EVOLUTION-MANAGER

Edit File: gdal_rpc.cpp

/******************************************************************************
 *
 * Project:  Image Warper
 * Purpose:  Implements a rational polynomial (RPC) based transformer.
 * Author:   Frank Warmerdam, warmerdam@pobox.com
 *
 ******************************************************************************
 * Copyright (c) 2003, Frank Warmerdam <warmerdam@pobox.com>
 * Copyright (c) 2009-2013, Even Rouault <even dot rouault at mines-paris dot org>
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included
 * in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 * DEALINGS IN THE SOFTWARE.
 ****************************************************************************/

#include "cpl_port.h"
#include "gdal_alg.h"

#include <cmath>
#include <cstddef>
#include <cstdlib>
#include <cstring>

#include <algorithm>
#include <string>

#include "cpl_conv.h"
#include "cpl_error.h"
#include "cpl_minixml.h"
#include "cpl_string.h"
#include "cpl_vsi.h"
#include "gdal.h"
#include "gdal_mdreader.h"
#include "gdal_priv.h"
#if defined(__x86_64) || defined(_M_X64)
#  define USE_SSE2_OPTIM
#  include "gdalsse_priv.h"
#endif
#include "ogr_api.h"
#include "ogr_spatialref.h"
#include "ogr_srs_api.h"

// #define DEBUG_VERBOSE_EXTRACT_DEM

CPL_CVSID("$Id: gdal_rpc.cpp 9ff327806cd64df6d73a6c91f92d12ca0c5e07df 2018-04-07 20:25:06 +0200 Even Rouault $")

CPL_C_START
CPLXMLNode *GDALSerializeRPCTransformer( void *pTransformArg );
void *GDALDeserializeRPCTransformer( CPLXMLNode *psTree );
CPL_C_END

constexpr int MAX_ABS_VALUE_WARNINGS = 20;
constexpr double DEFAULT_PIX_ERR_THRESHOLD = 0.1;

/************************************************************************/
/*                            RPCInfoToMD()                             */
/*                                                                      */
/*      Turn an RPCInfo structure back into its metadata format.        */
/************************************************************************/

char ** RPCInfoToMD( GDALRPCInfo *psRPCInfo )

{
    char **papszMD = nullptr;
    CPLString osField, osMultiField;

osField.Printf( "%.15g", psRPCInfo->dfLINE_OFF );
    papszMD = CSLSetNameValue( papszMD, RPC_LINE_OFF, osField );

osField.Printf( "%.15g", psRPCInfo->dfSAMP_OFF );
    papszMD = CSLSetNameValue( papszMD, RPC_SAMP_OFF, osField );

osField.Printf( "%.15g", psRPCInfo->dfLAT_OFF );
    papszMD = CSLSetNameValue( papszMD, RPC_LAT_OFF, osField );

osField.Printf( "%.15g", psRPCInfo->dfLONG_OFF );
    papszMD = CSLSetNameValue( papszMD, RPC_LONG_OFF, osField );

osField.Printf( "%.15g", psRPCInfo->dfHEIGHT_OFF );
    papszMD = CSLSetNameValue( papszMD, RPC_HEIGHT_OFF, osField );

osField.Printf( "%.15g", psRPCInfo->dfLINE_SCALE );
    papszMD = CSLSetNameValue( papszMD, RPC_LINE_SCALE, osField );

osField.Printf( "%.15g", psRPCInfo->dfSAMP_SCALE );
    papszMD = CSLSetNameValue( papszMD, RPC_SAMP_SCALE, osField );

osField.Printf( "%.15g", psRPCInfo->dfLAT_SCALE );
    papszMD = CSLSetNameValue( papszMD, RPC_LAT_SCALE, osField );

osField.Printf( "%.15g", psRPCInfo->dfLONG_SCALE );
    papszMD = CSLSetNameValue( papszMD, RPC_LONG_SCALE, osField );

osField.Printf( "%.15g", psRPCInfo->dfHEIGHT_SCALE );
    papszMD = CSLSetNameValue( papszMD, RPC_HEIGHT_SCALE, osField );

osField.Printf( "%.15g", psRPCInfo->dfMIN_LONG );
    papszMD = CSLSetNameValue( papszMD, RPC_MIN_LONG, osField );

osField.Printf( "%.15g", psRPCInfo->dfMIN_LAT );
    papszMD = CSLSetNameValue( papszMD, RPC_MIN_LAT, osField );

osField.Printf( "%.15g", psRPCInfo->dfMAX_LONG );
    papszMD = CSLSetNameValue( papszMD, RPC_MAX_LONG, osField );

osField.Printf( "%.15g", psRPCInfo->dfMAX_LAT );
    papszMD = CSLSetNameValue( papszMD, RPC_MAX_LAT, osField );

for( int i = 0; i < 20; i++ )
    {
        osField.Printf( "%.15g", psRPCInfo->adfLINE_NUM_COEFF[i] );
        if( i > 0 )
            osMultiField += " ";
        else
            osMultiField = "";
        osMultiField += osField;
    }
    papszMD = CSLSetNameValue( papszMD, "LINE_NUM_COEFF", osMultiField );

for( int i = 0; i < 20; i++ )
    {
        osField.Printf( "%.15g", psRPCInfo->adfLINE_DEN_COEFF[i] );
        if( i > 0 )
            osMultiField += " ";
        else
            osMultiField = "";
        osMultiField += osField;
    }
    papszMD = CSLSetNameValue( papszMD, "LINE_DEN_COEFF", osMultiField );

for( int i = 0; i < 20; i++ )
    {
        osField.Printf( "%.15g", psRPCInfo->adfSAMP_NUM_COEFF[i] );
        if( i > 0 )
            osMultiField += " ";
        else
            osMultiField = "";
        osMultiField += osField;
    }
    papszMD = CSLSetNameValue( papszMD, "SAMP_NUM_COEFF", osMultiField );

for( int i = 0; i < 20; i++ )
    {
        osField.Printf( "%.15g", psRPCInfo->adfSAMP_DEN_COEFF[i] );
        if( i > 0 )
            osMultiField += " ";
        else
            osMultiField = "";
        osMultiField += osField;
    }
    papszMD = CSLSetNameValue( papszMD, "SAMP_DEN_COEFF", osMultiField );

return papszMD;
}

/************************************************************************/
/*                          RPCComputeTerms()                           */
/************************************************************************/

static void RPCComputeTerms( double dfLong, double dfLat, double dfHeight,
                             double *padfTerms )

{
    padfTerms[0] = 1.0;
    padfTerms[1] = dfLong;
    padfTerms[2] = dfLat;
    padfTerms[3] = dfHeight;
    padfTerms[4] = dfLong * dfLat;
    padfTerms[5] = dfLong * dfHeight;
    padfTerms[6] = dfLat * dfHeight;
    padfTerms[7] = dfLong * dfLong;
    padfTerms[8] = dfLat * dfLat;
    padfTerms[9] = dfHeight * dfHeight;

padfTerms[10] = dfLong * dfLat * dfHeight;
    padfTerms[11] = dfLong * dfLong * dfLong;
    padfTerms[12] = dfLong * dfLat * dfLat;
    padfTerms[13] = dfLong * dfHeight * dfHeight;
    padfTerms[14] = dfLong * dfLong * dfLat;
    padfTerms[15] = dfLat * dfLat * dfLat;
    padfTerms[16] = dfLat * dfHeight * dfHeight;
    padfTerms[17] = dfLong * dfLong * dfHeight;
    padfTerms[18] = dfLat * dfLat * dfHeight;
    padfTerms[19] = dfHeight * dfHeight * dfHeight;
}

