 5-11) = 1 2 [ ( 90- L + x) + ( R x) ] = 1 2 [ ( R - L) ] ( 5-12)

131 122 ( 5-12),, x = 1 2 [ ( L + R) ] ( 5-13) ( 5-13) 3., : ( 1 ) :,, (, ;,, ),, L,, R ( 2 ),, 17, - 17, + 17,, L R,,,,,, J6 25, 5-5, /m / m No

132 123 4.,,,,,,, J2,,,,, 5-25( a),, 5-25( b), O, A ;,, A, A O,,, O A,, ,

133 124 1.,,,,,,,,,,, ( 1 ) 5-26, O, O, O O,, M, M, OCO M, MM, MMOC5-26 : OC = OO sinoo C = OO R sinoo C OOe, OO 0, OO C M, = e R sin( M + ) ( 5-14) 5-26, R, M M 5-26 M = M + ( 5-14) M ( 5-14),

134 125 sin( M + ) = - sin( 180+ M + ), 180 ( ),, ( 180 ),, DJ2, DJ6,,, ( 2 ) :, 5-27AO, c, A, A A,, a a A A a Oa = x c c A RtOaa RtOAA RtA a O sinx c = aa Oa a a = AA AA= OAsinc Oa= OAcos ( 5-15) x c c, x c = c cos ( 5-15) ( 5-16) 5-27 c,,,

135 126 c ( ), ( ),, x c ( 5-16), x c,, x c = 0, x c = c, + - x c,, L, L, L = L - x c ( 5-17), R, R,, R = R + x c ( 5-18) A = 1 2 ( L + R ) ( 5-19), c,,,,,, ( 5-17) ( 5-18) R = L 180 L - R 180= 2 x c ( 5-20) ( 5-16),, cos 1, x c c, ( 5-20) L - R 180= 2c ( 5-21),, 2c, 2c 2c, 2c, 2c, 2c J2 13, 2c,, 2 c J2 16, J6 20, ( 3 ), i, i 5-28H ( H 1 H 1 ), h H, HOh H 1 H 1 i A 1 A 1, HOh i AOh, A, a A hoa = x i i

136 Rta ho sinx i = a h ao RtAa h RtAa O, x i i, a h = Aa tani ao = Aa / tan x i = itan ( 5-22) i,,,,, i ( ), i ( ), x i x i,, x i ; = 0, x i = 0,, x i,, L, L, L = L - x i, R, R,, R = R+ x i A = 1 2 ( L + R ),, : L = L - x i - x c

137 128 R = L 180, ( 4 ) R = R + x i + x c L - R 180= 2( x c + x i ) = 2 c cos + itan ( 5-23),,,,, 5-29, OT, P, OT V, P, P P O 1 O 2 TOT,, V,, P, O 1 O 2 V ON, 5-29 OR, i v, R NON, N R P N R, N OR = RtR RO RtN NO RtR N O, V i v, sini v = R R OR R R = N N N N = ONsinV OR= ON cos ( 5-22), A x v : 2. i v = Vcos ( 5-24) x v = Vcostan ( 5-25) 5-30, O, O, (

138 129 ), ( ), e 5-30 = - ( ) 2 = - 1 = esin s 1 esin( + ), + O O s d= - = = e sin sin( + - ) ( 5-26) s 2, O O e d, d d, ( 5-26), m 2 = s 1 m 2 = [ d d ] 2 d 2 2 e 2 sinsin( + - ) 2 = 2 e s 1 2 s d s 2 sin 2 + sin2 ( + ) sinsin( ) d s 1 s 2 s sin 2 d= 0 2 sin 2 ( + ) d= 0 2 sinsin( + ) d= cos 0 m 2 = 2 e2 2 s cos s 2 2 s 1 s 2

139 130 2 = 2 e2 2 s 1 + s 2 2-2s 1 s 2 cos = 2 e2 s 2 1 s AB 2 s s 2 1 s 2 2 m = e 2 s AB ( 5-27) s 1 s 2 ( 5-27), s AB, 180, s AB = s 1 + s 2 ; s 1 s 2,,,, , A B, A B, 5-31, A A, A + 1 = A B + 2 = B = B - A = B A - 1 = = e 1 sin 1 ( 5-28) s 1 2 = e 2 sin 2 ( 5-29) s 2 - = 1-2 = e 1 sin 1 - e 2 sin 2 ( 5-30) s 1 s A, A e 1,, 1, A : ( 5-28), m 2 A = [ 1 1 ] 2 d

140 131 m 2 A = e s sin d 2 0 e 2 = sin 2 1 d 1 = s sin 2 1 d 1 e 2 m 2 A = 2 1 2s 2 1, ( 5-29), ( 5-31) : m 2 B e 2 = s 2 2 m = m 2 A + m 2 B = 1 2 e 2 1 s e2 2 s 2 2 ( 5-32) ( 5-32), s 1 s 2,,,,, e,,,,,,,, 4. :,,, : d= p v, p (, ), v, 20 10, p = 10, v = 25, d= 10 = , d k, d= k v,,, k = 1. 5; ( J2 ) 2 8km, k = 3 J6

141 132, 1 /10, 6,, 5.,,,,,,,,,,,,,,,, J6 m 1 = 6,, : m 1 = m 1 2 = 62 = 8. 5, : m = m 1 2 = 62 = 8. 5, : m = m 2 = 62 2 = 12 2, 24, : m 1d = m 1 2 = 62 = , ,,, 5-32, : VV( ) HH( ) CC LL, : ( 1 ) ; ( 2 ), ; ( 3 ),

142 ,,,, ( 1 ) ( 2),,, ;,,,, : ; ; ;,,, ;,,,, 1.,,, 180 ( ),,,

143 ,,, 5-33( a) 180,, 5-33 ( b) 2, ( b), LL, LLVV,,, 5-33 ( c),, 5-33( d), ,,,, ( 5-34),, 3. c, x c = c, x c, x i = 0, : A,, ( 180 ) 2 c : 2c = L - R 180 c, J2 8, J6 10,,, R: R = R+ c = 1 2 ( L+ R 180 )

144 , R A, (, ),, A 4., 5-35, P ( 30 ), m 1 ( 5-35 ( a) ), P, m 2 ( 5-35 ( b) ) m 1 m 2, ;,,,,, i,,, i, i, m 1 m 2 m P, Pm i : i = m 1 m 2 Pm 1 2 ( 5-33),,, m 1 m m 2 m P J2, i 15 ; J6, i 20,, m 1 m 2 m,,, P, P,,,,, :, ;,,,,,,

145 136, ,,,, :,, L R, ( 5-13) x, x,,,,, R, x, R( 5-24) : R= R - x R,,,, x, x, ; x,, x,,, 6. ( ) 5-36

146 137, ( a), 5-37( b) :, ( 1. 3m), A, 180, A, ; B,, AB, A (, 1. 3m 1. 0m), 5-37 A, 180, A, ; A B,, A B, K( 5-37 ),,,,,,, ,, : ( )

147 138 1.,,,,,, 30m 100N,,,, : l t = l + l + l( t - t 0 ) ( 5-34), l t t ( m) ; l, ( m) ; l t 0 ;, m /( m ) ; t 0,, 20; t, l,,, 2. 3, ( 1 ),,, 5-38, n, q, : D = nl + q ( 5-35) 5-38,,,, 1 AB m, m, :

148 139 K = D - D D = = K 1 / /1 000, ( 2 ),,,,,, 5-39,, AB L, A B h, :, D h D = L 2 - h 2 D = L + D h, D h = D - L = ( L 2 - h 2 ) L = L 1 - D h = L 1 - = - h 2 2L h 2 L h 2 2L 2 - h 4 L h 4 L h L,, :, 3. D h = - h 2 2 L D = Lcos ( 5-36),,,,,,,

149 140 : 5-40, L, D ( 1 ) D l = L l l ( 5-37), l ; l, ; D l ( 2 ) D t = L ( t - t 0 ) ( 5-38), t 0 ; t ; D t ( 3 ), h A B D h = D - L = - h 2 2L ( 5-39) D = L + D l + D t + D h ( 5-40),, 4.,,,, ( 1 ),,,, 0. 1m,, ( 2 ),,, 30m, 0. 4 m, 1 /11 250,, ( 3 ),, 1, 1 / ,,,, ( 4 ), p, l p : l p = pl EA

150 141 : E, N /cm 2 ; A 70N, 10-4,, ( 5 ),,,,, : : L f = - q2 l 3 24p : L = L f cos 2, L f L ; q ; l ; p ;,,,, ( 6 ),, ( 7 ),,, 1.,,, ( ),,, ( ),,,,,,,,,, 1 /300 1 / ( 1 ) L 1 L 2 ( 5-41 ), R,, L 2, 5-41

151 , R,, L 1 : S f 1 = l p S= f 1 p l, l, pl L 2, p ( l L 1 L 2 p p = b a ), p p, a, b, p, 1 b - 1 a 1 a = 1 f 2 = f 2 - b bf 2 p p = f 2 - b f 2 1 p = f 2 - b pf 2 S= f 1 ( f 2 - b) pf , S : l S = f 1( f 2 - b) pf 2 l + f 1 + ( 5-41)

152 143 b = b + b, b S b ( 5-41 ) S = f 1 ( f 2 - b - b) pf 2 l + f 1 + = f 1 ( f 2 - b ) pf 2 l - c = - K = f 1 ( f 2 - b ) pf 2 f 1 b l + f 1 pf 2 + f 1 b l + f 1 pf 2 + S = Kl + c ( 5-42), b l S,,, K = 100, f 1 b l f 1 pf 2 +, c, ( 5-42 ) : ( 2 ) S = Kl = 100l 5-42, B A,,,,,,, : ; 5-42 AB S ( 5-42 ), A, B, M G Q ( ), M G MQM= GQG= QMM=

153 144 QGG= ( ), QMM QGG 5-42 : V + V 1 = V cos+ V 1 cos= ( V 1, V + V 1 l, V + V 1 l 0, : ( 5-42), NQ : l 0 D = Kl 0 S cos, = lcos = Klcos + V 1 ) cos S = Klcos 2 ( 5-43) i v : 1. h = Stan+ i - v,, t, c, A B D, 5-43, A, B, D : D = 1 2 ct ( 5-44) 5-43,

154 145 : : :, :, ;,,,,, km /s,,,,, ( 5km), ( GaAs),,,,,, : 3 km ; ;, ;,,, ;,, ( ),,, m D = A + BD D = 1 km, m D 1km,, : m D 5mm, : 5mm < m D 10mm m D = A + BD, A, mm ; B, mm / km ; D, km 2. t, ( 5-44) 5-44 :,,,, ( ),, ( ),,

155 146 t t, ( t), T ( ),,,,,,,,, T,, ( ) ( ) n, t = nt( 5-44) D = 1 2 cnt l = 1 2 ct, T, D = nl ( 5-45) 5-44,, l, l ( 0. 1m) n, D,, ( ),,,, 3. ( 1 ) D 5-45,, ( ) ( ),

156 , , : : = N2+ = 2N + 2 ( 5-46) D = ( N + ) ( 5-47) 2, N, ; ; = /2, u = 2, D = u( N + ) ( 5-48) ( 5-48) u,, u = 2, N,, D ( 2 ) N ( 5-48), u D, N = 0,, D = u = un,,, 2

157 148 u = 2 = c 2f, c = km / s, ( ), 5-6 ( 10-3, m /2< 1 /1 000) ( 5-6 ),,,, ( ), ( ), 12, MHz 1. 5MHz 150kHz 15kHz 1. 5kHz 10m 100m 1km 10km 100km 1cm 10cm 1m 10m 100m, f 1, u 1 f 2, u 2 :, K = u 2 u 1 = f 1 f 2, = c 2f 1 ; = c 2f 2, ( 5-48 ) D = u 1 ( N 1 + N 1 ) D = u 2 ( N 2 + N 2 ) N 1 + N 1 = u 2 u 1 ( N 2 + N 2 ) = K( N 2 + N 2 ) ( 5-49) D < u 2, N 2 = 0N 1, N 1 1,, N 1 = KN 2 N 1, K N 2 ( 3 ), : = D +, D, 5-47,, A,, B,,,,

158 ; 2. ; 3. ; , = d + = D + ( 5-50), d 2d,,, = ( 5-50 ) D - d = D - d = -, D - d 2( D - d), D - d 4.,,,,,, 5-48( a) ( b) 5-48 ( b), 5-48 ( c), ADB ADC BDC, L i P i, L i BDC P 1, P 1 ADC P 2, P 2 ADB P 3, P 3 ABC P r L i ABC P r L r, L r L i,,, : Q r = 6. 5n ( 5-51), n ; 3 90 ; Q r, = 2, n1, Q r 3,, 5-49

