shapefile. Pythagoras Newtown. :

shapefile.. (). () ( )... - Pythagras.. Magellan Clumbus Newtwn. :....(- ).

(-) % ) MSL Mean Sea Level ( Geid. MSL ].[ ) (- ). ( -. : (-) Ellipse Spherid Ellipsid r Ellipsid f Revlutin.( ) : (-).

. :( ) a ( ) - b ( ) - : a ( ) - : f flattening - f = ( a b ) / a r f = 1- (b / a ) (4-1) (-) :(- ).( ) - ) -..( (-).

Datums.Reference Surface. : Plane ( ).Plane Surveying.. (a, f a, b ).... Re-Psitin.. A gedetic Datum, a lcal datum, r.simply a datum ). (.... Old Egyptian Datum =.OED1970. F1 ).(.

.. b a Helmert 1906 Clarcke 1866 Bassel 1841 Airy 1830 WGS72 WGS84. ) Clarke 1880.(. Hrizntal Datum ( ).Vertical Datum Tide Gauge. ( ). Leveling. -Bench Marks: BM Vertical Egyptian Datum. MSL.

- Crdinates. (). Tw-Dimensinal (r 2D).Crdinates.( ) Three- Dimensinal (r 3D) Crdinates ( ) Spherical. Gedetic Crdinates Gegraphic Crdinates Crdinates One-.Ellipsidal Crdinates Dimensinal (r 1D) Crdinates. Fur-Dimensinal (r 4D) Crdinates ( ). "". ) : ( ( ).. ( ).Lngitude ). (..... () ( ). - - - -.

.... Latitude.. (-) -- Earth-.ECEF Centered Earth-Fixed x z - ) x y.(.

(-) :(- ) 3D ( ) Lngitude ). ( ( ) Latitude ).( h Gedetic r Ellipsidal Height (-).

( ) (' ) 30 :.(" ).. 45' 52.3" (E ).(W ) ) (N ).(S -- Spherical Crdinates ( ).(- ). (-) -- () ( ) Cartesian Gedetic. X Crdinates X Y Z ().(- ) X, Y, Z :..

(-) -- (,, :(X, Y, Z) h) X = (c + h) cs cs Y = (c + h) cs sin (4-2) Z = [ h + c ( 1-e 2 ) ] sin first e radius f curvature c : eccentricity a c = ---------------------- (4-3) (1 e 2 sin 2 ) e = [ (a 2 - b 2 ) ] / a (4-4) (X, Y, Z) : (,, h) tan = Y / X Z / (X 2 + Y 2 ) tan = --------------------------------- (4-5) 1 e 2 (c / ( c + h) ) (X 2 +Y 2 ) h = ----------------- - c cs.

h c! - c Iterative c c Significant. -- (). :.. ( ).. A. C B. N.S ( ) :. (N ) NH36.H ( ) ( ).( : ).

(-) (-).

: O ' : O ' : :. = + (/) =. = + (/) = :() (-) =. =. =. H ( ) : (-) =. =. =.( ) : = + = N NH36 : : O ' " : O ' " : :. = + (/) + (/) =. = + (/) + (/) =.

:() =. =. =. E ( ) : =. =. =.( ) : = + = N NE37 : : NH36. N - : H - : = = = : = - " = " =.

= - : = = = : = - = - = NH36. :... = = = = : = + = = + =. = =.( ) F.

. =. =.( ) H.H G F : NF35, NG35, NH35, NF36, NG36, NH36 NF37. (-). (-).

: (-) () ()... - Map Prjectin - - ) ( ) :.(Grid Crdinates.(- ). (-) "Distrtin " (). ) :( - - - - -.

Equidistance Prjectin ) Cnfrmal Prjectin (.Equal-Area Prjectin : :Cylindrical Prjectins -.(- ) :Cnical; Prjectin -.(- ) :Azimuthal Prjectin: -.(- ). -. (-) (-).

(-) : :Mercatr Prjectin. Standard scale. Parallels.(- ) (-) :Transverse Mercatr Prjectin Central -.Meridian ( ).-.

.. Universal Transverse Mercatr :Prjectin.UTM.GPS UTM znes Central Meridian UTM.. UTM. meridian central. - ) O I X C.(!. scale factr... : UTM ) ( ) (. :.

UTM :.. UTM : UTM A.C.I O UTM : UTM (-) : ( - ) = : (-) : - ( ) = ) - -.(.

(-).

(-).

: O ' " : UTM O ' " : :. = + (/) + (/) =. = + (/) + (/) = :() : + ( ( + ) ) = + ( ( +. ) ) = + (. ) = +. =. =.( ) Q : (I, O C ) : : + ( ) = + (. ) = +. =. =.( ) : Q37 : UTM.

: UTM ( ).. X. Y False Easting.( ) False Easting ).( (-) ( ) UTM. () X.

( ) UTM.. n-line : http://www.rcn.mntana.edu/resurces/tls/crdinates.aspx http://gis.dep.wv.gv/cnvert/llutm_cnus.php http://www.ged.nrcan.gc.ca/tlsutils/tls_inf_e.php?apps=gsrug http://hme.hiwaay.net/~taylrc/tlbx/gegraphy/geutm.html.

UTM (-) ( http://www.uwgb.edu/dutchs/usefuldata/utmfrmulas.htm : ).

UTM (-) ( http://www.uwgb.edu/dutchs/usefuldata/utmfrmulas.htm : ).

: Sinusidal Equal-Area Prjectin.( : ) sin curves (- ).- (-) :Lambert Cnfrmal Cnic Prjectin ( ) Standard Parallels..(- ) (-).