/************************************************************************/
/* ==================================================================== */
/*                           GDALRPCTransformer                         */
/* ==================================================================== */
/************************************************************************/

/*! DEM Resampling Algorithm */
typedef enum {
  /*! Nearest neighbour (select on one input pixel) */ DRA_NearestNeighbour=0,
  /*! Bilinear (2x2 kernel) */                         DRA_Bilinear=1,
  /*! Cubic Convolution Approximation (4x4 kernel) */  DRA_Cubic=2
} DEMResampleAlg;

typedef struct {

GDALTransformerInfo sTI;

GDALRPCInfo sRPC;

double      adfPLToLatLongGeoTransform[6];
    double      dfRefZ;

int         bReversed;

double      dfPixErrThreshold;

double      dfHeightOffset;

double      dfHeightScale;

char        *pszDEMPath;

DEMResampleAlg eResampleAlg;

int         bHasDEMMissingValue;
    double      dfDEMMissingValue;
    int         bApplyDEMVDatumShift;

GDALDataset *poDS;
    double     *padfDEMBuffer;
    int         nDEMExtractions;
    int         nBufferMaxRadius;
    int         nHitsInBuffer;
    int         nBufferX;
    int         nBufferY;
    int         nBufferWidth;
    int         nBufferHeight;
    int         nLastQueriedX;
    int         nLastQueriedY;

OGRCoordinateTransformation *poCT;

int         nMaxIterations;

double      adfDEMGeoTransform[6];
    double      adfDEMReverseGeoTransform[6];

#ifdef USE_SSE2_OPTIM
    double      adfDoubles[20 * 4 + 1];
     // LINE_NUM_COEFF, LINE_DEN_COEFF, SAMP_NUM_COEFF and then SAMP_DEN_COEFF.
    double     *padfCoeffs;
#endif

bool        bRPCInverseVerbose;
    char       *pszRPCInverseLog;
} GDALRPCTransformInfo;

static bool GDALRPCOpenDEM( GDALRPCTransformInfo* psTransform );

/************************************************************************/
/*                            RPCEvaluate()                             */
/************************************************************************/
#ifdef USE_SSE2_OPTIM

static void RPCEvaluate4( const double *padfTerms,
                          const double *padfCoefs,
                          double& dfSum1, double& dfSum2,
                          double& dfSum3, double& dfSum4 )

{
    XMMReg2Double sum1 = XMMReg2Double::Zero();
    XMMReg2Double sum2 = XMMReg2Double::Zero();
    XMMReg2Double sum3 = XMMReg2Double::Zero();
    XMMReg2Double sum4 = XMMReg2Double::Zero();
    for( int i = 0; i < 20; i += 2 )
    {
        const XMMReg2Double terms =
            XMMReg2Double::Load2ValAligned(padfTerms + i);

// LINE_NUM_COEFF.
        const XMMReg2Double coefs1 =
            XMMReg2Double::Load2ValAligned(padfCoefs + i);

// LINE_DEN_COEFF.
        const XMMReg2Double coefs2 =
            XMMReg2Double::Load2ValAligned(padfCoefs + i + 20);

// SAMP_NUM_COEFF.
        const XMMReg2Double coefs3 =
            XMMReg2Double::Load2ValAligned(padfCoefs + i + 40);

// SAMP_DEN_COEFF.
        const XMMReg2Double coefs4 =
            XMMReg2Double::Load2ValAligned(padfCoefs + i + 60);

sum1 += terms * coefs1;
        sum2 += terms * coefs2;
        sum3 += terms * coefs3;
        sum4 += terms * coefs4;
    }
    dfSum1 = sum1.GetHorizSum();
    dfSum2 = sum2.GetHorizSum();
    dfSum3 = sum3.GetHorizSum();
    dfSum4 = sum4.GetHorizSum();
}

#else

static double RPCEvaluate( const double *padfTerms, const double *padfCoefs )

{
    double dfSum1 = 0.0;
    double dfSum2 = 0.0;

for( int i = 0; i < 20; i += 2 )
    {
        dfSum1 += padfTerms[i] * padfCoefs[i];
        dfSum2 += padfTerms[i+1] * padfCoefs[i+1];
    }

return dfSum1 + dfSum2;
}

#endif

/************************************************************************/
/*                         RPCTransformPoint()                          */
/************************************************************************/

static void RPCTransformPoint( const GDALRPCTransformInfo *psRPCTransformInfo,
                               double dfLong, double dfLat, double dfHeight,
                               double *pdfPixel, double *pdfLine )

{
    double adfTermsWithMargin[20+1] = {};
    // Make padfTerms aligned on 16-byte boundary for SSE2 aligned loads.
    double* padfTerms =
        adfTermsWithMargin + (reinterpret_cast<GUIntptr_t>(adfTermsWithMargin) % 16) / 8;

// Avoid dateline issues.
    double diffLong = dfLong - psRPCTransformInfo->sRPC.dfLONG_OFF;
    if( diffLong < -270 )
    {
        diffLong += 360;
    }
    else if( diffLong > 270 )
    {
        diffLong -= 360;
    }

const double dfNormalizedLong =
      diffLong / psRPCTransformInfo->sRPC.dfLONG_SCALE;
    const double dfNormalizedLat =
        (dfLat - psRPCTransformInfo->sRPC.dfLAT_OFF) /
        psRPCTransformInfo->sRPC.dfLAT_SCALE;
    const double dfNormalizedHeight =
        (dfHeight - psRPCTransformInfo->sRPC.dfHEIGHT_OFF) /
        psRPCTransformInfo->sRPC.dfHEIGHT_SCALE;

// The absolute values of the 3 above normalized values are supposed to be
    // below 1. Warn (as debug message) if it is not the case. We allow for some
    // margin above 1 (1.5, somewhat arbitrary chosen) before warning.
    static int nCountWarningsAboutAboveOneNormalizedValues = 0;
    if( nCountWarningsAboutAboveOneNormalizedValues < MAX_ABS_VALUE_WARNINGS )
    {
        bool bWarned = false;
        if( fabs(dfNormalizedLong) > 1.5 )
        {
            bWarned = true;
            CPLDebug(
                "RPC", "Normalized %s for (lon,lat,height)=(%f,%f,%f) is %f, "
                "i.e. with an absolute value of > 1, which may cause numeric "
                "stability problems",
                "longitude", dfLong, dfLat, dfHeight, dfNormalizedLong );
        }
        if( fabs(dfNormalizedLat) > 1.5 )
        {
            bWarned = true;
            CPLDebug(
                "RPC", "Normalized %s for (lon,lat,height)=(%f,%f,%f) is %f, "
                "ie with an absolute value of > 1, which may cause numeric "
                "stability problems",
                "latitude", dfLong, dfLat, dfHeight, dfNormalizedLat );
        }
        if( fabs(dfNormalizedHeight) > 1.5 )
        {
            bWarned = true;
            CPLDebug(
                "RPC", "Normalized %s for (lon,lat,height)=(%f,%f,%f) is %f, "
                "i.e. with an absolute value of > 1, which may cause numeric "
                "stability problems",
                "height", dfLong, dfLat, dfHeight, dfNormalizedHeight);
        }
        if( bWarned )
        {
            // Limit the number of warnings.
            nCountWarningsAboutAboveOneNormalizedValues++;
            if( nCountWarningsAboutAboveOneNormalizedValues ==
                MAX_ABS_VALUE_WARNINGS )
            {
                CPLDebug("RPC", "No more such debug warnings will be emitted");
            }
        }
    }

