/* * This file is part of RawTherapee. * * Copyright (c) 2004-2010 Gabor Horvath * * RawTherapee is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * RawTherapee is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with RawTherapee. If not, see . */ #include #include #include "curves.h" #include #include #include "mytime.h" #include #include "array2D.h" #include "LUT.h" #undef CLIPD #define CLIPD(a) ((a)>0.0f?((a)<1.0f?(a):1.0f):0.0f) #define CLIP(a) ((a)<65535 ? (a) : (65535)) namespace rtengine { Curve::Curve () { x = 0; y = 0; ypp = 0; hash = NULL; hashSize = 1000; // has to be initiallised to the maximum value } Curve::~Curve () { if (hash) delete [] hash; } void Curve::AddPolygons () { if (firstPointIncluded) { poly_x.push_back(x1); poly_y.push_back(y1); } for (int k=1; k<(nbr_points-1); k++) { double t = k*increment; double t2 = t*t; double tr = 1.-t; double tr2 = tr*tr; double tr2t = tr*2*t; // adding a point to the polyline poly_x.push_back( tr2*x1 + tr2t*x2 + t2*x3); poly_y.push_back( tr2*y1 + tr2t*y2 + t2*y3); } // adding the last point of the sub-curve poly_x.push_back(x3); poly_y.push_back(y3); } void Curve::fillHash() { hash = new unsigned short int[hashSize+2]; unsigned int polyIter = 0; double const increment = 1./hashSize; double milestone = 0.; for (unsigned int i=0; i<(hashSize+1);) { while(poly_x[polyIter] <= milestone) ++polyIter; hash[i] = polyIter-1; milestone = (++i)*increment; } hash[hashSize+1] = poly_x.size()-1; /* // Debug output to file FILE* f = fopen ("hash.txt", "wt"); for (int i=0; i<(hashSize+2); i++) fprintf (f, "%d: %d > %.6f, %.6f\n", i, hash[i], poly_x[hash[i]], poly_y[hash[i]]); fprintf (f, "\nppn: %d\npoly_x: %d\n", ppn, poly_x.size()); fclose (f); */ } // Wikipedia sRGB: Unlike most other RGB color spaces, the sRGB gamma cannot be expressed as a single numerical value. // The overall gamma is approximately 2.2, consisting of a linear (gamma 1.0) section near black, and a non-linear section elsewhere involving a 2.4 exponent // and a gamma (slope of log output versus log input) changing from 1.0 through about 2.3. const double CurveFactory::sRGBGamma = 2.2; const double CurveFactory::sRGBGammaCurve = 2.4; void fillCurveArray(DiagonalCurve* diagCurve, LUTf &outCurve, int skip, bool needed) { if (needed) { LUTf lutCurve (65536); for (int i=0; i<=0xffff; i+= i<0xffff-skip ? skip : 1 ) { // change to [0,1] range double val = (double)i / 65535.0; // apply custom/parametric/NURBS curve, if any val = diagCurve->getVal (val); // store result in a temporary array lutCurve[i] = (val); } // if skip>1, let apply linear interpolation in the skipped points of the curve if (skip > 1) { int prev = 0; for (int i=1; i<=0xffff-skip; i++) { if (i%skip==0) { prev+=skip; continue; } lutCurve[i] = ( lutCurve[prev] * (skip - i%skip) + lutCurve[prev+skip] * (i%skip) ) / skip; } } for (int i=0; i<=0xffff; i++) { outCurve[i] = (65535.0 * lutCurve[i]); } } else { for (int i=0; i<=0xffff; i++) { outCurve[i] = (float)i; } } } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% void CurveFactory::complexsgnCurve (double saturation, bool satlimit, double satlimthresh, const std::vector& acurvePoints, const std::vector& bcurvePoints, LUTf & aoutCurve, LUTf & boutCurve, LUTf & satCurve, int skip) { //colormult = chroma_scale for Lab manipulations //----------------------------------------------------- bool needed; DiagonalCurve* dCurve = NULL; // check if contrast curve is needed needed = (saturation<-0.0001 || saturation>0.0001); // Filling the curve if needed if (needed) { //%%%%%%%%%%%%%%%%% Saturation curve's control points %%%%%%%%%%%%%%%%% std::vector satcurvePoints; satcurvePoints.push_back((double)DCT_NURBS); if (saturation>0) { double satslope = (0.5+2*saturation/500.0)/(0.5-2*saturation/500.0); double scale = (satlimthresh/100.1); if (!satlimit) scale=100/100.1; satcurvePoints.push_back(0); //black point. Value in [0 ; 1] range satcurvePoints.push_back(0); //black point. Value in [0 ; 1] range //if (satlimit) { satcurvePoints.push_back(0.5-0.5*scale); //toe point satcurvePoints.push_back(0.5-0.5*scale); //value at toe point satcurvePoints.push_back(0.5-(0.5/satslope)*scale); //toe point satcurvePoints.push_back(0.5-0.5*scale); //value at toe point satcurvePoints.push_back(0.5+(0.5/satslope)*scale); //shoulder point satcurvePoints.push_back(0.5+0.5*scale); //value at shoulder point satcurvePoints.push_back(0.5+0.5*scale); //shoulder point satcurvePoints.push_back(0.5+0.5*scale); //value at shoulder point /*} else { satcurvePoints.push_back(0.25+saturation/500.0); //toe point satcurvePoints.push_back(0.25-saturation/500.0); //value at toe point satcurvePoints.push_back(0.75-saturation/500.0); //shoulder point satcurvePoints.push_back(0.75+saturation/500.0); //value at shoulder point }*/ satcurvePoints.push_back(1); // white point satcurvePoints.push_back(1); // value at white point } else { satcurvePoints.push_back(0); satcurvePoints.push_back(-(saturation/200.0)); satcurvePoints.push_back(1); satcurvePoints.push_back(1+saturation/200.0); } dCurve = new DiagonalCurve (satcurvePoints, CURVES_MIN_POLY_POINTS/skip); //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% fillCurveArray(dCurve, satCurve, skip, needed); delete dCurve; dCurve = NULL; } else { fillCurveArray(NULL, satCurve, skip, needed); } //----------------------------------------------------- needed = false; // create a curve if needed if (acurvePoints.size()>0 && acurvePoints[0]!=0) { dCurve = new DiagonalCurve (acurvePoints, CURVES_MIN_POLY_POINTS/skip); if (dCurve && !dCurve->isIdentity()) needed = true; } fillCurveArray(dCurve, aoutCurve, skip, needed); if (dCurve) { delete dCurve; dCurve = NULL; } //----------------------------------------------------- needed = false; if (bcurvePoints.size()>0 && bcurvePoints[0]!=0) { dCurve = new DiagonalCurve (bcurvePoints, CURVES_MIN_POLY_POINTS/skip); if (dCurve && !dCurve->isIdentity()) needed = true; } fillCurveArray(dCurve, boutCurve, skip, needed); if (dCurve) { delete dCurve; dCurve = NULL; } } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% void CurveFactory::complexCurve (double ecomp, double black, double hlcompr, double hlcomprthresh, double shcompr, double br, double contr, double gamma_, bool igamma_, const std::vector& curvePoints, LUTu & histogram, LUTu & histogramCropped, LUTf & hlCurve, LUTf & shCurve, LUTf & outCurve, LUTu & outBeforeCCurveHistogram, int skip) { //double def_mul = pow (2.0, defmul); /*printf ("def_mul= %f ecomp= %f black= %f hlcompr= %f shcompr= %f br= %f contr= %f defmul= %f gamma= %f, skip= %d \n",def_mul,ecomp,black,hlcompr,shcompr,br,contr,defmul,gamma_,skip);*/ // compute parameters of the gamma curve /*double start = exp(gamma_*log( -0.099 / ((1.0/gamma_-1.0)*1.099 ))); double slope = 1.099 * pow (start, 1.0/gamma_-1) - 0.099/start; double mul = 1.099; double add = 0.099; // gamma BT709*/ //normalize gamma to sRGB double start = exp(gamma_*log( -0.055 / ((1.0/gamma_-1.0)*1.055 ))); double slope = 1.055 * pow (start, 1.0/gamma_-1) - 0.055/start; double mul = 1.055; double add = 0.055; // a: slope of the curve, black: starting point at the x axis double a = pow (2.0, ecomp); // curve without contrast LUTf dcurve(0x10000); // check if inverse gamma is needed at the end bool needigamma = igamma_ && gamma_>0; // clear array that stores histogram valid before applying the custom curve outBeforeCCurveHistogram.clear(); //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // tone curve base. a: slope (from exp.comp.), b: black, def_mul: max. x value (can be>1), hr,sr: highlight,shadow recovery //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DiagonalCurve* brightcurve = NULL; // check if brightness curve is needed if (br>0.00001 || br<-0.00001) { std::vector brightcurvePoints; brightcurvePoints.push_back((double)DCT_NURBS); brightcurvePoints.push_back(0.); //black point. Value in [0 ; 1] range brightcurvePoints.push_back(0.); //black point. Value in [0 ; 1] range if(br>0) { brightcurvePoints.push_back(0.1); //toe point brightcurvePoints.push_back(0.1+br/150.0); //value at toe point brightcurvePoints.push_back(0.7); //shoulder point brightcurvePoints.push_back(MIN(1.0,0.7+br/300.0)); //value at shoulder point } else { brightcurvePoints.push_back(MAX(0.0,0.1-br/150.0)); //toe point brightcurvePoints.push_back(0.1); //value at toe point brightcurvePoints.push_back(0.7-br/300.0); //shoulder point brightcurvePoints.push_back(0.7); //value at shoulder point } brightcurvePoints.push_back(1.); // white point brightcurvePoints.push_back(1.); // value at white point brightcurve = new DiagonalCurve (brightcurvePoints, CURVES_MIN_POLY_POINTS/skip); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% float exp_scale = a; float scale = 65536.0; float comp = (MAX(0,ecomp) + 1.0)*hlcompr/100.0; float shoulder = ((scale/MAX(1,exp_scale))*(hlcomprthresh/200.0))+0.1; //printf("shoulder = %e\n",shoulder); //printf ("exp_scale= %f comp= %f def_mul=%f a= %f \n",exp_scale,comp,def_mul,a); for (int i=0; i<0x10000; i++) { // change to [0,1] range float val = (float)i-shoulder; if (comp>0.0) { if (val>0.0) { float R = val*comp/(scale-shoulder); hlCurve[i] = log(1.0+R*exp_scale)/R; } else { hlCurve[i]=exp_scale; } } else { hlCurve[i]=exp_scale; } //%%%%%%%%%%%%%%%%%%%%%%%%%% // change to [0,1] range if (i!=0) { val = (float)i / 65535.0f; } else { val = 1.0/65535.0; } float val2 = basecurve (val, 1.0, black, 1.0, 0.0, 1.5*shcompr/100.0); shCurve[i] = CLIPD(val2)/val; //%%%%%%%%%%%%%%%%%%%%%%%%%% // change to [0,1] range val = (double)i / 65535.0; // gamma correction if (gamma_>1) val = gamma (val, gamma_, start, slope, mul, add); // apply brightness curve if (brightcurve) val = brightcurve->getVal (val); // TODO: getVal(double) is very slow! Optimize with a LUTf // store result in a temporary array dcurve[i] = CLIPD(val); } if (brightcurve) delete brightcurve; //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // check if contrast curve is needed if (contr>0.00001 || contr<-0.00001) { // compute mean luminance of the image with the curve applied int sum = 0; float avg = 0; //double sqavg = 0; for (int i=0; i<=0xffff; i++) { float fi=i; fi = hlCurve[fi]*fi; avg += dcurve[(int)(shCurve[fi]*fi)] * histogram[i]; //sqavg += dcurve[i]*dcurve[i] * histogram[i]; sum += histogram[i]; } avg /= sum; //sqavg /= sum; //double stddev = sqrt(sqavg-avg*avg); //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% std::vector contrastcurvePoints; contrastcurvePoints.push_back((double)DCT_NURBS); contrastcurvePoints.push_back(0); //black point. Value in [0 ; 1] range contrastcurvePoints.push_back(0); //black point. Value in [0 ; 1] range contrastcurvePoints.push_back(avg-avg*(0.6-contr/250.0)); //toe point contrastcurvePoints.push_back(avg-avg*(0.6+contr/250.0)); //value at toe point contrastcurvePoints.push_back(avg+(1-avg)*(0.6-contr/250.0)); //shoulder point contrastcurvePoints.push_back(avg+(1-avg)*(0.6+contr/250.0)); //value at shoulder point contrastcurvePoints.push_back(1); // white point contrastcurvePoints.push_back(1); // value at white point DiagonalCurve* contrastcurve = new DiagonalCurve (contrastcurvePoints, CURVES_MIN_POLY_POINTS/skip); //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // apply contrast enhancement for (int i=0; i<=0xffff; i++) { dcurve[i] = contrastcurve->getVal (dcurve[i]); } delete contrastcurve; } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // create a curve if needed bool histNeeded = false; DiagonalCurve* tcurve = NULL; if (curvePoints.size()>0 && curvePoints[0]!