159 ND3000, 6.,,,,, 1, 2 4,,,,,,,

160 ND3000, ( ),, 5m,, 7.,, : ; ;, ( ) ( ), ( 10 km ),,, Wild DJ20 ( 1 ) 5-51,,, D 0 - d D,,, : k = D - ( D 0 - d),,,,,

161 152,,, ( ), 5-51 ( 2 ),,, f, f, : f = f - f R = f f, D, km, R mm / km ( 5-52) D R = RD ( 5-53),,,,,, ( 3 ) ( t P e) ( ),,,, : D = 1 2 V t V = c n, c, ; n

162 153 D = 1 2 c n t ( 5-54), ( t = + 12, P = hpa) n r,, n,, nn r ( 5-54) n, D = ct n = - n c n t n n = - D n n D, D t P, D, ( 5-55) D t P D tp = - D n - n r n r = D - D ( 5-55) = D n r - n ( n r - n) D ( 5-56) n r ( t = 0, P = hpa, e = 0 %, % ) n g, : n g = , :,, : ( 5-57) 4 n = 1 + n g t P e ( 5-58) 1 + t, ( ),, n = 1 + n g t P ( t = + 15, P = hpa), n r, n g n r = n ( 5-56) ( 5-59), D tp = P t ( 5-59) D ( 5-60), t ; P hpa ( ) ; D km ; D tp mm : D= D+ D t P,,,

163 154 ( 4 ), : D = D + K + D R + D tp h, : D h = - h 2 2D -, h S = D + D h, : ( 5 ) : h 4 8 D 3 ( 5-61) S = D cos ( 5-62) S = - S H R ( 5-63) H, ( 5-62 ) S ; ( 5-61) S 5. 7 ( 5-64), : m 2 D = m c c D = N c 2nf + 2 c 2nf + K ( 5-64) 2 + m n n 2 + m f f 2 D m 2 + m 2 K ( 5-65) 4, ( = c f ), m c, m n, m f, m, m K, :, m A, : m 2 D = m c c 2 + m n n 2 + m f f 2 D m 2 + m 2 K + m 2 A ( 5-66) 4 ( 5-66), : D,, ;,,,,,,, : m D = ( A + BD) ( 5-67), A, mm ; B, mm / km ; D,

164 155 km 1. c 0, 1975 c 0 = ( m / s), m c 0 = 410-9,, c 0 2. n c = c 0, n,,, n t p e, 1km, mm; 1hPa 0. 27mm; 1hPa 0. 04mm n, n, ( t p e) ;, 3. f : ;,,,,, m f ( 0. 5 f 1. 0)10-6, 10-4,,,,, 1.,,,,,,

165 156 ( 1 ),,,,, 1, ( 2 ),, 5-52 u 1 u 2 2, u 0,,, 5-52,, ( 3 ),,,,, 2.,, D, L a, L i, L r

166 157 t = 2L a + L r, 1 = L i ( 2L a + L r - L i ) 2D, ( t - 1 ) 2,,,,,, ( ),,, 5-53, E 1, E 2,, e 1 e 2,, : E 1 E 2 = e 1 cos( t + ) = e 2 cos t E 1 E 2 E k, e k, E 2, E k E k,, = e k cos( t + ) = e k cos cos t - e k sin sin t E k = E 1 + E 2 = e 1 cos( t + ) + e 2 cos t = ( e 1 cos+ e 2 ) cos t - e 1 sin sin t tan = e k cos = e 1 cos+ e 2 e k sin = e 1 sin e 1 sin e 1 cos+ e 2 = sin cos+ k, k = e 2 e , : = - = - arctan sin cos+ k ( 5-68) ( 5-68) 5-54,,, 2 E 2, E 1,,, ( 2 )

167 ( 5-68) 5-53, k, e 2, k,,, ;,,,,,,, 5. 8,,,,,,,,,, ; ;,,,,,,,,,, m

168 159,,,,,, 1., : (, ), 20m, 20m, m, 5-55,, 1 u ( u 40 ), 1, 2, 3, 4,, 40,,, D ; v 0 1 D 01 ; d ( 5-56) ; K ; D i z ( i = 1, 2,, 40) ; V i ; i D iz ; A ;

169 : : D 01 + v 01 = D 1 z + V 1 + K + Asin( ) D 01 + v 01 + d = D 2z + V 2 + K + Asin( ) D 01 + v d = D 4 0z + V K + Asin( ) V 1 = ( v 01 - K) - Asin( ) + ( D 01 - D 1z ) V 2 = ( v 01 - K) - Asin( ) + ( D 01 + d - D 2 z ) V 40 = ( v 01 - K) - Asin( ) + ( D d - D 40 z ) 1 = D 1z = 1 + d 360= = 1 + d + d 360 = = ( 5-69) ) d, = d 360 ( 2 1 = X = Acos 1 Y = Asin 1,,, X Y A = X 2 + Y 2 1 = arctan Y X A 1, 1. v i = Asin[ 1 + ( i - 1) ] ( 1 ), A B, AB 200m, AB C,

170 A B C, 5-57 ( 2 ) A C B, A D AC D AB ; C D AC D CB ; B D AB D CB ( 3 ) D AB D AC D CB, K = D AB - ( D AC + D CB ), 2., K, R ( ),,, 21, 0, 1, 2, 3, 4, 5, 6, : D 01 D 02 D 03 D 04 D 05 D 06 D 12 D 13 D 14 D 15 D 16 D 23 D 24 D 25 D 26 D 34 D 35 D 36 D 45 D 46, 21 D 01 D ; v 01 v ; D 01 D D 56 D v 01 + K + D 01 R = D 01 D v 02 + K + D 02 R = D 02 : D v 56 + K + D 56 R = D 56 v 01 = - K - D 01 R + l 01 v 02 = - K - D 02 R + l 02 ( 5-70), l 01 R v 56 = - K - D 56 R + l 56 l 5 6, l 01 = D 01 D 01 K

171 , 5-58 NTS-355, 5, 2 mm + 2ppmD( D ),,,, 1. ( ), 5-59, 360, 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; 22. ; 23. CE NTS ,,,

172 , 3, 0. 1 OPTON 5-60, 1, 6 4,, 7 2 ;, 4, ( ),, ( ) L ( ) T, ( ) 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; L, T, ( ) : Z = Z L + L V = V L + L ( 5-71)

173 164 H = H L + T/ tanz = H L + TcotZ = H L + TtanV ( 5-72), Z ( ) ; Z L ( ) ( L ) ; V L ( ) ; V ( ) ; H ( ) ; H L ( ) 3., :,, ;, ;,, 4.,,, ; ; ; ( 1 ) 5-61, S 1 S 2, h A1 h A2, P 1 P 2 C h 12 : C = S S 2 2-2S 1 S 2 cos h 12 = h A2 - h A1 ( 5-73) 5-61 ( 2 ),, 5-62,,,,, : H 1 = h 1 + h 2 h 2 = Ssinz 1 ( cotz 2 - cotz 1 ) ( 5-74)

174 , 5-63 TPS110,, :,, CCD,,,,,,,,, 5-63 TCA2003

175 ,,,,, ( ),, 5-64, A B h AB, A, B I A i, B M, B v, IM IN, A B S, 5-64 h AB : A H A, B : h AB = Stan+ i - v ( 5-75) H B = H A + h AB = H A + Stan+ i - v ( 5-76) 5-64,, Stan,, Stan A ( + ), B, i v, D, A B : h AB = Dsin+ i - v ( 5-77), ;,,

176 167 1.,, A B,,,,,,,,,,,,,,,, ( ) , S 0 A B A, ib, v, R A B PE AF P A PCPEP, PN P PN PM,, N, A P N 5-65

177 , A B : h 12 = BF = MC + CE + EF - MN - NB ( 5-78), EF i; NB v; CE MN CE = 1 2R S2 0 MN = 1 2R S2 0, R PNN R = K, R K MN = K 2R S2 0 A B S 0 R ( S 0 = 10km, S 0 5), PC OM, PCM90, PCM ( 5-78) MC : MC = S 0 tan ( 5-78), A B : 1 - K 2R h 12 = S 0 tan+ 1 2 R S2 0 + i - = S 0 tan+ 1 - K 2R S2 0 K 2R S2 0 + i - v = C, C, : - v h 12 = S 0 tan+ CS i - v ( 5-79) ( 5-79), i v, S 0, d : h = Dsin+ ( 1 - K) D2 2R cos2 + i - v ( 5-80), h,, D, K, i, v , H A H B A B ( ), H m = 1 2 ( H A + H B ), mm S 0 ( 10km ), S : S 0 S = R + H m R = 1 + H m R S 0 = S( 1 + H m R ) ( 5-81)

178 S 0, y m S S d : S = d( 1 - y 2 m 2R 2 ) ( 5-82) A B ( 5-82) ( 5-81), 4. S 0 ( 5-81) ( 5-79), h 12, CS 2, S 0 S 5. ( 5-82) ( 5-84),, h = dtan ( 5-85) : = d( 1 + H 2 m R - ym ) ( 5-83) 2R 2 = Stan 12 ( 1 + H m R ) + CS2 + i - v ( 5-84) h 12 = dtan+ Cd 2 + i - v + dtan ( H 2 m R - ym ) 2R 2 = dtan+ Cd 2 + i - v + h ( H 2 m R - ym ) ( 5-85) 2R 2 h 12 = h ( H m R - 2 y m 2R 2 ) ( 5-86) h 1 2 = dtan+ Cd 2 + i - v + h 12 ( 5-87)

179 170 ( 5-87) d ( 5-86) H m R, H m, H m R H m = m, h = 100m, H m R 0. 02m,,, y m = 300km, h = 100m, y 2 m 2R m 0. 1m, y2 m h 2R m,, ( 5-87) h 12 H m hy m 6., A B 12, B A 21 ( 5-87 ) A B : B A : h 12 h 21 = dtan 12 + i 1 - v 2 + C 1 2 d 2 + h 1 2 = dtan 21 + i 2 - v 1 + C 2 1 d 2 + h 2 1, i 1, v 1 i 2, v 2 A B ; C 1 2 C 2 1 A B B A,, K, C 12 h 12 h 2 1 : : h 12( ) = dtan 1 2 ( ) ( i 1 + v 1 ) - h 12 = H m R - 2 ym 2R 2 h h= dtan 1 2 ( ) = C 21, 1 2 ( i 2 + v 2 ) + h 12 ( 5-88),,,, ;,,, 1mm,, 1mm,,

180 171,,,, K,,,, K,,,, 10 16, K ,,, 400m,,,,,,, ; ;,,,, m 2. 0, 2 km,, m 1. 5, 3. 5km, ; 1. 2km

181 ,,,,,,,,,,,,,,,,,,,,,,,, ; ;,,, ;,,,,,,,,,, GPS( Global Positioning System) 1.,, ( ) ( ),,,, ( 6-1 ), ( 6-2),

182 ,,,, (, ), ( ), ( ),,,,, 3. ; ; 4., ( ),,,,,,,,,, 6-3, 20 25km,,, 13 km,, 8km, 2 6km15 20km 2, , ,,

183 , ( km) ( ) DJ1 DJ2 DJ6 ( ) / / / / /

184 ( km) ( km) ( ) ( mm) DJ1 DJ2 DJ6 ( ) n 1 / n 1 / n 1 / n 1 / n 1 /6 000 : n 10km 2,,,,,,,,, 5. GPS GPS GPS 20 80, ( GPS), GPS GPS GPS, A B C D E GPS, ( GPS) A 27 B 818, ( GPS) A 6-4,,,,,,,, 6-5,,,,, 6-3,,,,

185 ( GPS) A, 6-3 / mm / km / mm / mm R 4 L R 12 L R 20 L L : R, km; L, km,

186 , GPS,,,,,,,,,,,,,,, ;, ;, :, ;,,,,,

187 ( ; ),,,,, ( ), ( )

188 ( GPS), , AB AB, B, ( 6-11( a) ), BC BC : ( 6-11( b) ), BC BC : ( 6-1) ( 6-2) : BC = AB ( 6-1) BC = AB ( 6-2) = 180 ( 6-3) ( 6-3),, +,, - 360, 360,, 360

189 , A, B, A ( x A, y A ) A B S AB AB, B ( x B, y B ), , ( 6-4) : x B = x A + x AB ( 6-4) y B = y B + y AB x AB y AB, x AB y AB = S AB cos AB = S AB sin AB ( 6-5) x B = x A + S AB cos AB ( 6-6) y B = y B + S AB sin AB, 6-12, A B ( x A, y A ) ( x B, y B ), AB AB S AB :

190 181 AB = arctan y AB ( 6-7) x AB S AB = y AB = x AB = x 2 AB sin AB cos AB, x AB = x B - x A, y AB = y B - y A ( 6-8) S AB, + y 2 AB ( 6-8), ( 6-7) y AB x AB, R, 0 90,, R,, y AB x AB + + AB = R + - AB = R - - AB = 180+ R - + AB = R 6. 2,,,, ( a),, ( b),,,,, ( c),,,,