RPCComputeTerms( dfNormalizedLong, dfNormalizedLat,
                     dfNormalizedHeight, padfTerms );

#ifdef USE_SSE2_OPTIM
    double dfSampNum = 0.0;
    double dfSampDen = 0.0;
    double dfLineNum = 0.0;
    double dfLineDen = 0.0;
    RPCEvaluate4( padfTerms,
                  psRPCTransformInfo->padfCoeffs,
                  dfLineNum, dfLineDen, dfSampNum, dfSampDen );
    const double dfResultX = dfSampNum / dfSampDen;
    const double dfResultY = dfLineNum / dfLineDen;
#else
    const double dfResultX =
        RPCEvaluate( padfTerms, psRPCTransformInfo->sRPC.adfSAMP_NUM_COEFF )
        / RPCEvaluate( padfTerms, psRPCTransformInfo->sRPC.adfSAMP_DEN_COEFF );

const double dfResultY =
        RPCEvaluate( padfTerms, psRPCTransformInfo->sRPC.adfLINE_NUM_COEFF )
        / RPCEvaluate( padfTerms, psRPCTransformInfo->sRPC.adfLINE_DEN_COEFF );
#endif

// RPCs are using the center of upper left pixel = 0,0 convention
    // convert to top left corner = 0,0 convention used in GDAL.
    *pdfPixel = dfResultX * psRPCTransformInfo->sRPC.dfSAMP_SCALE
        + psRPCTransformInfo->sRPC.dfSAMP_OFF + 0.5;
    *pdfLine = dfResultY * psRPCTransformInfo->sRPC.dfLINE_SCALE
        + psRPCTransformInfo->sRPC.dfLINE_OFF + 0.5;
}

/************************************************************************/
/*                     GDALSerializeRPCDEMResample()                    */
/************************************************************************/

static const char* GDALSerializeRPCDEMResample(DEMResampleAlg eResampleAlg)
{
    switch(eResampleAlg)
    {
        case  DRA_NearestNeighbour:
            return "near";
        case DRA_Cubic:
            return "cubic";
        default:
        case DRA_Bilinear:
            return "bilinear";
    }
}

/************************************************************************/
/*                   GDALCreateSimilarRPCTransformer()                  */
/************************************************************************/

static
void* GDALCreateSimilarRPCTransformer( void *hTransformArg,
                                       double dfRatioX, double dfRatioY )
{
    VALIDATE_POINTER1( hTransformArg, "GDALCreateSimilarRPCTransformer", nullptr );

GDALRPCTransformInfo *psInfo =
        static_cast<GDALRPCTransformInfo *>(hTransformArg);

GDALRPCInfo sRPC;
    memcpy(&sRPC, &(psInfo->sRPC), sizeof(GDALRPCInfo));

if( dfRatioX != 1.0 || dfRatioY != 1.0 )
    {
        sRPC.dfLINE_OFF /= dfRatioY;
        sRPC.dfLINE_SCALE /= dfRatioY;
        sRPC.dfSAMP_OFF /= dfRatioX;
        sRPC.dfSAMP_SCALE /= dfRatioX;
    }

char** papszOptions = nullptr;
    papszOptions = CSLSetNameValue(papszOptions, "RPC_HEIGHT",
                                   CPLSPrintf("%.18g", psInfo->dfHeightOffset));
    papszOptions = CSLSetNameValue(papszOptions, "RPC_HEIGHT_SCALE",
                                   CPLSPrintf("%.18g", psInfo->dfHeightScale));
    if( psInfo->pszDEMPath != nullptr )
    {
        papszOptions =
            CSLSetNameValue(papszOptions, "RPC_DEM", psInfo->pszDEMPath);
        papszOptions =
            CSLSetNameValue(papszOptions, "RPC_DEMINTERPOLATION",
                            GDALSerializeRPCDEMResample(psInfo->eResampleAlg));
        if( psInfo->bHasDEMMissingValue )
            papszOptions =
                CSLSetNameValue(papszOptions, "RPC_DEM_MISSING_VALUE",
                                CPLSPrintf("%.18g", psInfo->dfDEMMissingValue));
        papszOptions =
            CSLSetNameValue(papszOptions, "RPC_DEM_APPLY_VDATUM_SHIFT",
                            (psInfo->bApplyDEMVDatumShift) ? "TRUE" : "FALSE") ;
    }
    papszOptions = CSLSetNameValue(papszOptions, "RPC_MAX_ITERATIONS",
                                   CPLSPrintf("%d", psInfo->nMaxIterations));

GDALRPCTransformInfo* psNewInfo =
        static_cast<GDALRPCTransformInfo*>(GDALCreateRPCTransformer(
            &sRPC, psInfo->bReversed, psInfo->dfPixErrThreshold, papszOptions));
    CSLDestroy(papszOptions);

return psNewInfo;
}

/************************************************************************/
/*                      GDALRPCGetHeightAtLongLat()                     */
/************************************************************************/

static
int GDALRPCGetDEMHeight( GDALRPCTransformInfo *psTransform,
                         const double dfXIn, const double dfYIn,
                         double* pdfDEMH );

static bool GDALRPCGetHeightAtLongLat( GDALRPCTransformInfo *psTransform,
                                       const double dfXIn, const double dfYIn,
                                       double* pdfHeight,
                                       double* pdfDEMPixel = nullptr,
                                       double* pdfDEMLine = nullptr )
{
    double dfVDatumShift = 0.0;
    double dfDEMH = 0.0;
    if( psTransform->poDS )
    {
        double dfX = 0.0;
        double dfY = 0.0;
        double dfXTemp = dfXIn;
        double dfYTemp = dfYIn;
        // Check if dem is not in WGS84 and transform points padfX[i], padfY[i].
        if( psTransform->poCT )
        {
            double dfZ = 0.0;
            if( !psTransform->poCT->Transform(1, &dfXTemp, &dfYTemp, &dfZ) )
            {
                return false;
            }

// We must take the opposite since poCT transforms from
            // WGS84 to geoid. And we are going to do the reverse:
            // take an elevation over the geoid and transforms it to WGS84.
            if( psTransform->bApplyDEMVDatumShift )
                dfVDatumShift = -dfZ;
        }

bool bRetried = false;
retry:
        GDALApplyGeoTransform(
            psTransform->adfDEMReverseGeoTransform,
            dfXTemp, dfYTemp, &dfX, &dfY );
        if( pdfDEMPixel )
            *pdfDEMPixel = dfX;
        if( pdfDEMLine )
            *pdfDEMLine = dfY;

if( !GDALRPCGetDEMHeight( psTransform, dfX, dfY, &dfDEMH) )
        {
            // Try to handle the case where the DEM is in LL WGS84 and spans
            // over [-180,180], (or very close to it ), presumably with much
            // hole in the middle if using VRT, and the longitude goes beyond
            // that interval.
            if( !bRetried && psTransform->poCT == nullptr &&
                (dfXIn >= 180.0 || dfXIn <= -180.0) )
            {
                const int nRasterXSize = psTransform->poDS->GetRasterXSize();
                const double dfMinDEMLong = psTransform->adfDEMGeoTransform[0];
                const double dfMaxDEMLong =
                    psTransform->adfDEMGeoTransform[0]
                    + nRasterXSize * psTransform->adfDEMGeoTransform[1];
                if( fabs( dfMinDEMLong - -180 ) < 0.1 &&
                    fabs( dfMaxDEMLong - 180 ) < 0.1 )
                {
                    if( dfXIn >= 180 )
                    {
                        dfXTemp = dfXIn - 360;
                        dfYTemp = dfYIn;
                    }
                    else
                    {
                        dfXTemp = dfXIn + 360;
                        dfYTemp = dfYIn;
                    }
                    bRetried = true;
                    goto retry;
                }
            }

if( psTransform->bHasDEMMissingValue )
                dfDEMH = psTransform->dfDEMMissingValue;
            else
            {
                return false;
            }
        }
#ifdef DEBUG_VERBOSE_EXTRACT_DEM
        CPLDebug("RPC_DEM", "X=%f, Y=%f -> Z=%f", dfX, dfY, dfDEMH);
#endif
    }

