C++****************************************************** VAX 9/25/81 C C PARABL.FOR C C ********************************************************************** C=* * C=* This file is part of: SPIDER - Modular Image Processing System. * C=* SPIDER System Authors: Joachim Frank & ArDean Leith * C=* Copyright 1985-2010 Health Research Inc., * C=* Riverview Center, 150 Broadway, Suite 560, Menands, NY 12204. * C=* Email: spider@wadsworth.org * C=* * C=* SPIDER is free software; you can redistribute it and/or * C=* modify it under the terms of the GNU General Public License as * C=* published by the Free Software Foundation; either version 2 of the * C=* License, or (at your option) any later version. * C=* * C=* SPIDER is distributed in the hope that it will be useful, * C=* but WITHOUT ANY WARRANTY; without even the implied warranty of * C=* merchantability or fitness for a particular purpose. See the GNU * C=* General Public License for more details. * C=* You should have received a copy of the GNU General Public License * C=* along with this program. If not, see * C=* * C ********************************************************************** C C PARABL 9/25/81 : PARABOLIC FIT TO 3 BY 3 PEAK NEIGHBORHOOD C C FORMULA FOR PARABOLOID TO BE FITTED INTO THE NINE POINTS: C C F = C1 + C2*Y + C3*Y**2 + C4*X + C5*XY + C6*X**2 C C THE VALUES OF THE COEFFICIENTS C1 - C6 ON THE BASIS OF THE C NINE POINTS AROUND THE PEAK, AS EVALUATED BY ALTRAN: C C--********************************************************************* SUBROUTINE PARABL(Z,XSH,YSH,PEAKV) REAL Z(3,3) C1 = (26.*Z(1,1) - Z(1,2) + 2*Z(1,3) - Z(2,1) - 19.*Z(2,2) 1 -7.*Z(2,3) + 2.*Z(3,1) - 7.*Z(3,2) + 14.*Z(3,3))/9. C C2 = (8.* Z(1,1) - 8.*Z(1,2) + 5.*Z(2,1) - 8.*Z(2,2) + 3.*Z(2,3) 1 +2.*Z(3,1) - 8.*Z(3,2) + 6.*Z(3,3))/(-6.) C C3 = (Z(1,1) - 2.*Z(1,2) + Z(1,3) + Z(2,1) -2.*Z(2,2) 1 + Z(2,3) + Z(3,1) - 2.*Z(3,2) + Z(3,3))/6. C C4 = (8.*Z(1,1) + 5.*Z(1,2) + 2.*Z(1,3) -8.*Z(2,1) -8.*Z(2,2) 1 - 8.*Z(2,3) + 3.*Z(3,2) + 6.*Z(3,3))/(-6.) C C5 = (Z(1,1) - Z(1,3) - Z(3,1) + Z(3,3))/4. C C6 = (Z(1,1) + Z(1,2) + Z(1,3) - 2.*Z(2,1) - 2.*Z(2,2) 1 -2.*Z(2,3) + Z(3,1) + Z(3,2) + Z(3,3))/6. C THE PEAK COORDINATES OF THE PARABOLOID CAN NOW BE EVALUATED AS: YSH = 0.0 XSH = 0.0 DENOM = 4. * C3 * C6 - C5 * C5 IF (DENOM .EQ. 0.) RETURN YSH = (C4*C5 - 2.*C2*C6) / DENOM - 2. XSH = (C2*C5 - 2.*C4*C3) / DENOM - 2. PEAKV = 4.*C1*C3*C6 - C1*C5*C5 - C2*C2*C6 + C2*C4*C5 - C4*C4*C3 PEAKV = PEAKV / DENOM C LIMIT INTERPLATION TO +/- 1. RANGE IF (YSH .LT. -1.) YSH = -1. IF (YSH .GT. +1.) YSH = +1. IF (XSH .LT. -1.) XSH = -1. IF (XSH .GT. +1.) XSH = +1. END