191 ( d), ( e),,,,,,,,, , 6-2, ;,, ,,,,,,,,, 2.,,,

192 183,, 3.,, 4., 6-14, i, i - 1 i + 1,, i i + 1,, i + 1, i, i - 1 i + 2,,,, 6-14,,,,,,,,,,,,,,,, ( ), ( ),

193 , : MA MA, ( 6-3), ( 6-5) ( 6-4) P 2, P 3,, P n , A B, P 2, P 3,, P n, i ( i = 1, 2,, n + 1), S i j, 6-16 B, x B y B, x B y B, f x f y, f x f y = x B - x B ( 6-9) = y B - y B,,, : : v x = - f x ij SS ij v y = - f y ij SS ij x i j y i j = x ij + v xij ( 6-10) ( 6-11) = y ij + v yij, ( 6-4 ) P 2, P 3,, B( P n + 1 )

194 185,, B,, f S S, k, k = 1 S f S ( 6-12), f S = f 2 x + f 2 y , B, MA BN B N,, BN 6-17 BN, f, f = BN - B N ( 6-13), f, v i, i, : v i = - f n + 1 ( 6-14) i, : v i = f n + 1 ( 6-15),,,, m 2 n + 1, f = 2 n + 1m ( 6-16) 6-5

195 S x y x y M ( ) ( ) / m / m / m / m / m A( P 1 ) P 2 P 3 P 4 P 5 B( P 6 ) N = n - 0 = = f S = f x = m f y = m = f 2 x + f 2 y = m x B - x A = m y B - y A = m f = - 42 ; f = 406 = 97 ; K = f S = S = < ,,,, 6-18

196 187 v i : f = [ ] n 1 - ( n - 2) 180 ( 6-17) v i = - f n ( 6-18),,, ( 6-19) : f x f y = [ x] n 1 = [ y] n 1, x i y i ( 6-19),,,, 5., :,,,,,, 6-19, A( x A, y A ) B( x B, y B ), S AB AB AB ; i S i i S i ; ( x i, y i ) ( x i, y i ) A1 A1,,, AB x AB y AB S AB AB 6-19, Q, : A1 S A1 = S A2 = = S Ai = = S AB = Q ( 6-20) S A1 S A2 S Ai S AB - A1 = A2 - A2 = = Ai - Ai = = AB - AB = ( 6-21) x Ai = x i - x A = S Ai cos Ai ; y Ai = y i - y A = S Ai sin Ai, ( 6-20) ( 6-21),

197 188 Q 1 x Ai y Ai = Qcos, Q 2 = Qsin, = QS Ai cos( Ai + ) = QS Ai ( cos Ai cos- sin Ai sin ) = QS Ai sin( Ai + ) = QS Ai ( sin Ai cos+ cos Ai sin ) x Ai y Ai i B, ( 6-22 ) : x AB y AB = Q 1 x Ai - Q 2 y Ai = Q 1 y Ai + Q 2 x = Q 1 x AB - Q 2 y AB = Q 1 y AB + Q 2 x AB Ai ( 6-22), x AB y AB, x AB y AB Q 1 Q 1 Q 2 = x AB x ( x AB ) 2 = x AB y ( x AB ) 2 + y AB y AB + ( y AB ) 2 - y AB x AB + ( y AB ) 2 Q 1 Q 2 ( 6-22), x i = x A + Q 1 ( x i - x A ) - Q 2 ( y i - y A ) y i = y A + Q 1 ( y i - y A ) + Q 2 ( x i - x A ) k, Q 2, ( 6-23) ( 6-24) k = 1 S AB f S, f S = S AB - S AB, S AB S AB ( 6-8) 6-6 ( 6-25) 6-6 A B x y x / m / m / m /m y / m x / m y / m Q 1 = Q 2 =

198 189 D AB = m; D AB = m; f D = D AB - D AB = m; k = f D 1 = D AB < , A B C, A B B C C, J, : 6-20 ( 1 ) ( JJ ) Z 1 Z 2 Z , n 1 n 2 n 3, P 1 = C 1 n 1 P 2 = C 1 P n 3 = C 1 ( C 1 2 n 3 : ), JJ J J = P P P 3 3 ( 6-26) P 1 + P 2 + P 3, JJ,,,

199 190 ( 2 ) ( x 1, y 1 ) ( x 2 y 2 ), ( x 3, y 3 ) S 1 S 2 S 3, P 1 = C 2 P 2 = C 2 P 3 = C 2 ( C 2 S 1 S 2 S 3 ), : x J = P 1 x 1 + P 2 x 2 + P 3 x 3 P 1 + P 2 + P 3 y J = P 1 y 1 + P 2 y 2 + P 3 y 3 P 1 + P 2 + P 3 ( 6-27) J,, Z 1 Z 2 Z 3 ( 3 ),, f i, = 1 r, f f n ( 6-28) = 1 r v v n ( 6-29), n, n ; r ( 1) x y,, x = 1 r y = 1 r, f x f x [ S] f y f y [ S] ( 6-30) x = 1 r y = 1 r v x v x [ S] v y v y [ S] ( 6-31), [ S] [ S], :

200 191 J : km = 2 x + 2 y ( 6-32), P J = P 1 + P 2 + P 3 m i 1 = km ( 6-33) P J,,,, 1., 6-21,, A B, B A,,, ( 5 ), A B, B A,,, ,,,, 6-22 de ee, BB ef ( 6-23), BB, 6-22, BB : tan= f y f x,, 90,,

201 ,, , A( P 1 ), P 2, P 3,, P n + 1, 1, 2,, n, S 6-24,,,, m t,,,, m u P n + 1 :, P n + 1 A S = ns,

202 193 : m s = S P n + 1, m t = m s = S ( 6-34) : 1 d 1,, P n + 1 u 1, u 1 = ns d 1, 2 d 2,, P n + 1 u 2, u 2 = ( n - 1) s d 2, 1, 2,, n d 1, d 2,, d n, P n + 1 : P n + 1 : m u P n + 1 : u = u 1 = ns d 1 + u u n + ( n - 1) s d 2 = m s n 2 + ( n - 1) = m s n( n + 1) ( 2n + 1) s d n m S n ( 6-35) ( 6-36) M P = m 2 t + m 2 u = 2 S + m 2 S n n+ 1 3 ( 6-37) ( 6-34) ( 6-36 ) ( 6-37) :,,, 2. A B ( 6-25 ),,,,,,,,,,,,, m t = S i ( i = 1, 2,, n + 1 ), i d i, v i, i, d i 6-25 : MA + [ ] - ( n + 1) 180- BN = 0

203 , f = MA + [ ] - ( n + 1) BN [ v] + f = 0, (, ), : v 1 = v 2 = = v n + 1 = - f n + 1 i d i : f i = i + v i = i - n + 1 = i - 1 n + 1 { MA + [ ] - ( n + 1) 180- B N } 1 d i = d i - n + 1 [ d ] ( 6-38) ( 6-35) d i d i u : ( 6-38), : u = ns d 1 + ( n - 1) s d s d n u = s n d 1-1 n + 1 [ d ] + ( n - 1) d 2 - = s nd 1 + ( n - 1) d d n - = s nd 1 + ( n - 1) d d n - = s n 2 d 1 +, m u m u : = m s 2 = m s n n + 1 [ d ] + + d n - n + ( n - 1) [ d ] n + 1 n 2 [ d ] n 2-1 d 2 + n 2-1 d n - + n n( n + 1) ( n + 2) 24 n 2 d n n + 1 [ d ]

204 195 m S n : M = m 2 t + m 2 u = 2 S + Sm 2 n ( 6-39), S, n ( ), M( ), ( 6-39) ( 6-37) :,,,, 3., K( 6-26), K A B S/2 K, A B K, A( B) K,, K 6-26 A( B) K m K, S/2 n ( 6-39) S n, K : m K 2 S m K = 2 + Sm = m K 2 = S + Sm 2 n n ( 6-40) 6. 3,,,,,,

205 , A B ( x A, y A ) B( x B, y B ),, 6-27 AB AB S AB, AB AP, AP S AP,, P, x B x P = x A + S AP cos AP y P = y A + S AP sin AP A B P, AP = AB -,, x P = x A + S AP cos( AB - ) = x A + S AP ( cos AB cos+ sin AB sin ) y P = y A + S AP sin( AB - ) = y A + S AP ( sin AB cos- cos AB sin ) - x A = S AB cos AB, y B : - y A = S AB sin AB, x P = x A + S AP sin S AB [ ( x B - x A ) cot+ ( y B - y A ) ] y P = y A + S AP sin S AB [ ( y B - y A ) cot- ( x B - x A ) ] S AP sin = sin S AB sinp ( 6-41), sin= sin sin = sin( + ) x P = x Acot+ x B cot+ ( y B - y A ) cot+ cot y P = y Acot+ y B cot- ( x B - x A ) cot+ cot 1 cot+ cot ( 6-41) ( 6-42) ( 6-42),,, : ( 6-42) ABP A( ) B( ) P ( ) A B P, :

206 197 x P = x Acot+ x B cot- ( y B - y A ) cot+ cot y P = y Acot+ y B cot+ ( x B - x A ) cot+ cot ( 6-43),, 6-28, 6-28 ABP A B 1 1 P ( x P, y P ), BCP B C 2 2 P ( x P, y P ), e, P,, e = M ( x P - x P ) 2 + ( y P - y P ) M( mm), P ( ) : M P = m S AB sin 2 sin2 + sin 2 ( 6-44) ( 6-44) : m S AB, ( ), /m /m P A B P x P y P cot x A y A cot x B y B x P y P

207 198 /m /m B C cot x B y B cot x C y C x P y P e = ( x P - x P ) 2 + ( y P - y P ) 2 = 0. 01m0. 2m( M 1 000),,, 6-29, A B C, P PA PC, PB PC, P PAC PBC, C, P P A B C ( ), P, ( P 1 /5), P,, P ABC, , A B C,, a b, 1 2, P = 360- ( + + ) ( 6-45)

208 199 a sin 1 sin = bsin 2 sin sin 1 = bsin sin 2 a sin = = ( + + ) = = sin 1 = bsin sin 2 a sin tan 2 = sin( - 2 ) = sincot 2 - cos sin 2 sin + cos ( 6-46) 2, ( 6-45) 1, P ( 6-46), ( ), P : x P = P Ax A + P B x B + P C x C P A + P B + P C ( 6-47) : y P = P Ay A + P B y B + P C y C P A + P B + P C P A = P B = P C = 1 cota - cot 1 cotb - cot 1 cotc - cot ( 6-48), : A B C A B C( 6-8 ), P A B C R a R b R c, A B C, P R a R b R c, A = AC - AB B = BA - BC C = CB - CA = R c - R b ( 6-49) = R a - R c ( 6-50) = R b - R a

209 200 ( 6-47) ( 6-48), A B C P, A B C x A y A x B y B x C y C x P = P A x A + P B x B + P C x C P A + P B + P C y P = P A y A + P B y B + P C y C P A + P B + P C P A = P B = P C = 1 cota- cot 1 cotb - cot 1 cotc - cot AB A P A x P BC B P B y P CA C P C ,, A B C D,,, P,,,,, 6-30, A B C, P, A B C, a b c AB CB S AB S CB ABP, AP = AB - A, cosa = S2 AB + a 2 - b 2 2a S AB x P = x A + a cos AP ( 6-51) y P = y A + a sin AP

210 , BCP, cosc = S2 CB + c 2 - b 2 CP 2cS CB = CB + C x P = x C + ccos CP ( 6-52) y P = y C + csin C P ( 6-51) ( 6-52),, P,,,, , k i N ki, ki 6-31 :

211 202 ki = Z k + N ki = Z 0 k + k + N ki + v ki ( 6-53), k Z 0 k, v ki ki N ki k i ( x 0 k, y 0 k ) ( x 0 i, y 0 i ), ( x k, y k ) ( x i, y i ), ki = arctan y i - y k = ( y 0 i x i - x k,, ki = y0 ki 2 x k - S 0 ki + y i ) - ( y 0 k ( x 0 i + x i ) - ( x 0 k + y k ) + x k ) ki = 0 ki + ki ( 6-54) 0 ki = arctan y0 i - y 0 k x 0 i - x 0 k x 0 ki 2 y k -, 0 kiki, S 0 ki S 0 ki y 0 ki 2 x i + x0 ki S 0 ki S 0 ki 2 y i ( 6-54) ( 6-53), S, x k, x i,, : a ki v ki = - k + a ki x k + b ki y k - a ki x i - b ki y i + l ki ( 6-55) = sin 0 ki ; b 10 4 S 0 ki = - ki cos 0 ki ; l 10 4 S 0 ki = 0 ki - N ki - Z 0 k ki ( 6-55), l Z 0 k ( ), y k y i, n k k Z 0 k = 1 n k n k ( 0 kj - N kj ) j = 1 k, i, x i = = 0, ( 6-55) : y i v ki = - k + a ki x k + b ki y k + l ki ( 6-56) ( 6-56) k, - 1,, k, v k1 = a k1 x k + b k1 y k + l k1 v k2 = a k2 x k + b k2 y k + l k2 v kn = a kn x k + b kn y k + l kn v k = [ a ] k x k + [ b] k y k + [ l] k v k m,, P = 2 / m 2, P M = n 2 /m , k i S ki, v S,, ki