*pdfHeight = dfVDatumShift + (psTransform->dfHeightOffset +
                                  dfDEMH * psTransform->dfHeightScale);
    return true;
}

/************************************************************************/
/*                      GDALCreateRPCTransformer()                      */
/************************************************************************/

/**
 * Create an RPC based transformer.
 *
 * The geometric sensor model describing the physical relationship between
 * image coordinates and ground coordinate is known as a Rigorous Projection
 * Model. A Rigorous Projection Model expresses the mapping of the image space
 * coordinates of rows and columns (r,c) onto the object space reference
 * surface geodetic coordinates (long, lat, height).
 *
 * RPC supports a generic description of the Rigorous Projection Models. The
 * approximation used by GDAL (RPC00) is a set of rational polynomials
 * expressing the normalized row and column values, (rn , cn), as a function of
 * normalized geodetic latitude, longitude, and height, (P, L, H), given a
 * set of normalized polynomial coefficients (LINE_NUM_COEF_n, LINE_DEN_COEF_n,
 * SAMP_NUM_COEF_n, SAMP_DEN_COEF_n). Normalized values, rather than actual
 * values are used in order to minimize introduction of errors during the
 * calculations. The transformation between row and column values (r,c), and
 * normalized row and column values (rn, cn), and between the geodetic
 * latitude, longitude, and height and normalized geodetic latitude,
 * longitude, and height (P, L, H), is defined by a set of normalizing
 * translations (offsets) and scales that ensure all values are contained i
 * the range -1 to +1.
 *
 * This function creates a GDALTransformFunc compatible transformer
 * for going between image pixel/line and long/lat/height coordinates
 * using RPCs.  The RPCs are provided in a GDALRPCInfo structure which is
 * normally read from metadata using GDALExtractRPCInfo().
 *
 * GDAL RPC Metadata has the following entries (also described in GDAL RFC 22
 * and the GeoTIFF RPC document http://geotiff.maptools.org/rpc_prop.html .
 *
 * <ul>
 * <li>ERR_BIAS: Error - Bias. The RMS bias error in meters per horizontal axis
 * of all points in the image (-1.0 if unknown)
 * <li>ERR_RAND: Error - Random. RMS random error in meters per horizontal axis
 * of each point in the image (-1.0 if unknown)
 * <li>LINE_OFF: Line Offset
 * <li>SAMP_OFF: Sample Offset
 * <li>LAT_OFF: Geodetic Latitude Offset
 * <li>LONG_OFF: Geodetic Longitude Offset
 * <li>HEIGHT_OFF: Geodetic Height Offset
 * <li>LINE_SCALE: Line Scale
 * <li>SAMP_SCALE: Sample Scale
 * <li>LAT_SCALE: Geodetic Latitude Scale
 * <li>LONG_SCALE: Geodetic Longitude Scale
 * <li>HEIGHT_SCALE: Geodetic Height Scale

* <li>LINE_NUM_COEFF (1-20): Line Numerator Coefficients. Twenty coefficients
 * for the polynomial in the Numerator of the rn equation. (space separated)
 * <li>LINE_DEN_COEFF (1-20): Line Denominator Coefficients. Twenty coefficients
 * for the polynomial in the Denominator of the rn equation. (space separated)
 * <li>SAMP_NUM_COEFF (1-20): Sample Numerator Coefficients. Twenty coefficients
 * for the polynomial in the Numerator of the cn equation. (space separated)
 * <li>SAMP_DEN_COEFF (1-20): Sample Denominator Coefficients. Twenty
 * coefficients for the polynomial in the Denominator of the cn equation. (space
 * separated)
 * </ul>
 *
 * The transformer normally maps from pixel/line/height to long/lat/height space
 * as a forward transformation though in RPC terms that would be considered
 * an inverse transformation (and is solved by iterative approximation using
 * long/lat/height to pixel/line transformations).  The default direction can
 * be reversed by passing bReversed=TRUE.
 *
 * The iterative solution of pixel/line
 * to lat/long/height is currently run for up to 10 iterations or until
 * the apparent error is less than dfPixErrThreshold pixels.  Passing zero
 * will not avoid all error, but will cause the operation to run for the maximum
 * number of iterations.
 *
 * Starting with GDAL 2.1, debugging of the RPC inverse transformer can be done
 * by setting the RPC_INVERSE_VERBOSE configuration option to YES (in which case
 * extra debug information will be displayed in the "RPC" debug category, so
 * requiring CPL_DEBUG to be also set) and/or by setting RPC_INVERSE_LOG to a
 * filename that will contain the content of iterations (this last option only
 * makes sense when debugging point by point, since each time
 * RPCInverseTransformPoint() is called, the file is rewritten).
 *
 * Additional options to the transformer can be supplied in papszOptions.
 *
 * Options:
 *
 * <ul>
 * <li> RPC_HEIGHT: a fixed height offset to be applied to all points passed
 * in.  In this situation the Z passed into the transformation function is
 * assumed to be height above ground, and the RPC_HEIGHT is assumed to be
 * an average height above sea level for ground in the target scene.
 *
 * <li> RPC_HEIGHT_SCALE: a factor used to multiply heights above ground.
 * Useful when elevation offsets of the DEM are not expressed in meters. (GDAL
 * >= 1.8.0)
 *
 * <li> RPC_DEM: the name of a GDAL dataset (a DEM file typically) used to
 * extract elevation offsets from. In this situation the Z passed into the
 * transformation function is assumed to be height above ground. This option
 * should be used in replacement of RPC_HEIGHT to provide a way of defining
 * a non uniform ground for the target scene (GDAL >= 1.8.0)
 *
 * <li> RPC_DEMINTERPOLATION: the DEM interpolation (near, bilinear or cubic)
 *
 * <li> RPC_DEM_MISSING_VALUE: value of DEM height that must be used in case
 * the DEM has nodata value at the sampling point, or if its extent does not
 * cover the requested coordinate. When not specified, missing values will cause
 * a failed transform. (GDAL >= 1.11.2)
 *
 * <li> RPC_DEM_APPLY_VDATUM_SHIFT: whether the vertical component of a compound
 * SRS for the DEM should be used (when it is present). This is useful so as to
 * be able to transform the "raw" values from the DEM expressed with respect to
 * a geoid to the heights with respect to the WGS84 ellipsoid. When this is
 * enabled, the GTIFF_REPORT_COMPD_CS configuration option will be also set
 * temporarily so as to get the vertical information from GeoTIFF
 * files. Defaults to TRUE. (GDAL >= 2.1.0)
 *
 * <li> RPC_PIXEL_ERROR_THRESHOLD: overrides the dfPixErrThreshold parameter, ie
  the error (measured in pixels) allowed in the
 * iterative solution of pixel/line to lat/long computations (the other way
 * is always exact given the equations).  (GDAL >= 2.1.0)
 *
 * <li> RPC_MAX_ITERATIONS: maximum number of iterations allowed in the
 * iterative solution of pixel/line to lat/long computations. Default value is
 * 10 in the absence of a DEM, or 20 if there is a DEM.  (GDAL >= 2.1.0)
 *
 * </ul>
 *
 * @param psRPCInfo Definition of the RPC parameters.
 *
 * @param bReversed If true "forward" transformation will be lat/long to
 * pixel/line instead of the normal pixel/line to lat/long.
 *
 * @param dfPixErrThreshold the error (measured in pixels) allowed in the
 * iterative solution of pixel/line to lat/long computations (the other way
 * is always exact given the equations). Starting with GDAL 2.1, this may also
 * be set through the RPC_PIXEL_ERROR_THRESHOLD transformer option.
 * If a negative or null value is provided, then this defaults to 0.1 pixel.
 *
 * @param papszOptions Other transformer options (i.e. RPC_HEIGHT=z).
 *
 * @return transformer callback data (deallocate with GDALDestroyTransformer()).
 */