Lambert Azimuthal Equal-Area :Prjectin ( )..(- ) (-) :Orthgraphic Prjectin ( ).(- ). (-).

- Prjected Crdinates 2D E Easting. x, y ) N Nrthing.(X, Y, Z. UTM. -- ETM () Egyptian Transverse Mercatr. ETM Znes Gedetic Datum.( ) Belts Helmert.(- ) 1906. : (Prjectin Parameters ) : Origin.Standard Parallel Central Meridian ( ) False :.False Nrthing Easting - -. - - - ) (. sftware.

:.. sftware.!.oed 1907 Old Egyptian Datum 1907 (). : :Red Belt - ( ) : ETM. False Easting = 615 000 m False Nrthing = 810 000 m Latitude = 30 0' 0" Lngitude = 31 0' 0" Scale n central Meridian = 1.00 Zne width = 4 0' 0" :Blue Belt - : ETM. False Easting = 300 000 m False Nrthing = 110 000 m Latitude = 30 0' 0" Lngitude = 35 0' 0" Scale n central Meridian = 1.00 Zne width = 4 0' 0" :Purple Belt - : ETM. False Easting = 700 000 m False Nrthing = 200 000 m.

Latitude = 30 0' 0" Lngitude = 27 0' 0" Scale n central Meridian = 1.00 Zne width = 4 0' 0" ETM (-) Extended Red ). Belt ( ).(!., MTM () GPS Mdified : ) MTM Transverse Maceratr.( MTM.. WGS84 MTM ( )..

: False Easting = 300 000 m False Nrthing = 0 m Latitude = 0 0' 0" Scale n central Meridian = 0.9999 Zne width = 3 0' 0" : Lngitude = 25 30' 0" Lngitude = 28 30' 0" Lngitude = 31 30' 0" Lngitude = 34 30' 0" Lngitude = 37 30' 0".

UTM -- UTM ( ) UTM.False Origin. UTM ).( UTM ) Internatinal Ellipsid 1924 ( = 1/f =. () UTM (-). UTM (-).

-..( ) ( ) :. WGS84 ( ) WGS84 ). Datum Shift (... (X,Y,Z).(,,h) (-) ( ) ) X, Y, Z. :Translatin Parameters ( X = X2 X1 Y = Y2 Y1 (4-10) Z = Z2 Z1.

(X1,Y1,Z1). (X2,Y2,Z2) (X,Y,Z) : (X',Y',Z') X' = X + X Y' = Y + Y (4-11) Z' = Z + Z ( ).. (X, Y, Z). : Rtatin Parameters.(- ) scale factr (-) : Rx X ( ) - Ry Y ( ) - Rz Z ( ) - scale factr -.s () (X, Y, Z, Rx, Ry, Rz, s). Transfrmatin Parameters.

( )....WGS84 WGS84 :.

WGS84 ( ) ( ) D Z D Y D X () - () - () Clark 1880 Adindan () - Clark 1880 Carthage () () - () - () - () Internatinal 1924 Eurpean 1950 () () Clark 1880 Merchich () () - () - () Clark 1880 Nrth Sahara 1959 () - () - () () - () () - () - () - () - () - () - () - - () - () - () () - - () - - - - () - () - () () () () () - Clark 1880 Helmert 1906 Internatinal 1924 Internatinal 1924 Clark 1880 Clark 1880 Clark 1880 Internatinal 1924 Internatinal 1924 Clark 1880 Virl 1960 Old Egyptian 1906 Ain El Abd 1970 Ain El Abd 1970 Nahrwan Nahrwan Oman Qatar Natinal Eurpean 1950 Virl 1874.

: WGS84 WGS84.( ). ( ).........(WGS84 ). ) WGS84 :( X = 123.842 ± 0.96 m Y = -114.878 ± 0.96 m Z = 9.590 ± 0.96 m Rx = -1.35314 ± 0.17 " Ry = -1.67408 ± 0.35 " Rz = 5.24269 ± 0.30 " s = -5.466 ± 0.78 ppm (part per millin) (WGS84 ) ) :(FIG X = -88.832 ± 0.02 m Y = 186.714 ± 0.03 m Z = 151.82 ± 0.01 m Rx = -1.305 ± 2.21 " Ry = 11.216 ± 1.57 " Rz = -6.413 ± 1.84 " s = -6.413 ± 1.84 ppm (part per millin).

Adindan ) http://www.ses-) (WGS84 sudan.rg/english/sespublicatins/ses_jur/47/1523gzulisesf :(rmat2.pdf X = -146.0 ± 0.89 m Y = -33.5 ± 0.89 m Z = 205,3 ± 89 m Rx = -1.64 ± 1.87 " Ry = 2.18 ± 1.87 " Rz = -14.8 ± 2.6 " s = -1.34 ± 1.35 ppm (part per millin) ( ) ) - - WGS1984 : ( FIG X = 4559545.892 m Y = 3808252.221 m Z = 2314350.329 m X = 41.650 m Y = 286.321 m Z = 89.132 m Rx = -1.91577 " Ry = 10.28662 " Rz = -14.08571 " s = -7.1256 ppm (part per millin). ) WGS84 Q37 UTM : (GPS. - =. - = :. - - X :.

. - - Y :.WGS84 UTM - - X :.WGS84 UTM - - Y : ) Q37 UTM ( ) UTM WGS84 : (. - =. = :. UTM - X :. UTM - Y :.WGS84 UTM - - X :.WGS84 UTM - - Y : ( ) WGS84 : ( ).