=0) { tcurve = new DiagonalCurve (curvePoints, CURVES_MIN_POLY_POINTS/skip); if (outBeforeCCurveHistogram /*&& histogramCropped*/) histNeeded = true; } if (tcurve && tcurve->isIdentity()) { delete tcurve; tcurve = NULL; } for (int i=0; i<=0xffff; i++) { float val; if (histNeeded) { float fi=i; float hval = hlCurve[i]*fi; hval = dcurve[shCurve[hval]*hval]; //if (needigamma) // hval = igamma2 (hval); int hi = (int)(255.0*(hval)); outBeforeCCurveHistogram[hi] += histogram/*Cropped*/[i] ; } // apply custom/parametric/NURBS curve, if any if (tcurve) { val = tcurve->getVal (dcurve[i]); // TODO: getVal(double) is very slow! Optimize with a LUTf } else { val = (dcurve[i]); } // if inverse gamma is needed, do it (standard sRGB inverse gamma is applied) if (needigamma) val = igamma (val, gamma_, start, slope, mul, add); outCurve[i] = (65535.0 * val); } if (tcurve) delete tcurve; /*if (outBeforeCCurveHistogram) { for (int i=0; i<256; i++) printf("i= %d bchist= %d \n",i,outBeforeCCurveHistogram[i]); }*/ } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% void CurveFactory::complexLCurve (double br, double contr, const std::vector& curvePoints, LUTu & histogram, LUTu & histogramCropped, LUTf & outCurve, LUTu & outBeforeCCurveHistogram, int skip) { // curve without contrast LUTf dcurve(65536,0); // clear array that stores histogram valid before applying the custom curve if (outBeforeCCurveHistogram) outBeforeCCurveHistogram.clear(); //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // tone curve base. a: slope (from exp.comp.), b: black, def_mul: max. x value (can be>1), hr,sr: highlight,shadow recovery //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // check if brightness curve is needed if (br>0.00001 || br<-0.00001) { std::vector brightcurvePoints; brightcurvePoints.push_back((double)((CurveType)DCT_NURBS)); brightcurvePoints.push_back(0.); // black point. Value in [0 ; 1] range brightcurvePoints.push_back(0.); // black point. Value in [0 ; 1] range if (br>0) { brightcurvePoints.push_back(0.1); // toe point brightcurvePoints.push_back(0.1+br/150.0); //value at toe point brightcurvePoints.push_back(0.7); // shoulder point brightcurvePoints.push_back(MIN(1.0,0.7+br/300.0)); //value at shoulder point } else { brightcurvePoints.push_back(0.1-br/150.0); // toe point brightcurvePoints.push_back(0.1); // value at toe point brightcurvePoints.push_back(MIN(1.0,0.7-br/300.0)); // shoulder point brightcurvePoints.push_back(0.7); // value at shoulder point } brightcurvePoints.push_back(1.); // white point brightcurvePoints.push_back(1.); // value at white point DiagonalCurve* brightcurve = new DiagonalCurve (brightcurvePoints, CURVES_MIN_POLY_POINTS/skip); //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // Applying brightness curve for (int i=0; i<32768; i++) { // L values range up to 32767, higher values are for highlight overflow // change to [0,1] range float val = (float)i / 32767.0; // apply brightness curve val = brightcurve->getVal (val); // store result in a temporary array dcurve[i] = CLIPD(val); } delete brightcurve; } else { for (int i=0; i<32768; i++) { // L values range up to 32767, higher values are for highlight overflow // set the identity curve in the temporary array dcurve[i] = (float)i / 32767.0; } } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // check if contrast curve is needed if (contr>0.00001 || contr<-0.00001) { // compute mean luminance of the image with the curve applied int sum = 0; float avg = 0; //float sqavg = 0; for (int i=0; i<32768; i++) { avg += dcurve[i] * histogram[i]; //sqavg += dcurve[i]*dcurve[i] * histogram[i]; sum += histogram[i]; } avg /= sum; //sqavg /= sum; //float