void *GDALCreateRPCTransformer( GDALRPCInfo *psRPCInfo, int bReversed,
                                double dfPixErrThreshold,
                                char **papszOptions )

{
/* -------------------------------------------------------------------- */
/*      Initialize core info.                                           */
/* -------------------------------------------------------------------- */
    GDALRPCTransformInfo *psTransform = static_cast<GDALRPCTransformInfo *>(
        CPLCalloc(sizeof(GDALRPCTransformInfo), 1));

memcpy( &(psTransform->sRPC), psRPCInfo, sizeof(GDALRPCInfo) );
    psTransform->bReversed = bReversed;
    const char* pszPixErrThreshold =
        CSLFetchNameValue( papszOptions, "RPC_PIXEL_ERROR_THRESHOLD" );
    if( pszPixErrThreshold != nullptr )
        psTransform->dfPixErrThreshold = CPLAtof(pszPixErrThreshold);
    else if( dfPixErrThreshold > 0 )
        psTransform->dfPixErrThreshold = dfPixErrThreshold;
    else
        psTransform->dfPixErrThreshold = DEFAULT_PIX_ERR_THRESHOLD;
    psTransform->dfHeightOffset = 0.0;
    psTransform->dfHeightScale = 1.0;

memcpy( psTransform->sTI.abySignature,
            GDAL_GTI2_SIGNATURE,
            strlen(GDAL_GTI2_SIGNATURE) );
    psTransform->sTI.pszClassName = "GDALRPCTransformer";
    psTransform->sTI.pfnTransform = GDALRPCTransform;
    psTransform->sTI.pfnCleanup = GDALDestroyRPCTransformer;
    psTransform->sTI.pfnSerialize = GDALSerializeRPCTransformer;
    psTransform->sTI.pfnCreateSimilar = GDALCreateSimilarRPCTransformer;

#ifdef USE_SSE2_OPTIM
    // Make sure padfCoeffs is aligned on a 16-byte boundary for SSE2 aligned
    // loads.
    psTransform->padfCoeffs =
        psTransform->adfDoubles +
        (reinterpret_cast<GUIntptr_t>(psTransform->adfDoubles) % 16) / 8;
    memcpy(psTransform->padfCoeffs,
           psRPCInfo->adfLINE_NUM_COEFF,
           20 * sizeof(double));
    memcpy(psTransform->padfCoeffs+20,
           psRPCInfo->adfLINE_DEN_COEFF,
           20 * sizeof(double));
    memcpy(psTransform->padfCoeffs+40,
           psRPCInfo->adfSAMP_NUM_COEFF,
           20 * sizeof(double));
    memcpy(psTransform->padfCoeffs+60,
           psRPCInfo->adfSAMP_DEN_COEFF,
           20 * sizeof(double));
#endif

/* -------------------------------------------------------------------- */
/*      Do we have a "average height" that we want to consider all      */
/*      elevations to be relative to?                                   */
/* -------------------------------------------------------------------- */
    const char *pszHeight = CSLFetchNameValue( papszOptions, "RPC_HEIGHT" );
    if( pszHeight != nullptr )
        psTransform->dfHeightOffset = CPLAtof(pszHeight);

/* -------------------------------------------------------------------- */
/*                       The "height scale"                             */
/* -------------------------------------------------------------------- */
    const char *pszHeightScale =
        CSLFetchNameValue(papszOptions, "RPC_HEIGHT_SCALE");
    if( pszHeightScale != nullptr )
        psTransform->dfHeightScale = CPLAtof(pszHeightScale);

/* -------------------------------------------------------------------- */
/*                       The DEM file name                              */
/* -------------------------------------------------------------------- */
    const char *pszDEMPath = CSLFetchNameValue( papszOptions, "RPC_DEM" );
    if( pszDEMPath != nullptr )
    {
        psTransform->pszDEMPath = CPLStrdup(pszDEMPath);
    }

/* -------------------------------------------------------------------- */
/*                      The DEM interpolation                           */
/* -------------------------------------------------------------------- */
    const char *pszDEMInterpolation =
        CSLFetchNameValueDef(papszOptions, "RPC_DEMINTERPOLATION", "bilinear");
    if( EQUAL(pszDEMInterpolation, "near" ) )
    {
        psTransform->eResampleAlg = DRA_NearestNeighbour;
    }
    else if( EQUAL(pszDEMInterpolation, "bilinear" ) )
    {
        psTransform->eResampleAlg = DRA_Bilinear;
    }
    else if( EQUAL(pszDEMInterpolation, "cubic") )
    {
        psTransform->eResampleAlg = DRA_Cubic;
    }
    else
    {
        CPLDebug("RPC", "Unknown interpolation %s. Defaulting to bilinear",
                 pszDEMInterpolation);
        psTransform->eResampleAlg = DRA_Bilinear;
    }

/* -------------------------------------------------------------------- */
/*                       The DEM missing value                          */
/* -------------------------------------------------------------------- */
    const char *pszDEMMissingValue =
        CSLFetchNameValue(papszOptions, "RPC_DEM_MISSING_VALUE");
    if( pszDEMMissingValue != nullptr )
    {
        psTransform->bHasDEMMissingValue = TRUE;
        psTransform->dfDEMMissingValue = CPLAtof(pszDEMMissingValue);
    }

/* -------------------------------------------------------------------- */
/*      Whether to apply vdatum shift                                   */
/* -------------------------------------------------------------------- */
    psTransform->bApplyDEMVDatumShift =
        CPLFetchBool( papszOptions, "RPC_DEM_APPLY_VDATUM_SHIFT", true );

psTransform->nMaxIterations = atoi( CSLFetchNameValueDef(
        papszOptions, "RPC_MAX_ITERATIONS", "0" ) );

/* -------------------------------------------------------------------- */
/*      Debug                                                           */
/* -------------------------------------------------------------------- */
    psTransform->bRPCInverseVerbose =
        CPLTestBool( CPLGetConfigOption("RPC_INVERSE_VERBOSE", "NO") );
    const char* pszRPCInverseLog = CPLGetConfigOption("RPC_INVERSE_LOG", nullptr);
    if( pszRPCInverseLog != nullptr )
        psTransform->pszRPCInverseLog = CPLStrdup(pszRPCInverseLog);

