EPSG:9630 DEPRECATED

Reversible polynomial (4th-order)

Attributes

Data source: EPSG

Information source: EPSG guidance note #7.

Revision date: 2000-03-07

Remarks: Reversibility is subject to constraints. See Guidance Note 7 for clarification.

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Formula

See EPSG Guidance Note 7.

Example

For geodetic transformation ED50 to ED87 (1)

Offset unit:  degree
Ordinate 1 of evaluation point X0  =   55° 00' 00.000"N  = +55 degrees
Ordinate 2 of evaluation point Y0  =     0° 00' 00.000"E   =   +0 degrees

Parameters:
A0 = -5.56098E-06   A1 = -1.55391E-06   ...   A14 = -4.01383E-09
B0 = +1.48944E-05   B2 = +2.68191E-05  ...   B14 = +7.62236E-09

Forward calculation for: 
ED50 Latitude     = Xs =52* 30’30"N   =     +52.508333333 degrees
ED50 Longitude  = Ys =  2*E=      +2.0 degrees   

U = XS - X0 =  * ED50 - X0  = 52.508333333 - 55.0 = -2.491666667 degrees
V = YS - Y0 =  * ED50 - Y0   = 2.0 - 0.0 = 2.0 degrees

dX = A0 + A1.U + ... + A14.V4
      = -5.56098E-06 + (-1.55391E-06 * -2.491666667) + ... + (-4.01383E-09 * 2.0^4)
      = -3.12958E-06 degrees

dY = B0 + B1.U + ... + B14.V4
      = +1.48944E-05 + (2.68191E-05 * -2.491666667) + ... + (7.62236E-09 * 2.0^4)
      = +9.80126E-06 degrees

Then  ED87 Latitude  =   XT = XS + dX
                                  =  52.508333333 - 3.12958E-06   degrees
                                  = 52* 30’ 29.9887" N

ED87 Longitude  =   YT = YS + dY
                           = 2* 00’ 00.0353" E

Reverse calculation for transformation ED50 to ED87 (1).
The transformation method for the ED50 to ED87 (1) transformation, 4th-order reversible polynomial, is reversible. The same formulas may be applied for the reverse calculation, but coefficients A0 through A14 and B0 through B14 are applied with reversal of their signs. Sign reversal is not applied to the coordinates of the evaluation point. Thus:
Ordinate 1 of evaluation point X0  =   55° 00' 00.000"N  = +55 degrees
Ordinate 2 of evaluation point Y0  =     0° 00' 00.000"E   =   +0 degrees
A0  = +5.56098E-06   A1 = +1.55391E-06   ...   A14 = +4.01383E-09
B0  = -1.48944E-05    B1 = -2.68191E-05    ...   B14 = -7.62236E-09

Reverse calculation for: 
ED87 Latitude     = XS = 52° 30’29.9887"N   =     +52.5083301944 degrees
ED87 Longitude  = YS =   2° 00’ 00.0353" E   =     +2.0000098055 degrees   

U = 52.5083301944 - 55.0 = -2.4916698056 degrees
V = 2.0000098055 - 0.0 = 2.0000098055 degrees

dX = A0 + A1.U + ... + A14.V4
      = +5.56098E-06 + (1.55391E-06 * -2.491666667) + ... + (4.01383E-09 * 2.0000098055^4)
      = +3.12957E-06 degrees

dY = B0 + B1.U + ... + B14.V4
      = -1.48944E-05 + (-2.68191E-05 * -2.491666667) + ... + (-7.62236E-09 * 2.0000098055^4)
      = -9.80124E-06 degrees

Then ED50 Latitude  =   XT = XS + dX
                                 = 52.5083301944 + 3.12957E-06   degrees
                                 = 52° 30’ 30.000" N

ED50 Longitude  =   YT = YS + dY
                           = 2° 00’ 00.000" E
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