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Program # 9
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5 PRINT "Snyder (USGS), Iterations (algebraic)":
INPUT "N",M:E=0.066943644:REM GRS 80 (NAD 83)
REM M=-(N +/- S) see program #1 line 301 - 304
10 PRINT "X=";X:REM see line 500
12 INPUT"E&H",E,H:L=A/(-E*SinO^2+1)^.5
19 INPUT "K,M,O", K,M,O:REM K=L or R
20 T=(K+H)*CosO*CosM+X
23 W=(K+H)*CosO*SinM+Y
25 Q=(K*(1-E)+H)*SinO+Z
30 N=Atn(W/T):PRINT N
33 E=?:REM GRS 80 (NAD 83);KYMAK E=0
35 INPUT "E,H",E,H
37 P=Asn(Q/A):INPUT "P,A",P,A
39 S=H
40 P=Asn(Q/(A*(1-E)/(-E*SinP^2+1)^.5+H))
50 H=(T^2+W^2)^.5/CosP-A/(-E*SinP^2+1)^.5
52 IF H=S THEN 54
53 GOTO 39
54 PRINT H:END
484 X=-0.9956:Y=-1.9013:Z=-0.5215:GOTO :REM See Program #1
500 X=X: Y=-Y: Z=-Z: GOTO 10
527 A=6378206.4:E=0.006768658
537 X= -6.730951453:Y= 155.5736993:
Z= 177.2965000:GOTO 5
583 A=6378137:B=6356752:E= :
REM b=a-fa:1/f=298.+ verify
588 X= :Y= :Z= GOTO 5
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KYMAK parametric datum transformation formulas by KYMAK agent, c. 1/19/1986:
(How formulas were derived.)
Old Datum eg. NAD 1927 Clarke ellipsoid
New Datum eg. NAD 1983 GRS 1980 ellipsoid
(WGS 1972: dX=-22;dY=157;dZ=176)
Revised:
(WGS84: dX=-9;dY=161;dZ=179)
T=parametric angle; P=parallel (latitude); a=equatorial radius; b=polar radius; e=eccentricity; r=radius of parallel; z=polar axis; M=meridian (longitude)
1) T=arctan((b/a)*tan P); b/a=(1-e^2)^.5 = tan T/tan P
Cartesian coordinates
(old datum):
2) r1=a1*cos T1
3) z1=b*sin T
4) d=varies (see footnote a,b,c,d)
new datum):
5) m=((dX+(dY/tan M1))*sin M1
6) dM=arctan(M1/(r1+d)) ; exact
7) T2'=arcsin((z1-dZ)/b2)
8) P2'=arctan(a2/b2)*tanT2'
9) r2'=a2*cosT2'
10) dr'=r2'-(r1+d) p2' to p1'
11) L'=dr'*sin P2' about=L ; (B2 to p2)
12) dz=L*cos P2 about=L'*cosP2'=dz'
13) z2=(z1-dZ)-dz'
14) T2=arcsin(z2/b2) ; prob. error very slight
15) P2=arctan((a2/b2)*tan T2) ; prob. error very slight
16) dH=dz*sinP2 ; p2 to p1
checks (12)(11)(15) ; verify P2
17) dr=dr'-r2 ; (10)(18)
18) rd'=dz'*tanP2 ; (12)(15) ; (p2' to A)
19) S'about=dr'*tan dM ; arc of r2'(17)(6) ;
4a) M1=90 west: d=dY: m=dX
b) M1>90 west and=or
d=(dY/sin M)+(dX+(dY/tan M)cos M
c) M1>90 west but=or>arctan(dY/dX:
d=(dX+(dY/tan M))cosM +
(dY/sin M)
d) M1<90 west; d=(dY/sin M-(dX+(dY/tan M)/sinM))/tan M
20) Md=S'/r2' radians ; (19)(9) central angle (02,A.B)
21) dS=rd'*tan dM ; (18)(16)
22) S=S'/dS (19)(21) arc of r2 ; (p2 to p2'
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