stddev = sqrt(sqavg-avg*avg); //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% std::vector contrastcurvePoints; contrastcurvePoints.push_back((double)((CurveType)DCT_NURBS)); contrastcurvePoints.push_back(0.); // black point. Value in [0 ; 1] range contrastcurvePoints.push_back(0.); // black point. Value in [0 ; 1] range contrastcurvePoints.push_back(avg-avg*(0.6-contr/250.0)); // toe point contrastcurvePoints.push_back(avg-avg*(0.6+contr/250.0)); // value at toe point contrastcurvePoints.push_back(avg+(1-avg)*(0.6-contr/250.0)); // shoulder point contrastcurvePoints.push_back(avg+(1-avg)*(0.6+contr/250.0)); // value at shoulder point contrastcurvePoints.push_back(1.); // white point contrastcurvePoints.push_back(1.); // value at white point DiagonalCurve* contrastcurve = new DiagonalCurve (contrastcurvePoints, CURVES_MIN_POLY_POINTS/skip); //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // apply contrast enhancement for (int i=0; i<32768; i++) { dcurve[i] = contrastcurve->getVal (dcurve[i]); } delete contrastcurve; } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // create a curve if needed DiagonalCurve* tcurve = NULL; bool histNeeded = false; if (curvePoints.size()>0 && curvePoints[0]!=0) { tcurve = new DiagonalCurve (curvePoints, CURVES_MIN_POLY_POINTS/skip); if (outBeforeCCurveHistogram /*&& histogramCropped*/) histNeeded = true; } if (tcurve && tcurve->isIdentity()) { delete tcurve; tcurve = NULL; } if (tcurve) { // L values go up to 32767, last stop is for highlight overflow for (int i=0; i<32768; i++) { float val; if (histNeeded) { float hval = dcurve[i]; int hi = (int)(255.0*CLIPD(hval)); outBeforeCCurveHistogram[hi]+=histogram/*Cropped*/[i] ; } // apply custom/parametric/NURBS curve, if any val = tcurve->getVal (dcurve[i]); outCurve[i] = (32767.0 * val); } } else { // Skip the slow getval method if no curve is used (or an identity curve) // L values go up to 32767, last stop is for highlight overflow for (int i=0; i<32768; i++) { if (histNeeded) { float hval = dcurve[i]; int hi = (int)(255.0*CLIPD(hval)); outBeforeCCurveHistogram[hi]+=histogram/*Cropped*/[i] ; } outCurve[i] = 32767.0*dcurve[i]; } } for (int i=32768; i<65536; i++) outCurve[i]=(float)i; if (tcurve) delete tcurve; /*if (outBeforeCCurveHistogram) { for (int i=0; i<256; i++) printf("i= %d bchist= %d \n",i,outBeforeCCurveHistogram[i]); }*/ } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% void CurveFactory::RGBCurve (const std::vector& curvePoints, LUTf & outCurve, int skip) { //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% // create a curve if needed DiagonalCurve* tcurve = NULL; bool histNeeded = false; if (curvePoints.size()>0 && curvePoints[0]!=0) { tcurve = new DiagonalCurve (curvePoints, CURVES_MIN_POLY_POINTS/skip); } if (tcurve && tcurve->isIdentity()) { delete tcurve; tcurve = NULL; } if (tcurve) { for (int i=0; i<65536; i++) { // apply custom/parametric/NURBS curve, if any float val = tcurve->getVal ((float)i/65536.0f); outCurve[i] = (65536.0f * val); } } else { // Skip the slow getval method if no curve is used (or an identity curve) for (int i=0; i<65536; i++) { outCurve[i] = i; } } if (tcurve) delete tcurve; } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LUTf CurveFactory::gammatab; LUTf CurveFactory::igammatab_srgb; LUTf CurveFactory::gammatab_srgb; void CurveFactory::init () { gammatab(65536,0); igammatab_srgb(65536,0); gammatab_srgb(65536,0); for (int i=0; i<65536; i++) gammatab_srgb[i] = (65535.0 * gamma2 (i/65535.0)); for (int i=0; i<65536; i++) igammatab_srgb[i] = (65535.0 * igamma2 (i/65535.0)); for (int i=0; i<65536; i++) gammatab[i] = (65535.0 * pow (i/65535.0, 0.454545)); /* FILE* f = fopen ("c.txt", "wt"); for (int i=0; i<256; i++) fprintf (f, "%g %g\n", i/255.0, clower (i/255.0, 2.0, 1.0)); fclose (f);*/ } }