212 203 : S ki + v Ski = [ ( x 0 i + x i ) - ( x 0 k + x k ) ] 2 + [ ( y 0 i + y i ) - ( y 0 k + y k ) ] 2,, : v S ki = c ki x k + d ki y k - c ki x i - d ki y i + l S ki ( 6-57) c ki d ki = - x0 ki S 0 ki = - y0 ki S 0 ki = - cos ki = - sin ki : l S ki = S 0 ki - S ki S 0 ki = ( x 0 i - x 0 k ) 2 + ( y 0 i - y 0 k) 2 ( 6-57), k, i, x i = y i = 0, v S ki = c ki x k + d ki y k + l S ki ( 6-58) m s,, P S = 2 x k A i, y k B i, L i, P i, : v i = A i x k + B i y k + L i,,, :, : [ PAA] x k + [ PAB] y k + [ P AL] = 0 [ PAB] x k + [ PBB] y k + [ P BL] = 0 x k = y k = [ PAB] [ P BL] - [ P BB] [ P AL] [ P AA] [ PBB] - [ PAB] 2 [ PAB] [ P AL] - [ P AA] [ P BL] [ PAA] [ PBB] - [ PAB] 2 x k = x 0 k + x k 10 y k = y 0 k + y k 10 m 2 S ( 6-59) 2,, : ki = ( v ki S ki / ) 2 + v 2 S ki

213 ,, ( ),,,,,,,,, GPS,, :, ( 6-1 ),,, ;, ( 6-2 ),,, ( 6-2 ( a) ) ( 6-2 ( b) ) : ( ) ; ( ) : ( ), ( ) 6-32, A B C D a i b i c i, a i b i c i,, ( ), a i b i, b i, ( ), c i : 1. ( 1 ) 180,

214 f i = a i + b i + c i ( 6-60),, : v a i = v bi = v c i = - ( 2 ) f i 3 ( 6-61) 6-32,,, AB CD 0 n, c i ( + ; - ),, n, f, f = n - n, (, ) : v c i = f n,,, :, : v a i = v b i = - v c i 2 ( 6-62) v a i = - v bi = - f i 3 f 2 n f i 3 f 2n ( 6-63) 2. v c i = - f i 3 f n AB( S 0 ),

215 206 S 1 = S 0 sina 1 sinb 1 sina 2 sina 1 S 2 = S 1 = S 0 sina 2 sinb 2 sinb 1 sinb 2 S n = S n - 1 sina n sinb n = S 0 sina 1 sinb 1 sina 2 sinb 2 sina n sinb n, : S 0 sina 1 sina 2 sina n S n sinb 1 sinb 2 sinb n = 1 ( 6-64), : S = S 0 sina 1 sina 2 sina n - 1 ( 6-65) S n sinb 1 sinb 2 sinb n F = S 0 S n sina 1 sina 2 sina n sinb 1 sinb 2 sinb n ( 6-66) S = F - 1 ( 6-67) S a i b i, S, a i b i da i db i ( a i ), : b i S 0 sin( a 1 + da 1 ) sin( a 2 + da 2 ) sin( a n + da n ) S n sin( b 1 + db 1 ) sin( b 2 + db 2 ) sin( b n + db n ) da i db i a i b i, : = 1 ( 6-68) f( x + x) = f( x) + f ( x) x ( 6-69) f ( x), F a i b i : F = S 0 sina 1 sina 2 cosa i sina n sina i a i S n sinb 1 sinb 2 sinb i sinb n sina i F = S 0 sina 1 sina 2 sina i sina n cosb i b i S n sinb 1 sinb 2 sinb i sinb n sinb i = Fcota i = - Fcotb i,, : da 1 = da 2 = = da n = da db 1 = db 2 = = db n = db, ( 6-68) ( 6-69 ) ( 6-70) ( 6-71) ( 6-66) : F + Fcota da - F cotbdb = 1 ( 6-70) ( 6-71) Fcotada - F cotbdb + S = 0 ( 6-72)

216 207 F 1, da = - db, : da = - db= - S cota + cotb ( 6-73) :,,, 3. AB( S 0 ), : S 1 = S 0 sina 1 sinb 1 ; S 2 = S 1 sina 2 sinb 2 ; ; S n = S n - 1 sina n sinb n, CD( S n ), 4.,,, 6-9, cota cotb / m a b c a b c

217 208 cota cotb / m a b c a b c f = - 9 S = da = - db = x v x y v y x y / m /m /mm / m / mm /m /m A B C D f x = m, f y = m, f S = f 2 x + f 2 y = m

218 , A B, i i i 6-33,,,, f i = i + i + i ( 6-74) - 360= 0 ( 6-75),, S = sin 1sin 2 sin n - 1 ( 6-76) sin 1 sin 2 sin n ( 6-74) ( 6-75 ) ( 6-76),, 6-34, A B, C D 8, = = = 360 ( 6-77) sin 1 sin 2 sin 3 sin 4 = 1 ( 6-78) sin 1 sin 2 sin 3 sin 4

219 ( 6-77) ( 6-78 ),, 6. 5,,,,,, 1985,,,,,, ( 6-35 ( a) ), ( 6-35( c) ),,,,, ( 6-35( b) ),, ( 6-35 ( d) ) ;, ( 6-35 ( e) )

220 ,,,,,,, i,,,, ;,,,, : 100m,,, 1. 5mm, 100m,, m,, 6-36, 6-36 ( a), I 1 b 1 I 2 b 2, 10m, 6-36( b) ( c), I 1 b 2 I 2 b 1,, 6-37,,,, 1 /25 000, 5,,,,

221 , 6-36 ( a) I 1, b 1,, B 1 I 2,, A 1, I 2 I 1,, B 2, b 2,, A 2 b 1 b 2 : h b1 b 2 = 1 2 [ ( B 1 - A 1 ) + ( B 2 - A 2 ) + ( h b1 I 1 + h I2 b 2 ) ], h b1 I 1 h b2 I 2 b 1 I 1 b 2 I 2 i,, 6-36( b) ( c) I, b, b 1 b 2,,, : ( 1 ), ( 2), 1m

222 213, ( 3 ), M M w ( 4),, ( 5 ), ( 3. 6) ( ) , A B, 1, 2, 3,, n - 1, h i ( i = 1, 2, 3,, n) : 6-38 ( 1 ), A B, f h, f h = H A + h 1 + h 2 + h h n - H B = [ h] - ( H B - H A ) ( 6-79) v i,,, : [ v i ] + f h = 0 ( 6-80) P i = C L i P i = C n i ( 6-81), C, L i, n i : ( 6-81),, v i = - f h [ L] L i v i = - f h [ n] n i ( 6-82), h i H i, ( 2 ) h i = h i + v i H i = H A + h 1 + h h i ( 6-83)

223 214 : =, N, t :, P i = C C + [ L] i 1 [ L] n i + 1 m i [ P vv] n - t = P i, :, ( ),, : ( 6-79),,, ;, ( 6-82 ),,, ( 3 ) 6-11, A B, h / m L / km P = 1 L v /mm H /m Pvv ( 1) ( 2) ( 3) ( 4) ( 5) ( 6) ( 7) A 1 2 B f h = h + ( H A - H B ) = ( ) = - 33 mm : = [ Pvv] N - t 1 : m 1 = P 1 = : m 1 = P 2 = = = 7. 6 mm 3-2 = mm = mm

224 215 2.,, ( 6-79 ), H A = H B, : f h = h 1 + h h n = [ h] ( 6-84) ( 6-84) 3.,,,,,,, ( ) :,,,,,, 6-39, A 1 A 2, D, h i, L i A A 1 A H i, P i, A 3 H i = H Ai + h i ( 6-85) P i = C/ L i, i = 1, 2, 3,,, H D = P 1 H 1 + P 2 H 2 + P 3 H 3 P 1 + P 2 + P 3

225 216, H 0 H D = H 0 + [ P ] [ P ] D, 1 = H 1 - H 0, 2 = H 2 - H 0, 3 = H 3 - H 0 2. ( 6-86),, v i f i : v i = - f i = H D - H i, i = 1, 2, 3 ( 6-87) ( 6-82), ( 6-83 ) 3. ( 1 ) : = [ Pvv] n - 1, n, v ( 2 ) m D :, P D = P 1 + P 2 + P 3 4. m D = 6-39, 6-12 P D 6-12 / m h / m L /km P = 100 L / m / mm P v / mm Pvv ( 1) ( 2) ( 3) ( 4) ( 5) ( 6) ( 7) ( 8) ( 9) ( 10) ( 11) 1 A A A H 0 = D : H D = H 0 + [ P ] = [ P] = m : = [ Pvv] n - 1 = = 22. 1mm 3-1 D : m D = = = 5. 0mm P D 19. 7

226 217 ( ) 1.,, :,, 6-40,, F ; Z 1, 2 Z 1 Z 2 Z 1, 2 Z 3 Z 1, 2 + 3, F, Z 1, Z 4 Z Z 1, 2 E : : : Z 1, F : : : H E( 1, 2 ) = P 1 ( H A + h 1 ) + P 2 ( H B + h 2 ) P 1 + P 2 ( 6-88) P 1, 2 = P 1 + P 2 = C L 1 + C L 2 ( 6-89) L 1, 2 = C P 1, 2 = L 1 L 2 L 1 + L 2 ( 6-90) H F ( 1, 2 + 3) = H E( 1, 2 ) + h 3 ( 6-91) L 1, = L 1, 2 + L 3 ( 6-92) P 1, = C L 1, ( 6-93),, F, Z 1, E

227 218 E F, Z 1 Z 2 Z 3 Z 4 Z 5 2. : = [ Pvv] r, v, r( ) F :, P F = P 1, P 4 + P 5 3. m F = P F ,, H h L 1 / L P / [ P] v Pvv /m /m /km / m / mm Z 1 A - E Z 2 B - E Z 1, 2 ( R) - E H E = Z 3 E - F Z 1, ( R) E - F Z 4 C - F Z 5 D - F H F = = [ Pvv] r = = 4. 5mm; M F = = 5. 7 mm; M E = = 5. 3 mm 0. 73

228 219,,,, : : P = C 2S 2, S,, C P = C S ( GPS) ( GPS, Global Positioning System) GPS, GPS : GPS GP S GPS, GPS ( GPS ) 1. GPS GPS 24, 21, 3, 24 6 ( 6-41 ), 55, 60, km, GPS, 4 GPS, GPS 4, GPS, GPS : L 1 ( C/ A P ) ; L 2 ( P ), :,, L 1 ( 19 ) L 2 ( 24 ) C/ A GPS,, C/ A 1ms, 1 023, m, m, C/A L 1, P, 7, 6. 2, 29. 3m, 2. 93

229 GPS L 1 L 2,, P, 2. GPS 9, 5, GPS,, 1,, 3,,,,, 3. GPS GPS, GPS,, GP S GPS ;, 1. GPS GPS ( t) ( c),

230 221 GPS, t, t,,,,, t, : = c t ( 6-94) ( ), WGS - 84 ( x s, y s, z s ), ( x, y, z), : = ( x s - x) 2 + ( y s - y) 2 + ( z s - z) 2 ( 6-95),,, =,, ( x s, y s, z s ),,, ( x, y, z), 4, 4, 2. GPS,,,, 1 2mm t 0 GPS, S ( S), K, ( K), = ( K) - ( S), 0, t 0 : = = ( N 0 + ) ( 6-96),,, 6-42, t i, i, N 0 t k, k, Int( ), t i t k,, N 0, t k : k = N 0 + Int( ) + k ( 6-97) ( 6-97) ( 6-96),,,

231 ,,, Int( ) N 0, N 0 + Int( ) GPS GPS, ( ), GPS,,, GPS, GPS,,,,, 1 2, GPS, GPS,,, ( RTK, Real Time Kinematic), GP S, GPS, GPS : GPS ; GPS ; GPS GPS,, GPS, GPS

232 223,,, GPS,, GPS,,,,,,,,,, GPS,, GPS,, GPS,, GPS, GP S GPS GPS, GPS GPS, 6-43 N GPS, : 6-43 GPS n b = N N N - 1 GPS, GPS 6-43 GPS, 6-44 GPS N3, GPS ( ), : n r = n b - ( N - 1) = ( N - 1) N - 2 2, GPS, GPS, GPS