/* -------------------------------------------------------------------- */
/*      Open DEM if needed.                                             */
/* -------------------------------------------------------------------- */

if( psTransform->pszDEMPath != nullptr &&
        !GDALRPCOpenDEM(psTransform) )
    {
        GDALDestroyRPCTransformer( psTransform );
        return nullptr;
    }

/* -------------------------------------------------------------------- */
/*      Establish a reference point for calcualating an affine          */
/*      geotransform approximate transformation.                        */
/* -------------------------------------------------------------------- */
    double adfGTFromLL[6] = {};
    double dfRefPixel = -1.0;
    double dfRefLine = -1.0;
    double dfRefLong = 0.0;
    double dfRefLat = 0.0;

if( psRPCInfo->dfMIN_LONG != -180 || psRPCInfo->dfMAX_LONG != 180 )
    {
        dfRefLong = (psRPCInfo->dfMIN_LONG + psRPCInfo->dfMAX_LONG) * 0.5;
        dfRefLat  = (psRPCInfo->dfMIN_LAT  + psRPCInfo->dfMAX_LAT ) * 0.5;

double dfX = dfRefLong;
        double dfY = dfRefLat;
        double dfZ = 0.0;
        int nSuccess = 0;
        // Try with DEM first.
        if( GDALRPCTransform( psTransform, !(psTransform->bReversed), 1,
                          &dfX, &dfY, &dfZ, &nSuccess) )
        {
            dfRefPixel = dfX;
            dfRefLine = dfY;
        }
        else
        {
            RPCTransformPoint( psTransform, dfRefLong, dfRefLat, 0.0,
                               &dfRefPixel, &dfRefLine );
        }
    }

// Try with scale and offset if we don't can't use bounds or
    // the results seem daft.
    if( dfRefPixel < 0.0 || dfRefLine < 0.0
        || dfRefPixel > 100000 || dfRefLine > 100000 )
    {
        dfRefLong = psRPCInfo->dfLONG_OFF;
        dfRefLat  = psRPCInfo->dfLAT_OFF;

double dfX = dfRefLong;
        double dfY = dfRefLat;
        double dfZ = 0.0;
        int nSuccess = 0;
        // Try with DEM first.
        if( GDALRPCTransform( psTransform, !(psTransform->bReversed), 1,
                               &dfX, &dfY, &dfZ, &nSuccess) )
        {
            dfRefPixel = dfX;
            dfRefLine = dfY;
        }
        else
        {
            RPCTransformPoint( psTransform, dfRefLong, dfRefLat, 0.0,
                               &dfRefPixel, &dfRefLine );
        }
    }

psTransform->dfRefZ = 0.0;
    GDALRPCGetHeightAtLongLat(psTransform, dfRefLong, dfRefLat,
                              &psTransform->dfRefZ);

/* -------------------------------------------------------------------- */
/*      Transform nearby locations to establish affine direction        */
/*      vectors.                                                        */
/* -------------------------------------------------------------------- */
    double dfRefPixelDelta = 0.0;
    double dfRefLineDelta = 0.0;
    double dfLLDelta = 0.0001;

RPCTransformPoint( psTransform, dfRefLong+dfLLDelta, dfRefLat,
                       psTransform->dfRefZ,
                       &dfRefPixelDelta, &dfRefLineDelta );
    adfGTFromLL[1] = (dfRefPixelDelta - dfRefPixel) / dfLLDelta;
    adfGTFromLL[4] = (dfRefLineDelta - dfRefLine) / dfLLDelta;

RPCTransformPoint( psTransform, dfRefLong, dfRefLat+dfLLDelta,
                       psTransform->dfRefZ,
                       &dfRefPixelDelta, &dfRefLineDelta );
    adfGTFromLL[2] = (dfRefPixelDelta - dfRefPixel) / dfLLDelta;
    adfGTFromLL[5] = (dfRefLineDelta - dfRefLine) / dfLLDelta;

adfGTFromLL[0] = dfRefPixel
        - adfGTFromLL[1] * dfRefLong - adfGTFromLL[2] * dfRefLat;
    adfGTFromLL[3] = dfRefLine
        - adfGTFromLL[4] * dfRefLong - adfGTFromLL[5] * dfRefLat;

if( !GDALInvGeoTransform(adfGTFromLL,
                             psTransform->adfPLToLatLongGeoTransform) )
    {
        CPLError(CE_Failure, CPLE_AppDefined, "Cannot invert geotransform");
        GDALDestroyRPCTransformer(psTransform);
        return nullptr;
    }

return psTransform;
}

/************************************************************************/
/*                 GDALDestroyReprojectionTransformer()                 */
/************************************************************************/

/** Destroy RPC tranformer */
void GDALDestroyRPCTransformer( void *pTransformAlg )

{
    if( pTransformAlg == nullptr )
        return;

GDALRPCTransformInfo *psTransform =
        static_cast<GDALRPCTransformInfo *>(pTransformAlg);

CPLFree( psTransform->pszDEMPath );

if( psTransform->poDS )
        GDALClose(psTransform->poDS);
    CPLFree(psTransform->padfDEMBuffer);
    if( psTransform->poCT )
        OCTDestroyCoordinateTransformation(
            reinterpret_cast<OGRCoordinateTransformationH>(psTransform->poCT));
    CPLFree( psTransform->pszRPCInverseLog );

CPLFree( pTransformAlg );
}

/************************************************************************/
/*                      RPCInverseTransformPoint()                      */
/************************************************************************/

static bool
RPCInverseTransformPoint( GDALRPCTransformInfo *psTransform,
                          double dfPixel, double dfLine, double dfUserHeight,
                          double *pdfLong, double *pdfLat )

{
    // Memo:
    // Known to work with 40 iterations with DEM on all points (int coord and
    // +0.5,+0.5 shift) of flock1.20160216_041050_0905.tif, especially on (0,0).

/* -------------------------------------------------------------------- */
/*      Compute an initial approximation based on linear                */
/*      interpolation from our reference point.                         */
/* -------------------------------------------------------------------- */
    double dfResultX =
        psTransform->adfPLToLatLongGeoTransform[0] +
        psTransform->adfPLToLatLongGeoTransform[1] * dfPixel +
        psTransform->adfPLToLatLongGeoTransform[2] * dfLine;

double dfResultY =
        psTransform->adfPLToLatLongGeoTransform[3] +
        psTransform->adfPLToLatLongGeoTransform[4] * dfPixel +
        psTransform->adfPLToLatLongGeoTransform[5] * dfLine;

if( psTransform->bRPCInverseVerbose )
    {
        CPLDebug("RPC", "Computing inverse transform for (pixel,line)=(%f,%f)",
                 dfPixel, dfLine);
    }
    VSILFILE* fpLog = nullptr;
    if( psTransform->pszRPCInverseLog )
    {
        fpLog =
            VSIFOpenL( CPLResetExtension(psTransform->pszRPCInverseLog, "csvt"),
                       "wb" );
        if( fpLog != nullptr )
        {
            VSIFPrintfL( fpLog, "Integer,Real,Real,Real,String,Real,Real\n" );
            VSIFCloseL( fpLog );
        }
        fpLog = VSIFOpenL( psTransform->pszRPCInverseLog, "wb" );
        if( fpLog != nullptr )
            VSIFPrintfL(
                fpLog,
                "iter,long,lat,height,WKT,error_pixel_x,error_pixel_y\n" );
    }

