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145 lines
4.2 KiB
Fortran
145 lines
4.2 KiB
Fortran
SUBROUTINE sla_UNPCD ( DISCO, X, Y )
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*+
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* - - - - - -
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* U N P C D
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* - - - - - -
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*
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* Remove pincushion/barrel distortion from a distorted [x,y] to give
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* tangent-plane [x,y].
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*
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* Given:
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* DISCO d pincushion/barrel distortion coefficient
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* X,Y d distorted coordinates
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*
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* Returned:
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* X,Y d tangent-plane coordinates
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*
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* Notes:
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*
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* 1) The distortion is of the form RP = R*(1+C*R^2), where R is
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* the radial distance from the tangent point, C is the DISCO
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* argument, and RP is the radial distance in the presence of
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* the distortion.
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*
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* 2) For pincushion distortion, C is +ve; for barrel distortion,
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* C is -ve.
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*
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* 3) For X,Y in "radians" - units of one projection radius,
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* which in the case of a photograph is the focal length of
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* the camera - the following DISCO values apply:
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*
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* Geometry DISCO
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*
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* astrograph 0.0
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* Schmidt -0.3333
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* AAT PF doublet +147.069
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* AAT PF triplet +178.585
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* AAT f/8 +21.20
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* JKT f/8 +13.32
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*
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* 4) The present routine is a rigorous inverse of the companion
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* routine sla_PCD. The expression for RP in Note 1 is rewritten
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* in the form x^3+a*x+b=0 and solved by standard techniques.
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*
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* 5) Cases where the cubic has multiple real roots can sometimes
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* occur, corresponding to extreme instances of barrel distortion
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* where up to three different undistorted [X,Y]s all produce the
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* same distorted [X,Y]. However, only one solution is returned,
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* the one that produces the smallest change in [X,Y].
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*
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* P.T.Wallace Starlink 3 September 2000
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*
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* Copyright (C) 2000 Rutherford Appleton Laboratory
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*
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* License:
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program (see SLA_CONDITIONS); if not, write to the
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* Free Software Foundation, Inc., 59 Temple Place, Suite 330,
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* Boston, MA 02111-1307 USA
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*
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*-
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IMPLICIT NONE
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DOUBLE PRECISION DISCO,X,Y
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DOUBLE PRECISION THIRD
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PARAMETER (THIRD=1D0/3D0)
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DOUBLE PRECISION D2PI
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PARAMETER (D2PI=6.283185307179586476925286766559D0)
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DOUBLE PRECISION RP,Q,R,D,W,S,T,F,C,T3,F1,F2,F3,W1,W2,W3
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* Distance of the point from the origin.
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RP = SQRT(X*X+Y*Y)
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* If zero, or if no distortion, no action is necessary.
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IF (RP.NE.0D0.AND.DISCO.NE.0D0) THEN
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* Begin algebraic solution.
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Q = 1D0/(3D0*DISCO)
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R = RP/(2D0*DISCO)
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W = Q*Q*Q+R*R
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* Continue if one real root, or three of which only one is positive.
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IF (W.GE.0D0) THEN
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D = SQRT(W)
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W = R+D
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S = SIGN(ABS(W)**THIRD,W)
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W = R-D
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T = SIGN((ABS(W))**THIRD,W)
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F = S+T
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ELSE
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* Three different real roots: use geometrical method instead.
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W = 2D0/SQRT(-3D0*DISCO)
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C = 4D0*RP/(DISCO*W*W*W)
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S = SQRT(1D0-MIN(C*C,1D0))
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T3 = ATAN2(S,C)
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* The three solutions.
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F1 = W*COS((D2PI-T3)/3D0)
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F2 = W*COS((T3)/3D0)
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F3 = W*COS((D2PI+T3)/3D0)
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* Pick the one that moves [X,Y] least.
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W1 = ABS(F1-RP)
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W2 = ABS(F2-RP)
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W3 = ABS(F3-RP)
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IF (W1.LT.W2) THEN
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IF (W1.LT.W3) THEN
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F = F1
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ELSE
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F = F3
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END IF
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ELSE
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IF (W2.LT.W3) THEN
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F = F2
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ELSE
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F = F3
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END IF
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END IF
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END IF
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* Remove the distortion.
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F = F/RP
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X = F*X
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Y = F*Y
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END IF
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END
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