233 GPS, GPS GPS,,, GPS GPS GPS , GPS,,, 2., 6-46 GPS,,,, , 6-47,,,,,

234 225 4.,, 4 GPS,, GPS, 5 6 GPS, GPS 6-48, 16, 22 GPS, GPS GPS, GPS, GPS, GPS GP S GPS GPS,, GPS,,,, ( ),,,,, GPS GPS,, GPS

235 ,, ;,,,,, ( ), ( ),,,, ( ),,,, :,,,,,, :, ; ;, ; ; ; ;,,,,,,

236 227 1.,, 60cm2 4cm,,,,,,,,, :,,,,, mm,,,,, 10cm10 cm, : 0. 3mm;,

237 mm; 0. 2 mm,,, 7-2, 2 x 2 = m y 2 = m, 2 klnm, m n ( ) mm, a b, k m mm, c d ab cd 2 7-2,, ( ), 0. 3mm,, 3. ( 1 ),, ( 2),, ( 3 ), ( ),,, ( 4 ) ( 2) ( 3), ( 5 ),,,, ( ) 7-3, A,,

238 229 B ( ) A, a, P, ( ),,, P, 7-3 GPS, : GPS :,, GPS,,,,,,,,,,,,

239 230, :,,,,,,,,,,,,,,,,,,,,, ( ),, 1cm,,,,,,,,,,,, ;,,, ( ) 7. 2, 1. ( P ),,,,,, 7-4 ( a) 0, : x = x P + S 0 cost 0 ( 7-1) y = y P + S 0 sint 0,,,

240 231, 4, 7-4( b) 1 2, 3 4, S i l i ( i = 0, 1, 2, 3, 4), : : 2 : 3 : x = x P + ( S 1 + l 1 ) cost 1 ( 7-2) y = y P + ( S 1 + l 1 ) sint 1 x = x P + ( S 2 - l 2 ) cost 2 ( 7-3) y = y P + ( S 2 - l 2 ) sint 2 4 : x = x P + S l 2 3 cos( T 3 + arctan l 3 S 3 ) y = y P + S l 2 3 sin( T 3 + arctan l 3 S 3 ) ( 7-4) x = x P + S l 2 4 cos( T 4 - arctan l 4 S 4 ) y = y P + S l 2 4 sin( T 4 - arctan l 4 S 4 ) ( 7-5) ( 7-1) ( 7-5), x P y P, T i, 2., ( 1 ) 7-5, A B, x A y A x B y B, J, A B J, :

241 232 T AJ = T AB - S AJ = S AB sin sin( + ) ( 7-6) x J = x A + S AJ cost AJ y J = y A + S AJ sint AJ, T AJ AJ ; S AJ A J ; ( 2 ) 7-6, P, x P y P, J T P J AB, A x A y A, A B T AB, J : x J = ( L 1 L A - L 2 L P ) / LL y J = ( M 1 L A - M 2 L p ) / LL L 1 = sint P J M 1 = cost P J L 2 = sint AB M 2 = cost AB ( 7-7) LL = L 1 M 2 - L 2 M 1 L p = M 1 x p - L 1 y p L A = M 2 x A - L 2 y A PJ AB, J, P AB, L 2 = - M 1 M 2 = L 1 L A = L 1 x p + M 1 y A L p = M 1 x p - L 1 y p, ( 7-7) : x J = L 1 L A - L 2 L p y J = M 1 L A - M 2 L p P AB, L 2 = M 1, M 2 = - L 1, L A = - L 1 x P - M 1 y A, L p = M 1 x P - L 1 y P, ( 7-7 ) : 3. x J = - L 1 L A + L 2 L P y J = - M 1 L A + M 2 L P, ( 1 ) 7-7, A B S AJ S BJ, A B x A y A x B y B, A B J, J : x J = x A + S AJ cos( T AB - ) y J = y A + S AJ sin( T AB - ) ( 7-8)

242 233 : = 2 arccos L( L - S BJ ) S AJ S AB ( 2 ) L = 1 2 ( S AJ + S BJ + S AB ) 7-8, A B, x A y A x B y B, J, JA JB , S BJ, J : J AB, J AB, : x J = x A + S AJ cos( AB - ) y J = y A + S AJ sin( AB - ) x J = x A + S AJ cos( AB + ) y J = y A + S AJ sin( AB + ) ( 7-9) ( 7-10) ( 3 ) S AJ = S 2 AB - S 2 BJ = arcsin S BJ S AB, ( 7-9 J A J B ),, S 1 S 2 J 1 J 2 : 7-9 S = ( x B - x A ) 2 + ( y B - y A ) 2 ( 7-11)

243 234 x 1 = x A + S 1 S ( x B - x A ) y 1 = y A + S 1 S ( y B - y A ) ( 7-12) 4. x 2 = x A + S + S 2 ( x B - x A ) S y 2 = y A + S + S 2 ( y B - y A ) S ( 7-13) 7-10, P, A, J, AJ S, PJ T P J, J : x = x A + Scos( T P J + r) y = y A + Ssin( T P J + r) ( 7-14), r = arcsin S AP S sin, S AP = ( x A - x P ) 2 + ( y A - y P ) 2, = T P J - T P A, T P A = arctan y A - y P x A - x P 5. ( ) 7-11, A B AB, A x A y A, J, J AB JM, S AM S MJ, : x M = x A + S AM cost AB J AB, J AB, y M = y A + S AM sint AB x J = x M + S MJ cos( T AB - 90 ) y J = y M + S MJ sin( T AB - 90 ) x J = x M + S MJ cos( T AB + 90 ) y J = y M + S MJ sin( T AB + 90 ) ( 7-15) ( 7-16), ( ) ( ), :

244 235 H = H klsin2+ i - v : H 0, i, v, k ( k = 100), l, : H = H 0 + Dsin+ i - v : H 0, i, v, D, :,,,,, ;,, ;,,,,,,,, 1.,

245 236,,,, 2.,,,,, 3.,,,,,,, : ( 1) ( ) ( 7-12( a) ) ; ( 2 ) ( ), ( 7-12( b) ) ; ( 3 ) ( ),, ( 7-12( c) ) ; ( 4 ) ( ), ( 7-12( d) ) ; ( 5 ) ( ), ( 7-12( e) ) , : ( 1 ) ;

246 237 ( 2 ),, ;, ( 3 ),,,,,,,, ;,,, 1.,,,,,, ,,, 0. 5mm,,, ( ) 0. 4mm( 0. 6mm) , 3., ( 1 ), ,, m,,,, ;, ( 2 ),,,

247 238,,, ( ),, 0. 2mm,, ( 3 ),,,, 1 /2 0. 6mm,, ( 4 ),,, 1mm 1 mm,,, 4.,,,,,, 5.,,, ( ) ( ) ( ),,, 0. 5mm 1m ( m),,,,,,,,, 6.,,

248 239,,,,, 1mm( mm), 7. 4,,,, ,,,,,,,, ,,,,,,,,,,,

249 240,, 7-14 ( a ), 7-14 ( b),,,,,, ,, ( 7-15 ) ( 1 ) ( ),, ( 2 ), 0m 4,,, ( 3 ), 1 /2, ( ),,

250 ( 4 ), 1 /4,, 4., : ( 1 ),, :, ( 2 ), :,, ;,, ;,, ( 3 ),,,,, 7-16 ( 4 ), ( 5 ),,, ;,,,

251 ,,,,, ( ) :, 1.,,,,, 7-17,,,,,,,,,,,,,,,,,, 2.,,,,,

252 ,, 7-18, ; ; 7-18,,,,,,,,,,,,,,

253 ,, ;, ;, 7-19,,,,,,, 4.,,,,,,,,,, ,,,,,, 6.

254 ,,,,, 7.,, ( ), ,,, :,,,, 7-22 (

255 246 ),,,,,, :,,, : 1.,, 0. 2mm 2. ( ),, 0. 2mm ;,,, 3.,,,, 0. 2mm ;,, 4., ;, 5.,,, 0. 2mm 6., 0. 2 mm ;,,, 3 5mm 3 4 ; 7., ;

256 247 ( ), 0. 2mm 8., 9.,, 5 15, 0. 5 m, ( cm), 0. 5 m, ( dm)

257 ,,,,,,,,,, 8-1, W xb W yl, W xt W yr, 8-1, X,, Y,,,, x,, y,,,, 8-2,,, , [ ] [ 0 767],,,,

258 , mm : x = x 0 + ( Y - W yl ) /M y = y 0 + ( X - W xb ) / M ( 8-1), X Y, W xb W yl, x 0 y 0 ( W xb, W yl ), M : X v = ( x - w xl ) S x ( 8-2) Y v = ( w yt - y) S y S x = V wid th /( w xr - w xl ) S y = V he ight ( w yt - w yb ) ( 8-3), x y w xl w yb, w xr w yt, V wi dth, V h ei ght, S x S y x y,, S x S y : X P = X P 0 + ( x - w xl ) n Y P = Y P 0 + ( y - w yb ) n ( 8-4), x y, w xl w yb, X P 0 Y P 0 ( w xl, w yb ), n 1., w xl w yb, w xr w yt x y, w xl xw xr w yb y w yt,, 2., 9

259 250,,,, , : 1, ; 1, ; 1, ; 1, 0, 1, 0, ( MN) ; 0, ( EF, 0100),,, 8-3 AB, AC CB, AC, CB CD DB, CD, DB,,,, : : : : x = x A + ( w yt - y A ) ( x B - x A ) /( y B - y A ) y = w yt ( 8-5) x = x A + ( w yb - y A ) ( x B - x A ) / ( y B - y A ) y = w yb ( 8-6) : x = w xl y = y A + ( w xl - x A ) ( y B - y A ) /( x B - x A ) ( 8-7)

260 251 x = w xr y = y A + ( w xr - x A ) ( y B - y A ) / ( x B - x A ) ( 8-8) ( x A, y A ) ( x B, y B ) A B, w yt y, w yb y w xl x, w xr x 3.,,,,,,,, : ( 1) P i ( i = 1, 2,, n),, P i, P i, ( 2) P i P i - 1 ( i = 1, P 1 P n ), P i P i - 1 ;, P i P i - 1, ( 3) P 1, P 2,, P n,, ( 1) ( 2),, 8-4, P 1 P 2 P 3 P 4 P 5 P 6 Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 8-4

261 252 4.,, 8. 2,,,,,,, 20,,, ;, ;, ;,, 8-5, 8-1, 2, 1 1, 0, 1 3, 2 x, 2 y ,,,,,

262 253 1.,,, : N ( x i, y i ) ( i = 1, 2, 3,, N), D 1, D 2 D 3 D 2 = 0, ; D 3 = 0, ; 0, : D 3 = 0, 8-6( a), D 1 D 2,,, : D 2 = 0, 8-6( b), D 1 D 3, D 1, D 3, ,,,, : ( ) ( x i, y i ) ( i = 1, 2, 3,, N ), w,, 8-7,, ( x i, y i ), ( x i, y i ), 8-7 : x i = x i + l i cos( i - i 2 ) y i = y i + l i sin( i - i 2) l i = w sin( i 2), i i, i i, i : ( 8-9)

263 254 i = arctan[ ( y i y i ) ( x i x i ) ], i = 1 i = N,, 1 = n =, i = N, n = n ,,,, ;,,, 8-8, : 8-8 S = ( x i x i ) 2 + ( y i y i ) 2 n = [ S/ D 1 ] D 3 = S - D 1 n cos( ) = ( x i x i ) / S sin( ) = ( y i y i ) / S D x1 = D 1 cos( ), D y1 = D 1 sin( ) D x2 = - D 2 sin( ), D y2 = D 2 cos( ) D x3 = D 2 sin( ), D y3 = - D 2 cos( ), [ ], S, n, D 1, D 2, D 3, ( D x1, D y1 ), ( D x2, D y2 ) ( D x3, D y3 ),,

264 255,,, 1. : N, ( x i, y i ) ( i = 1, 2,, N ), D x, 8-9 : 8-9 ( 1 ), y,,, xoy ( 90 - ), x o y, x, : x i = x i sin( ) - y i cos( ) y i = y i sin( ) + x i cos( ) ( 8-10), ( x i, y i ) xoy, ( x i, y i ) x o y ( 2 ) x x ma x x min, M : M = [ ( x ma x - x min ) / D ] [ ( x ma x - x min ) /D ] D = x ma x - x mi n, M - 1, 1, M ( 3 ), j, x j = x mi n + Dj ( 8-11), j = 1, 2,, M j i,