/* -------------------------------------------------------------------- */
/*      Now iterate, trying to find a closer LL location that will      */
/*      back transform to the indicated pixel and line.                 */
/* -------------------------------------------------------------------- */
    double dfPixelDeltaX = 0.0;
    double dfPixelDeltaY = 0.0;
    double dfLastResultX = 0.0;
    double dfLastResultY = 0.0;
    double dfLastPixelDeltaX = 0.0;
    double dfLastPixelDeltaY = 0.0;
    double dfDEMH = 0.0;
    bool bLastPixelDeltaValid = false;
    const int nMaxIterations =
        (psTransform->nMaxIterations > 0) ? psTransform->nMaxIterations :
        (psTransform->poDS != nullptr) ? 20 : 10;
    int nCountConsecutiveErrorBelow2 = 0;

int iIter = 0;  // Used after for.
    for( ; iIter < nMaxIterations; iIter++ )
    {
        double dfBackPixel = 0.0;
        double dfBackLine = 0.0;

// Update DEMH.
        dfDEMH = 0.0;
        double dfDEMPixel = 0.0;
        double dfDEMLine = 0.0;
        if( !GDALRPCGetHeightAtLongLat(psTransform, dfResultX, dfResultY,
                                       &dfDEMH, &dfDEMPixel, &dfDEMLine) )
        {
            if( psTransform->poDS )
            {
                CPLDebug(
                    "RPC", "DEM (pixel, line) = (%g, %g)",
                    dfDEMPixel, dfDEMLine);
            }

// The first time, the guess might be completely out of the
            // validity of the DEM, so pickup the "reference Z" as the
            // first guess or the closest point of the DEM by snapping to it.
            if( iIter == 0 )
            {
                bool bUseRefZ = true;
                if( psTransform->poDS )
                {
                    if( dfDEMPixel >= psTransform->poDS->GetRasterXSize() )
                        dfDEMPixel = psTransform->poDS->GetRasterXSize() - 0.5;
                    else if( dfDEMPixel < 0 )
                        dfDEMPixel = 0.5;
                    if( dfDEMLine >= psTransform->poDS->GetRasterYSize() )
                        dfDEMLine = psTransform->poDS->GetRasterYSize() - 0.5;
                    else if( dfDEMPixel < 0 )
                        dfDEMPixel = 0.5;
                    if( GDALRPCGetDEMHeight( psTransform, dfDEMPixel,
                                             dfDEMLine, &dfDEMH) )
                    {
                        bUseRefZ = false;
                        CPLDebug(
                            "RPC", "Iteration %d for (pixel, line) = (%g, %g): "
                            "No elevation value at %.15g %.15g. "
                            "Using elevation %g at DEM (pixel, line) = "
                            "(%g, %g) (snapping to boundaries) instead",
                            iIter, dfPixel, dfLine,
                            dfResultX, dfResultY,
                            dfDEMH, dfDEMPixel, dfDEMLine );
                    }
                }
                if( bUseRefZ )
                {
                    dfDEMH = psTransform->dfRefZ;
                    CPLDebug(
                        "RPC", "Iteration %d for (pixel, line) = (%g, %g): "
                        "No elevation value at %.15g %.15g. "
                        "Using elevation %g of reference point instead",
                        iIter, dfPixel, dfLine,
                        dfResultX, dfResultY,
                        dfDEMH);
                }
            }
            else
            {
                CPLDebug("RPC", "Iteration %d for (pixel, line) = (%g, %g): "
                          "No elevation value at %.15g %.15g. Erroring out",
                          iIter, dfPixel, dfLine, dfResultX, dfResultY);
                if( fpLog )
                    VSIFCloseL(fpLog);
                return false;
            }
        }

RPCTransformPoint( psTransform, dfResultX, dfResultY,
                           dfUserHeight + dfDEMH,
                           &dfBackPixel, &dfBackLine );

dfPixelDeltaX = dfBackPixel - dfPixel;
        dfPixelDeltaY = dfBackLine - dfLine;

if( psTransform->bRPCInverseVerbose )
        {
            CPLDebug(
                "RPC", "Iter %d: dfPixelDeltaX=%.02f, dfPixelDeltaY=%.02f, "
                "long=%f, lat=%f, height=%f",
                iIter, dfPixelDeltaX, dfPixelDeltaY,
                dfResultX, dfResultY, dfUserHeight + dfDEMH);
        }
        if( fpLog != nullptr )
        {
            VSIFPrintfL(
                fpLog, "%d,%.12f,%.12f,%f,\"POINT(%.12f %.12f)\",%f,%f\n",
                iIter, dfResultX, dfResultY, dfUserHeight + dfDEMH,
                dfResultX, dfResultY, dfPixelDeltaX, dfPixelDeltaY);
        }

const double dfError =
            std::max(std::abs(dfPixelDeltaX), std::abs(dfPixelDeltaY));
        if( dfError < psTransform->dfPixErrThreshold )
        {
            iIter = -1;
            if( psTransform->bRPCInverseVerbose )
            {
                CPLDebug( "RPC", "Converged!" );
            }
            break;
        }
        else if( psTransform->poDS != nullptr &&
                 bLastPixelDeltaValid &&
                 dfPixelDeltaX * dfLastPixelDeltaX < 0 &&
                 dfPixelDeltaY * dfLastPixelDeltaY < 0 )
        {
            // When there is a DEM, if the error changes sign, we might
            // oscillate forever, so take a mean position as a new guess.
            if( psTransform->bRPCInverseVerbose )
            {
                CPLDebug(
                    "RPC", "Oscillation detected. "
                    "Taking mean of 2 previous results as new guess" );
            }
            dfResultX =
                ( fabs(dfPixelDeltaX) * dfLastResultX +
                  fabs(dfLastPixelDeltaX) * dfResultX ) /
                (fabs(dfPixelDeltaX) + fabs(dfLastPixelDeltaX));
            dfResultY =
                ( fabs(dfPixelDeltaY) * dfLastResultY +
                  fabs(dfLastPixelDeltaY) * dfResultY ) /
                (fabs(dfPixelDeltaY) + fabs(dfLastPixelDeltaY));
            bLastPixelDeltaValid = false;
            nCountConsecutiveErrorBelow2 = 0;
            continue;
        }

double dfBoostFactor = 1.0;
        if( psTransform->poDS != nullptr &&
            nCountConsecutiveErrorBelow2 >= 5 && dfError < 2 )
        {
          // When there is a DEM, if we remain below a given threshold (somewhat
          // arbitrarily set to 2 pixels) for some time, apply a "boost factor"
          // for the new guessed result, in the hope we will go out of the
          // somewhat current stuck situation.
          dfBoostFactor = 10;
          if( psTransform->bRPCInverseVerbose )
          {
              CPLDebug("RPC", "Applying boost factor 10");
          }
        }

if( dfError < 2 )
            nCountConsecutiveErrorBelow2++;
        else
            nCountConsecutiveErrorBelow2 = 0;

const double dfNewResultX = dfResultX
            - ( dfPixelDeltaX * psTransform->adfPLToLatLongGeoTransform[1] *
                dfBoostFactor )
            - ( dfPixelDeltaY * psTransform->adfPLToLatLongGeoTransform[2] *
                dfBoostFactor );
        const double dfNewResultY = dfResultY
            - ( dfPixelDeltaX * psTransform->adfPLToLatLongGeoTransform[4] *
                dfBoostFactor )
            - ( dfPixelDeltaY * psTransform->adfPLToLatLongGeoTransform[5] *
                dfBoostFactor );

dfLastResultX = dfResultX;
        dfLastResultY = dfResultY;
        dfResultX = dfNewResultX;
        dfResultY = dfNewResultY;
        dfLastPixelDeltaX = dfPixelDeltaX;
        dfLastPixelDeltaY = dfPixelDeltaY;
        bLastPixelDeltaValid = true;
    }
    if( fpLog != nullptr )
        VSIFCloseL( fpLog );

if( iIter != -1 )
    {
        CPLDebug( "RPC", "Failed Iterations %d: Got: %.16g,%.16g  Offset=%g,%g",
                  iIter,
                  dfResultX, dfResultY,
                  dfPixelDeltaX, dfPixelDeltaY );
        return false;
    }