265 256 x, ( x i - x j ) ( x i x j ) 0, j i : x J ( i, j) y J ( i, j) = x min + Dj = ( y i x i y i + 1 x i ) / ( x i x i ) + ( y i y i ) x J( i, j) ( x i x i ), x J ( i, j) y J ( i, j) j i, ( x i, y i i ) ( x i + 1 ( 8-12), y i + 1 ),,,,, x i ( 0. 01), x i = x j, x i = x i ( 4 ), y, 8-10, j yj 4 J 6 J 7 J 1, J 4 J 6, J 7 J 1 j,, xoy, : x J ( i, j) y J ( i, j) = x J ( i, j) sin( ) + y J ( i, j) cos( ) = y J ( i, j) sin( ) - x J ( i, j) cos( ) ( 8-13) : N, ( x i, y i ) ( i = 1, 2,, N), D X, d, 8-11 : ( 1 ) ( 2) ( ), d,

266 257 ( 3 ),, , 8-12, A B C D E 5, AB BC, ,,,, 8-12,,,,,,,,,,

267 258 0, ;,,,, ( x i, y i ) ( i = 1, 2,, n ), x 1 < x 2 < < x n,, 0 y = f( x), : y i = f( x i ), i = 1, 2,, n f ( x) - 2 f( x), [ x i, x i + 1 ] ( i = 1, 2,, n - 1 ), x f ( x) - 2 f( x) = f ( x i ) - 2 i x x - x y i + H f ( x i + 1 ) - 2 i y i + 1 ( 8-14) i H i, H i = x i x i ( 8-14), : f( x) = y + y y f ( x) - 2 f( x) = 0, y = c 1 e 2 x + c 2 e - 2 x, y, y = ax + b, c 1 a b : f( x) = 1 2 sinh( H i ) { f ( x i) sinh[ ( x i x) ] + f ( x i + 1 ) sinh[ ( x - x i ) ] } + y i - f ( x i ) x i x + 2 H i y i + 1 -, x i xx i + 1, H i = x i x i, i = 1, 2,, n - 1 f ( x i + 1 ) x - x i ( 8-15) 2 H i, f ( x i ),, ( 8-15) : f ( x) = f ( x i + 1 ) cosh[ ( x - x i ) ] } sinh( H i ) { - f ( x i ) cosh[ ( x i x) ] + 1 y H i - f ( x i) - y i 2 i f ( x i + 1 ) ( 8-16) 2, x i xx i + 1, H = x i x i, ( i = 1, 2,, n - 1), f( x + i ) = f( x - i : : c 2 ) f ( x i - 1 ) f ( x i ) f ( x i + 1 ) a i + b 2 i + c 2 i = d 2 i ( 8-17)

268 259 a i = 1 H i sinh( H i - 1 ) b i = coth( H i - 1 ) - c i = 1 H i - sinh( H i ) 1 H i coth( H i ) - 1 H i ( 8-18) d i = y i y i H i - y i - y i - 1 H i - 1, i = 1, 2,, n n f ( x i) ( i = 1, 2,, n) n - 2 2,,,,,, f ( x 1 ) = y 1 ( 8-19) f ( x n ) = y n, : i = 1 i = n - 1, ( 8-19 ) ( 8-16), b 1 a n f ( x 1 ) f ( x 2 ) + c 2 1 = d 2 1 ( 8-20) f ( x n - 1 ) f ( x n ) + b 2 n = d 2 n ( 8-21) b 1 = coth( H 1 ) - c 1 = 1 H 1 - sinh( H 1 ) 1 H 1 ( 8-22) d 1 = y 2 - y 1 H 1 a n = b n 1 H n y 1 sinh( H n - 1 ) = coth( H n - 1 ) - 1 H n - 1 ( 8-23) d n = y n - y n - y n - 1 H n - 1, ( 8-17) ( 8-20) ( 8-21) :

269 260 b 1 c 1 a 2 b 2 c 2 a n - 1 b n - 1 c n - 1 a n b n f ( x 1 ) 2 f ( x 2 ) 2 f ( x n - 1 ) 2 f ( x n ) 2 = d 1 d 2 d n - 1 d n ( 8-24) ( 8-24), x 1 < x 2 < < x n,,, : x = X( S) y = Y( S) x i = X ( S i ) y i = Y( S i ) X( S) Y( S), i = 1, 2,, n : X( S) = X ( S i ) sinh( ( S i S) ) 2 sinh( H i ) x i + X ( S i + 1 ) sinh( ( S - S i) ) 2 sinh( i ) - X ( S i ) S i S + 2 H x i X ( S i + 1 ) S - S i ( 8-25) i 2 H i Y( S) = Y ( S i) sinh( ( S i S) ) 2 sinh( H i ) y i S i, H i + Y ( S i + 1 ) sinh( ( S - S i ) ) 2 sinh( i ) - Y ( S i ) S i S + y 2 H i Y ( S i + 1 ) S - S i ( 8-26) i 2 H i, S, S 1 < S 2 < < S n,, X ( S i ) Y ( S i ) f ( x i ) X ( S i ) Y ( S i ) f ( x i ), ( 8-18 ), ( 8-22), ( 8-23 ) ( 8-24 ) X ( S i ) Y ( S i ), ( 8-25), ( 8-26) X( S) Y( S),,,, ,

270 261,,,,,,, 4 10,,,, 4 10,,, 4 10, 8-13 ( x 0, y 0 ), ( x i, y i ), : : D 1 = ( x i - x 0 ) 2 + ( y i - y 0 ) 2 z = ( z i /D i ) ( 1 /D i ) 8-13

271 262,,,,,,,,,, 8-14,, cosc = ( a 2 + b 2 - c 2 ) /2 ab,,,,,,,, 8-14,, z, z,, : z = ( z - z 1 ) ( z - z 2 ) ( 8-27) z0,,, ( 8-27) z 1 z 2 z = 0,,, ( m), z, 1., y i = 1, 2,, m, x

272 263 j = 1, 2,, n, mn, Z 0( i, j), ny, nx, , z A, A A S ( i, j), S ( i, j) = nx( z - z 0 ( i, j) ) /( z 0 ( i, j + 1) - z 0( i, j) ) ( 8-28) nx, : S ( i, j) = ( z - z 0 ( i, j) ) /( z 0 ( i, j + 1) - z 0( i, j) ) ( 8-29), z A, A A H ( i, j),

273 264 H ( i, j) = ny( z - z 0 ( i, j) ) /( z 0 ( i + 1, j) - z 0( i, j) ) ( 8-30) ny, : H ( i, j) = ( z - z 0 ( i, j) ) /( z 0 ( i + 1, j) - z 0( i, j) ) ( 8-31) : a x a y = ( j + F S ( i, j) ) nx ( 8-32) = ( i + ( 1 - F ) H ( i, j) ) ny, F a, a, F = 1; a, F = 0 2. z, ( x 1, y 1, z 1 ) ( x 2, y 2, z 2 ), : x z = x 1 + x 2 - x 1 z 2 - z 1 ( z - z 1 ) y z = y 1 + y 2 - y 1 z 2 - z 1 ( z - z 1 ) ( 8-33), 8 17,, a 1 a 2, a 2, a 1, a 1 i 1, j 1, a 2 i 2, j 2,, i 1 j 1 < i 2,, 8-17( a) < j 2,, 8-17( b) a 2 a 2, j 2 nx < a 2 x,, 8-17( c),, 8-17( d), a 1 a 2, a 2,, a 1,, a 2, a 2 a 1,, ( ),,,,,,,,,,,,,, ( ), ,

274 ,,, ,,

275 266,,,,,,

276 ,,,,,, 9-1 x y, x y,,,,,, RS-232C 9-1, mm;, mm; A 1 A 0

277 268,,,, x y 4, 4, ( ), 3 5, : xoy (, x, ), O X 0 O XO Y, 9-2 Y 0 O 9-2 P ( X, Y) ( x, y) : X - X 0 Y - Y 0 = ( x - u) cos+ ( y - v) sin = ( - x + u) sin+ ( y - v) cos,, u v O, a = cos, b = sin ( 9-1) X = ( x - u) a + ( y - v) b + X 0 Y = ( - x + u) b + ( y - v) a + Y 0 Q x = - ( a u + bv) + X 0 Q y = bu - a v + Y 0, Q x Q y a b X = a x + by + Q x Y = - bx + a y + Q y ( 9-2)

278 269 n, : V Xi = Q x + x i a + y i b - X i ( 9-3 ) V Yi = Q y + y i a - x i b - Y i, i = 1, 2,, n,, : nq x + [ x] a + [ y] b - [ X] = 0 nq y + [ y] a + [ x] b - [ Y] = 0 ( 9-4) [ x] Q x + [ y] Q y + [ x 2 + y 2 ] a - [ xx + yy] = 0 [ y] Q x - [ x] Q y + [ x 2 + y 2 ] b - [ yx - xy] = 0 : Q x = 1 n Q y = 1 n ( [ X] - [ x] a - [ y] b) ( [ Y] - [ y] a + [ x] b) a = b = n[ xx + yy] - [ x] [ X] - [ y] [ Y] n[ x 2 + y 2 ] - [ x] 2 - [ y] 2 n[ yx - xy] - [ y] [ X] + [ x] [ Y] n[ x 2 + y 2 ] - [ x] 2 - [ y] 2 x m = [ x] n, y m = [ y] n x= x - x m, y= y - y m X m = [ X] n, Y m = [ Y] n X= X - X m, Y= Y - Y m Q x = X m - x m a - y m b Q y = Y m - y m a + x m b a = [ x X+ y Y ] [ x 2 + y 2 ] b = [ y X - x Y ] [ x 2 + y 2 ] ( 9-5) ( 9-6) ( 9-6) a b, a, b ( 9-5) Q x Q y, ( x, y), ( 9-2) ( 9-2), X Y,, : X = a 0 Y = b 0 + a 1 x + a 2 y + b 1 x + b 2 y ( 9-7)

279 270 ( 9-7) 6, x y X Y, 6, 3 ( ),,,, ( 9-6) ( 9-5),,,,, 1., (,, ),,,,, ( 1 ) X s Y s X m Y m,,,,, ( 2 ) 3 5,,,,, 2.,,, ( ),, 9-3,,,, : : X = L, Y = 0 : X = 0, Y = 0 : X = 0, Y = W, L, W,

280 271 GPS # 9-3,,,,,, ( ),,,, 3.,,,,,,,,,,,, ( ), 9-4 (

281 272 ),, 9-4 ( a), 9-4( b),,,, 9-4( c), ( ), 9-4( d),, 9-4( e),, 9-4( f ),, 9-4 ( g),, 9-4( h) ( ),, ( ), 9-4 ( i), ( ),, 9-4 ( j) ;, ( ),, 9-4 ( k), ( ),,,, ( ), ( ), 9-4, 9-5 :, 1, 2, 3, 4, 5, 6, 1 ;, : 2, 13, 12, 11, 10, 9, 8, 7, 6, 2, 2 2, 5 4 3,

282 273 1.,,, 9-6, ABCN, ABCN,, ( x 1, y 1 ), ( x 2, y 2 ),, ( x n, y n ), : : P = 1 2 ( x 1 + x 2 ) ( y 2 - y 1 ) ( x 2 + x 3 ) ( y 3 - y 2 ) ( x 3 + x 4 ) ( y 4 - y 3 ) ( x n + x 1 ) ( y 1 - y n ), n, x n + 1 = x 1, y n + 1 = y 1 n P = 1 2 ( x i + x i + 1 ) ( y i + 1 i = 1 - y i ) ( 9-8) n P = 1 2 ( x i y i + 1 i = 1 - x i + 1 y i ) ( 9-9) , , ( 9-8),, , ,,,,, 9-7, : ( 1 ) ( 2 ), ( 3 ) ( 4 ) , ( 5 ),

283 ( 6 ) ( 7 ) , ( 8), ( 9 ),,, : ( 1 ) ( 2 ),,, ( 3 ) 3 7 2,,, ( 4 ),, 9. 2,,,,, X, ( ), f( x, y), f( x, y) ( x, y),

284 275,,,, f( x, y) ( x i, y i ) ( i = 0, 1,, m - 1; j = 0, 1, 2,, n - 1 ),, m n x y, ,, G, G,,, K ( ), G = 2 K, K , ( 1, 0 ),, m n,,,, 1., 9-9,, 10, ( 0 1 ) 2., 9-10, ( a), ( b) 3.,,

285 , ( ), 0 1,, ( DLG), ( DRG), : x y ; x y ; x y : ;,, ;

286

287 ,, PCX GIF TIFF BMP,,, x y,, x y x, y, x,, 0, 1, mm, 0. 1 mm, / s, A 1 A 0,,, : X = a 0 Y = b 0 + a 1 x + a 2 y + a 3 xy + b 1 x + b 2 y + b 3 xy ( 9-10), a 0 a 1 a 2 a 3 b 0 b 1 b 2 b 3 8 x y, X Y, 4, 4 4, ( 9-10) 4, 8, ( 9-10),,,,, 1. V, V, 1, 0 1, V 4 V,

288 279,, V 1, 0, 9-13( a) 9-13( b), 9-13 ( c) V ( a ) ( b ) ( c ) ,, ( ) 9-14, ( i - 1, j ), ( i - 2, j ),,,, ( i, j), ( i, j), 9-14( a), ( i + 1, j + 1 ), 9-14( b), ( i + 1, j - 1) 9-14, ( i, j), NB9-14( a), NB = 1 1, S 1 = { ( i - 1, j) ( i - 1, j + 1 ) ( i, j + 1) ( i + 1, j + 1 ) } 9-14( b), ( i, j), NB = 2, 2, S 1 = { ( i - 1, j) ( i, j + 1 ) ( i + 1, j + 1 ) }, S 2 = { ( i + 1, j - 1) }, NB 0,, NB < 2, ( i, j) ;, NB2,,

289 280 ( ),, 1, 3,, 2 (, ), : 3 0, 2 1,,,,, :,,, ( 1 ) 1 ; ( 2), ( ), 1 ; ( 3 ),,, ; ( 4 ) ( 2) ( 3),, ( )

290 281 ( ) ; ( 5 ) ( 1) ( 4),, 9-16,, 9-16,,,,,,,,,,,,,,,

291 , ,,,,,,,,,, 1500, , , , , ,, :,,,,,,,,, ( ),,,,,,

292 283,, 100 km 2,,, 3, 1 /2 900,, 3, 1. 5, 1985,,,,,, ( ), ( ),,,,,, ( ),,,,, ( ),,,,,, 10. 2,,,,,,, GPS RTK,, 0. 1 mm, 1 /10 ( ),,, , , , , ,

293 284,,,,,,,,,,,,,,, 0. 2 mm, 1 /6,,,,,,,,, 1. i : : x i = itan L = L - x i R = R + x i, L R, 2. c : : x c = c/ cos L = L - x c R = R + x c, L R,, x i x c,, x i x c, 3. x, : = 90 - ( L - x)

294 285 = ( R - x) - 270, L R, 10. 3, GPS RTK,,,,, ( ), ;,, GPS RTK,,,,,,, :,,,,, PDA,,, :,,,,, ( x y ), x y,,,,, 10-1, 8 A 1,

295 286, A 2, A 3, A 4, A 5, A 6 A 7 A 8 x y A 1 A 2 A 3 A 4 A 5 A 6 A 7 A GB , , , 9 : ( ),,, 1 9,, 2110, 2120, 2430, 4310, 4320, 4330,,,,, 1 2 3,,,, 0, 1, 2 1.,,,,,,,, PDA,, 2., 3 3 ( ),,,,,, 3.,

296 287,, : ( 1 ),,, ( 2 ),,, ( 3 ), ( 4 ),,,,,, ( A4 ),,,,,,,,,

297 ,,, ( ) :,,,,,,,,,, ( ), 10-3,, D01 D02 D03, 10-4, 10-3 : x y ( 10-1) : ( 10-2)

298 x y : (

299 ) , 4, ,, , 4,,, : x y :,,,,, 1.,,,, 2.,,,,, x, y x y, x y, x i = x i + x y i = y i + y,,, 3.,,,, :

300 291 x i = x i cos + y i sin y i = y i cos - x i sin,,,, ( ) ( ) ( ), ( ),,,,,, ( ),,,,,,,,,,,, , 3, , 0. 6mm

301 292, m, m,, m, m 100 cm : GB , :,,,,,,,, 1., ,, 20 50, ( 10-1) : M x M y = = n i = 1 ( X i - X i ) 2 n - 1 n ( Y i - Y i ) 2 i = 1 n - 1 ( 10-1), M x X, M y Y, X i X, X i X

302 293 Y i Y, Y i Y, n ( 10-2) : M s n S 2 i i = 1 = n - 1, S i, n ( 10-3) : ( 10-2) M h = n ( H i - H i ) 2 i = 1 n - 1 ( 10-3), H i, H i n,, 10 %,,,,,,, 10. 6,, : ( 1 ),, ( 2),,,,, ( 3 ) ( DBMS),,,,

303 294 1.,,,, ( ), ;, m( m0 ),, 10-5 E, ,, ( ), ( ), ( ) E 10-5 E 10-6

304 295 2.,,,,,,, 10-5 E 10-7 : ( 1 ), ; ( 2 ), : ( 1 ),, ( 2),,, ,,, : R( A 1, A 2,, A n ) R, A i ( i = 1, 2,, n) R,,,,, n n 10-8,

305 : ( P) ( P#) ( O) ( A) ( F) : ( E ) ( P#) ( E#) a 30 b 22 c 16 d 25 c 16 e 14 f : - ( N) ( E#) ( BN) ( EV) a 1 2 b 2 3 c 3 4 d 4 1 e 3 5 f 4 5

306 : ( C) ( N#) x y ,,,, 1 2 ( ),, 2 3, GIS,,,, , ( 1 ),,,, ( 2 ),,,, ( ),,, ( 3 ),, 1.,

307 298, 2.,,, 3.,,,, ,,,,,,, :,,,

308 ,,,,, ( ),,,,,,,,, Auto CAD,,,,, ( DTM) DTM,,,, ( GIS),,,,,,

309 , P, P, P X Y eg fh, af a e, X P = X a + a f Y P = Y a + a e, X a Y a P ( 11-1) 11-1, ( 9-1 ),,,,, 11-2, P,

310 , k, k mn, mn d, mk d 1, k H k,, H m m, h H k = H m + d 1 h ( 11-2) d D h,, i, i = tan= h D = h dm ( 11-3), d, h, D, M i ( % ) ( ),,,,,,, : 11-3( a), MN, MN, a, b, c,, i11-3( b), MN, ; M MN, M a, b, c,, N, 11-3 ( b) M MN a, b, c,, N, 11-3 ( b),,,, MN, 10 20, ( ),,

311 , ;,,, 11-4 A, A,, 11-4, BC CD DE EF FB, 11-4,,,

312 303 : d min = h 0 im ( 11-4), h 0, i, M 11-5,, d m in, A,, 54m a ; a, 55m b;, B, Aa b B, 11-5, m, : 201 m 202m, m, m ;, 204 m 2. 3m, 198 m 3. 7m, 11-7, A B C m m ma b c,

313 304 ab bc ac bc, bc 153 m 152m 151m d e f, A ( m) k, ak, m d e f ak, 11-6, ( ),, 11-7, 11-7, M, m, m, M 0. 6m : 9-1

314 305 ( 9-6) ( 9-7),,, ( 9-7) x i, y i,, m xi = m yi = m c ( 11-5) : m P = m c 2 i = 1 n D 2 i + 1, i - 1 ( 11-6), D i + 1, i - 1 i ( ), ,,, P m c,,,,,,, 1.,, 11-9, 100 m,,, F 0 F 1 F 2 F 3, h, h k

315 V 1 = 1 2 ( F 0 + F 1 ) h V 2 = 1 2 ( F 1 + F 2 ) h V 3 = 1 2 ( F 2 + F 3 ) h ( 11-7) V 4 = 1 3 F 3 h k V = V i n i = 1 2. ( ),,, d i, 11-10, S i, i : V i = 1 2 d i( S i S i ) ( 11-8) : n V = V i = 1 n i = 1 2 d i ( S i S i ) ( 11-9) i =

316 307 3., d( 5 20 m), 11-11,, H 0, h i : h i = H 0 - H i,,,, ( 1 ) V = h a + h b + h c + h d d 2 ( 11-10) ( 2 ), ( 11-12( a) ) V = V = ( h a + h c ) 2 4( h a + h b + h c + h d ) d2 ( h b + h d ) 2 4( h a + h b + h c + h d ) d2 ( 3 ), ( 11-12( b) ) ( 11-11) V = 2h b + 2h c + h d - h a 6 V = d 2 h 3 a 6( h a + h b ) ( h a + h c ) d 2,, ( 11-12) ( 4 ), ( 11-12( c) )

317 V = 2h a + 2h d - h b - h c d 2 6 V = h 3 b ( h b + h a ) ( h b + h d ) + h 3 2 c ( h c + h a ) ( h c + h d ) d 6 ( 11-13),, 11. 4,,, DEM ( Digital Elevation Model),,, x y ( ) DEM DEM x y Z :, DEM D, ( ), X i, Y i, Z i {V i = ( X i, Y i, Z i ), i = 1, 2, 3,, n} ( 11-14) ( X i, Y i ),, DEM, {Z i, i = 1, 2, 3,, n} ( 11-15) DTM( Digital Terrain Model) DTM,, DTM DEM, DEM DTM, DEM DTM,

318 309 DEM,, DEM : ( 1 ),,,, ( 2 ),, DEM,,,, DEM, ( 3 ),, DEM,,, : ;, l m DEM 10m 100m DEM ; DEM DEM, DEM ( Grid),,, DEM DEM,,, P ( x, y), P, P ( x, y) Q 1 Q 2 Q 3, ( x 1, y 1, z 1 ), ( x 2, y 2, z 2 ) ( x 3, y 3, z 3 ), Q 1 Q 2 Q 3 : x - x 1 y - y 1 z - z 1 x 21 = x 2 - x 1, x 3 1 = x 3 - x 1 x 2 - x 1 y 2 - y 1 z 2 - z 1 = 0 ( 11-16) x 3 - x 1 y 3 - y 1 z 3 - z 1 y 21 = y 2 - y 1, y 3 1 = y 3 - y 1

319 310 P : Z = Z 1-2. DEM z 21 = z 2 - z 1, z 31 = z 3 - z 1 ( x - x 1 ) ( y 21 z 31 - y 31 z 2 1 ) + ( y - y 1 ) ( z 21 x 31 - z 31 x 21 ) x 2 1 y 31 - x 31 y 21 ( 11-17), DEM: ( 1 ), 8. 4, DEM ( 2 ),,, ( 11-13),,,, ( ),,, ( 3 ), 8. 4, DEM, DEM ,,,

320 , DEM 1. DEM DEM, z = a 0 + a 1 x + a 2 y + a 3 xy ( 11-18), x( y), z y( x) : P 1 ( x 1, y 1, z 1 ), P 2 ( x 2, y 2, z 2 ), P 3 ( x 3, y 3, z 3 ), P 4 ( x 4, y 4, z 4 ) ( 11-19) a 0 a 1 a 2 a 3 a 0 1 x 1 y 1 x 1 y 1-1 z 1 a 1 = 1 x 2 y 2 x 2 y 2 z 2 ( 11-19) a 2 1 x 3 y 3 x 3 y 3 z 3 a 3 1 x 4 y 4 x 4 y 4 ( ), 11-14, A B C D, L, P z A x y, P : z P = ( 1-2. x L ) ( 1 - y L ) z A + x L ( 1 - y L ) z B + x L y L z C + ( 1 - x L ) y L z D ( 11-20),,,, : A = P ( P - S 1 ) ( P - S 2 ) ( P - S 3 ) ( 11-21), P = 1 2 ( S 1 + S 2 + S 3 ), S i, :

321 S i = x 2 + y 2 + z 2 DEM ( ), : V 3 = h 1 + h 2 + h 3 A 3 3 V 4 = h ( 11-22) 1 + h 2 + h 3 + h 4 A 4 4, h i, A 3 A 4, DEM DEM 4. DEM, DEM, DEM,,, DEM P i P i ( x i, y i, z i ), : n - 1 z i + z i + 1 A = D i, i + 1 ( 11-23) i = 1 2, n, D i, i + 1 P i P i + 1 : D i, i + 1 = ( x i x i ) 2 + ( y i y i ) 2, 5. ;,,, N Z ( 11-15), 33, DEM :

322 : tan= tan= z x 2 + z y - z y z x 2 ( 11-24) ( 11-25) ( ) ( 11-25), z x z y, ( i, j) : z = z i, j z i, j - 1 x ij 2 x, x, y x, y ; z = z i + 1, j - z i - 1, j y i j 2 y,,,,, , 9,, DEM,, : ;

323 314, ( a) ( b) 11-17,,,,,,, ( ) ( ),, 11-18,,, : ( 1 ) ( ( a) ), ( 2 ) ( 11-18( b) ),, p, d ; d d, p ; p

324 P c ( x c, y c, z c ), z vp, P ( x, y, z) ( x p, y p ), : x= x - xu y= y - yu z= z - ( z - z c ) u ( 11-26) u 0 1, ( x, y, z ) u = 0, P ( x, y, z) ; u = 1, ( 0, 0, z c ),, z = z vp, u : u = z vp u x y, : z c - z - z ( 11-27) x p = x z vp - z z c - z = xd p z c - z y p = y z vp - z z c - z = yd p z c - z ( 11-28),,, 11-20, ( a) xy, z, z, ; ( b), x z, y, x z,

325 316 ( a) ( b) DEM,,,,,,,,,,,,, ( ),,,,,, 11-21,,,,,, 11-21,,,,

326 317 DEM,,, DEM, DEM DEM

327 ,,,,,,,,,,, ( ),,,,,,,,,, ( ),,

328 319,,,, / km / m DJ 2 DJ 6 ( ) ( ) n 1 / n 1 / / m : n, 500 m, 1 / /2 000, 1994,,, /m / m , 1990, / cm / cm / cm : ; GB/ T , ( ) : m;

329 m; m,,,,,,,, ( ) ( ),,,, ( ), ;, ;,,,,,,,, ;,,,,,,,,,

330 321,,, ( ) 1.,, ( ), : ( 1 ) ; ( 2 ) ; ( 3 ) ; ( 4 ) ; ( 5 ) ; ( 6 ) ( ) ; ( 7 ) ; ( 8 ),,, ( ),, 2. : ; ;,,,,,,, ( ),,,, ( ) ( )

331 322,,,,,,,,,,, 1, ( ), ;,, : ( ),,,,, ( ) 1.,, : ( 1 ),,,, ( 12-2),,

332 ,,, ( 2 ),, 2. ( 1 ),, ( ),,,,,,, ;, ( 2 ) ( ),, ;, ( 3 ) ( 4 ),,,,,,

333 324 ( ),,,,,,,,,,,,,,, ,,,,,,,,,, ( ),

334 325 : ( 1 ) ; ( 2) ; ( 3) ; ( 4) ; ( 5 ) ; ( 6) ; ( 7) ; ( 8) ; ( 9) ; ( 10) ; ( 11 ) ; ( 12) ( ),, : ( 1) ; ( 2), ; ( 3 ), ; ( 4 ),,, : ( 1 ), ; ( 2),, ( ) : ( 1) ; ( 2 ), ; ( 3) ; ( 4 ) ; ( 5 ) ; ( 6 ) ; ( 7), ( ),,,,,,,,,, 12. 3,,,, :,

335 326 ( ) 1. : ( 1 ) ( ) :,,,, ( 2 ),,, 0. 8 mm, 1 mm,, ( 3 ) ;, ( 4 ), , 15, 5 ; 5

336 327 ( ) 8 ; ( ), , ( 5 ), ( ),, ( 6 ),,, 0. 1 m 2, ( 7 ) ( 8 ), 12-4 ( ) 11, ;, ; 1. 0, ( ), 50% 70% 13 14, 15

337 ( 25 ), , ( 1 ), ( ) ( 2 ), 6 m 2,, : ( 3 ),,,,, ( 4 ), ( 5 ),,

338 329, ( 6 ), ( 7 ),,,,, 3. ( ), ( ), ( ),,,,,,, ( ),, 12-5 ( 12) ( 21) ( 23) ; ,, 251 ; , 23 1, 211, 1. : ( 1 ),, ( xy ) ; 3 - ( 4) -7, ( ), 16 ( 2 ) O, 7, 242 (, 242 ),, m 2

339 ( 3 ) 0. 8 mm ( ), 1, 1 9, 0. 3 mm, ( 4 ) 4, ( 5 ) ( ),, 4568 ( 6 ), ( 7 ), 2., 32K16 K8K,,,, ;, 3. ( 1 ),,,

340 331 ( 2 ),, ( 3 ),,, 12-6 : : ,,,,,

341 332 ( ),,, ( ),,, ;,, 1, 2, 3,,,,,, ;,,,,, 1, 2, 3,,,,, A, B, C,, ( ),, ;, ;,, ;,, ;,,,, ; ( ),, : 8 ;

342 333, 30, 12-5, ( ) ( ), ( ),, 4 ; 11, , ( ) ( ), 6, , 12-7,

343 ,,,,,,,,,,,,, ( ), 1982,,,,,, ;,,,,,,,,,, ( ),,

344 ( ),, ( ), ( ), ( ),,,,,,,,,, 1500, : ( 1 ), ;, ;, ( 2 ),, ( ),, ( ) ( 3 ), 0. 2 mm,,,,,,,,,

345 336, 1 mm ( 4 ) ( ),,,,, ( 5 ),,,,,,,,,,,,,, ,,,, ;,, ; ;,,,,,,,,,, 12-7 ( ) 0. 3 mm 0033, 0034, 0035,, 0047, 0048, 0049, 0048, 48-1, 48-2,, 48-7, 33 ( ) 2308, 2, ; 3, ; 08, 8 ( 2), 2, 33 ( ) 287

346 ,,,,,,, , 32K16K8 K4K, ( ),,,,,, m,,,,,,,, ;,,

347 , J, ( : m 2 ) 6, 4 4, , 2, 3, 04 4, ,,,, 1200,,,, 32K 16K

348 339, m,, 3, 0. 2 mm ( ), m m m ( ) 1., ( 1 ),,

349 340,, 2. 2 m 2. 2 m ( ), 2. 2 m,,, 2. 2 m,,,,,, ( 2 ), ( 3 ) 2. 2 m, 2.,,,,, 3.,,,,,, : = + : ;, = ( ), : ( ),, ;, ( )

350 341,, P i : P i = KP i K = P i P i : P i, P i, P i, K

351 ,,,,,,,,,,, ( ),,,,,,, : ( 1 ) : ( 2 ) : ( 3 ) : ( 4 ) : ( 5 ) : ( 6) :,,,,,

352 343 :,, ( 13-1), ( 13-2 ), ,,,, :,,, : ( 1 ), ( 2), ( 3)

353 344, ( 4 ),,,,,,,, : ( 1 ),, : ( ) ( ), ( ) ( ) ( 2 ), ( ),,, ( 3 ),,,, : ( 1 ) ; ( 2 ) ( 2003 ), 13-1

354 h h 2 5 cm 3 cm mm : 1 ; 2 ; 3 ; h, 5%, /2, 1% 13. 2,,,,,,, :,,,,,,, :, ( ),,,,,,,,,,,,,,

355 346 ( ),,,,,, ( ),,, ( ), ( ),,,, ( ) ( ), BK-C, BK-C,,, 13-3,,,,, ( 13-4 ) MC,,, ( 13-4 ),,, 45, e,,,, e h ( 13-5 ),,,,,, ( 13-4 ) ( ) 1. : ( ) 5 10 m, 1 m, :, ( 1 ) : ( ),,,

356 347 ( 2) :,, :,, 45,,,, 3., 50 Hz, ( ) : ( ), ;

357 348, ( ),,,,,,,,,,,,, ;,,,,, : ( 1 ) ( ) : :, ( ) ;, ( ) ( 2) :, : cm, cm, 5 10 cm ( 3 ) : ( 4) :,,, ( 5 ) : ( 6) :, ;,, ( ), 1.,, 13-6, T1 T3, X1 X6

358 ,, ( ), 13-7 ABCD, T1 T4, X2X3X4, X1, X5X ,, 3,, ( ), 1. ( ),, 5 km, 2 km DS3, 100 m 40 Lmm ( L, ), 20 mm 2.,

359 350 ( ) DJ6, DJ2, 40 [ D 2 ] mm ( D, ) ( ),,, ( 1 mm), ( GPS) ( RTK), ( ) ( ),, : /,,, ( ), ( ),, ( ),, ( ),,,, : ; ;, , ( ) ( ),,, ( ),,, 10,, 13-9

360

361

362 , m, 1., 1 m,,,,,,, l m,, 14-1,,,, ,,,,,,,,,,

363 354,,, ( 1 ),,, ( 2 ) : ; ; ; ; ; ( 3 ),, 10 cm 5 cm,, ( )

364 355,, ( ) ( ), ( ),, K , m,,,, 20 m 50 m (, 20 m10 m 5 m), 100 m,,,,,, : ( ), ( ) ( ),,, 14-3, AP, P, P : AP, : AB, : tan AP = Y P - Y A X P - X A = AP - AB ( 14-1) S = Y P - Y A = X P - X A ( 14-2) sin AP cos AP A P,, A, B, AP, AP P, AP,, P,,, P, 14-4

365 , P x P y, P P P P, 14-4 ( ),, 14-5, AB, P, : tan AB = Y B - Y A X B - X A tan AP = Y P - Y A X P - X A tan B P = Y P - Y B X P - X B 1 = AB - AP ( 14-3)

366 = BP - ( AB 180) ( 14-4) ( ),, , P,,, ( ),, 14-6, P, P AB S A S B A B S A 14-6 S B, P ( ),,

367 358,,,,, , ( ZY) ; ( QZ) ; ( YZ) R T L E q ( : ) R, : 14-7 T = Rtan 2 L = ( 14-5) R ( 14-6) 180 E = Rsec 2-1 ( 14-7) q = 2 T - L ( 14-8) 2.,, (

368 359 ),,, R, , ( ZH ) ; ( HY) ; ( QZ) ; ( YH) ; ( HZ) R l 0 T L E q R l 0, 14-8 T = m + ( R + P) tan 2 ( 14-9) L = R( ) + 2l 0 ( 14-10) 180 E = ( R + P ) sec 2 - R ( 14-11), q = 2 T - L ( 14-12) m, P, 0 m P 0, : 0 = l 0 2R

369 360 ( ) m = l l0 240R 2 P = l2 0 24R , ZH, ZH x, ZH y l, : 14-9 x i = l i - l 5 i 40R 2 l ( 14-13) y i = l 3 i 6Rl 0 + ( 14-14), l i ZH, l 0, R l i = l 0, ( HY) : x 0 = l 0 - l R 2 y 0 = l2 0 6R, 14-10, i,, i x i y i : x i y i = Rsin i + m ( 14-15) = R( 1 - cos i ) + p ( 14-16)

370 = 180 R ( l i - l 0 ) + 0, l i ZH, l 0, R, m, p HZ, HZ x, HZ y, x i y i, ZH 14-11, HZ : HZ ZH x H Z = T 1 + T 2 cos ( 14-17) y H Z = T 2 sin ( 14-18) HZ x ZH 180 +, HZ y ZH y, 2., x i = x H Z - x i cos- y i sin ( 14-19) y i = y H Z - x i sin+ y i cos ( 14-20) ZH ZH

371 362 A, ZH, ZH X ZH Y ZH, : ZH,, X i = X ZH + x i cosa - y i sina ( 14-21) Y i = Y ZH + x i sina + y i cosa ( 14-22) : X i = X ZH + x i cosa + y i sina Y i = Y ZH + x i sina - y i cosa , m, 80 m, ZH X ZH = 0Y ZH = 0 X JD = Y JD = 0, 20 m ( 14-9) ( 14-10) ( 14-11) ( ) m, m, m, m ( 14-13) ( 14-14) ( ) ( 14-16), ( 14-19) ( ) ( 14-21) ( ),, 20 m 14-1, 14-1 X Y 1 K ZH 2 K K K K HY 6 K K K QZ 9 K K K YH 12 K K K K HZ 14. 3,,,

372 363,,,,,,,, ( ),,,,, :,, ;,,,,, ( ),,,,, km ;,,,, km ;, 1 2 km,,,, m,,,,,,, ( ),,,, ( TP ),,,,,,,, 14-12, 1, BM1, TP1,

373 ; BM1 TP1, BM , ( ) BM ZY TP1 TP TP QZ. 1

374 365 TP TP YZ. 1 TP JD BM ( ) 2, TP1, TP2,,, BM2, : = + = - = -,,, f h f h f h = 50 L mm ( L, km),,,,,, m m,,, ( ), AZ ( ZY) Y ( YZ) aa zzyy P 1 P 2, p 1 p 1 p 2 p 2, 14-14, A, 1 1 JD

375 ZD, 22 A, 14-14, 3 3, ZY P 1, 14-16, ZY, 11, 22 ZY 3 3 P 1, P 1, 22 ZY,, 3 3 P 1 P 2, P 1,,, 33 P 2, P 2, 22 P 1, 33 P 2

376 ( ),, 14-17,,,,, 14-3,,

377 ( ) ( ) ,,,,,,,, ( ), ( ) XY, Z, Y,, X, X Y ( ), YX( ),

378 , P ( X P, Y P ) :, X P = ( X P - X 0 ) cos+ ( Y P - Y 0 ) sin Y P = ( X P - X 0 ) sin+ ( Y P - Y 0 ) cos ( 14-23) X 0 Y 0 ; X X, ( ), : ( 1 ) P 1, P 2, ( 2 ),, X = 0, Y = 0 ( 3 ),,, X = 0,,,, Y,, 14. 4,,,,,, 10 20,,

379 370, , ,,, ;, : ; ; ; ; : ( 1 ), ( ),, ( 2 ), ( 3 ),,,,

380 371 ( 4 ),,,,, RTLE ( 5 ), ( 6 ),, ( ),, : : = - ( 7), = + ( 8), : = -,,,,, , ( 14-21),,, 14-21,,, 14-22, ( ), ( )

381