*pdfLong = dfResultX;
    *pdfLat = dfResultY;
    return true;
}

static
double BiCubicKernel( double dfVal )
{
    if( dfVal > 2.0 )
        return 0.0;

const double xm1 = dfVal - 1.0;
    const double xp1 = dfVal + 1.0;
    const double xp2 = dfVal + 2.0;

const double a = xp2 <= 0.0 ? 0.0 : xp2 * xp2 * xp2;
    const double b = xp1 <= 0.0 ? 0.0 : xp1 * xp1 * xp1;
    const double c = dfVal <= 0.0 ? 0.0 : dfVal * dfVal * dfVal;
    const double d = xm1 <= 0.0 ? 0.0 : xm1 * xm1 * xm1;

return
        0.16666666666666666667 * (a - (4.0 * b) + (6.0 * c) - (4.0 * d));
}

/************************************************************************/
/*                        GDALRPCExtractDEMWindow()                     */
/************************************************************************/

static bool GDALRPCExtractDEMWindow( GDALRPCTransformInfo *psTransform,
                                     int nX, int nY, int nWidth, int nHeight,
                                     double* padfOut )
{
    psTransform->nDEMExtractions++;
    if( psTransform->padfDEMBuffer == nullptr )
    {
        // Should only happen in case of failed memory allocation.
        return psTransform->poDS->GetRasterBand(1)->
                                  RasterIO(GF_Read, nX, nY, nWidth, nHeight,
                                           padfOut, nWidth, nHeight,
                                           GDT_Float64, 0, 0,
                                           nullptr) == CE_None;
    }

// Instead of reading just nWidth * nHeight pixels (with those being <= 4),
    // target a larger buffer since small extractions can be costly, particular
    // with VRT.
    if( !(nX >= psTransform->nBufferX &&
          nX + nWidth <= psTransform->nBufferX + psTransform->nBufferWidth &&
          nY >= psTransform->nBufferY &&
          nY + nHeight <= psTransform->nBufferY + psTransform->nBufferHeight ) )
    {
#ifdef DEBUG_VERBOSE_EXTRACT_DEM
        CPLDebug("RPC", "Current request: %d,%d-%dx%d",
                  nX, nY, nWidth, nHeight);
        CPLDebug("RPC", "Hits in last DEM buffer: %d (%d pixels)",
                 psTransform->nHitsInBuffer,
                 psTransform->nBufferWidth * psTransform->nBufferHeight);
        CPLDebug("RPC", "Last DEM buffer: %d,%d-%dx%d",
                 psTransform->nBufferX,
                 psTransform->nBufferY,
                 psTransform->nBufferWidth,
                 psTransform->nBufferHeight);
#endif
        const int nRasterXSize = psTransform->poDS->GetRasterXSize();
        const int nRasterYSize = psTransform->poDS->GetRasterYSize();
        // If we have only queried a few points, no need to extract on a large
        // window We will progressively extend the window up to its maximum size
        // if we extract a significant number of points.
        int nRadius = psTransform->nBufferMaxRadius;
        if( psTransform->nDEMExtractions <
            psTransform->nBufferMaxRadius * psTransform->nBufferMaxRadius )
        {
            nRadius = static_cast<int> (
                  sqrt(static_cast<double>(psTransform->nDEMExtractions)) );
            CPLAssert( nRadius <= psTransform->nBufferMaxRadius );
        }
        // Check if there's some overlap between consecutive requests to decide
        // if we must have a buffer around the interest window.
        const int nDiffX = nX - psTransform->nLastQueriedX;
        const int nDiffY = nY - psTransform->nLastQueriedY;
        if( psTransform->nLastQueriedX >= 0 &&
            (nDiffX > nRadius || -nDiffX > nRadius ||
             nDiffY > nRadius || -nDiffY > nRadius) )
        {
            nRadius = 0;
        }
        psTransform->nBufferX = nX - nRadius;
        if( psTransform->nBufferX < 0 )
            psTransform->nBufferX = 0;
        psTransform->nBufferY = nY - nRadius;
        if( psTransform->nBufferY < 0 )
            psTransform->nBufferY = 0;
        psTransform->nBufferWidth = nWidth + 2 * nRadius;
        if( psTransform->nBufferX + psTransform->nBufferWidth > nRasterXSize )
            psTransform->nBufferWidth = nRasterXSize - psTransform->nBufferX;
        psTransform->nBufferHeight = nHeight + 2 * nRadius;
        if( psTransform->nBufferY + psTransform->nBufferHeight > nRasterYSize )
            psTransform->nBufferHeight = nRasterYSize - psTransform->nBufferY;
#ifdef DEBUG_VERBOSE_EXTRACT_DEM
        CPLDebug("RPC", "New DEM buffer: %d,%d-%dx%d",
                 psTransform->nBufferX,
                 psTransform->nBufferY,
                 psTransform->nBufferWidth,
                 psTransform->nBufferHeight);
#endif
        CPLErr eErr = psTransform->poDS->GetRasterBand(1)->RasterIO(GF_Read,
                        psTransform->nBufferX, psTransform->nBufferY,
                        psTransform->nBufferWidth, psTransform->nBufferHeight,
                        psTransform->padfDEMBuffer,
                        psTransform->nBufferWidth, psTransform->nBufferHeight,
                        GDT_Float64, 0, 0, nullptr);
        if( eErr != CE_None )
        {
            psTransform->nBufferX = -1;
            psTransform->nBufferY = -1;
            psTransform->nBufferWidth = -1;
            psTransform->nBufferHeight = -1;
            return false;
        }
#ifdef DEBUG_VERBOSE_EXTRACT_DEM
         psTransform->nHitsInBuffer = 1;
#endif
    }
    else
    {
#ifdef DEBUG_VERBOSE
        psTransform->nHitsInBuffer++;
#endif
    }
    psTransform->nLastQueriedX = nX;
    psTransform->nLastQueriedY = nY;

for( int i=0; i<nHeight; i++)
    {
        memcpy( padfOut + i * nWidth,
                psTransform->padfDEMBuffer + (nY - psTransform->nBufferY + i) *
                    psTransform->nBufferWidth + nX - psTransform->nBufferX,
                nWidth * sizeof(double) );
    }

return true;
}

/************************************************************************/
/*                        GDALRPCGetDEMHeight()                         */
/************************************************************************/

static
int GDALRPCGetDEMHeight( GDALRPCTransformInfo *psTransform,
                         const double dfXIn, const double dfYIn,
                         double* pdfDEMH )
{
    const int nRasterXSize = psTransform->poDS->GetRasterXSize();
    const int nRasterYSize = psTransform->poDS->GetRasterYSize();
    int bGotNoDataValue = FALSE;
    const double dfNoDataValue =
        psTransform->poDS->GetRasterBand(1)->GetNoDataValue( &bGotNoDataValue );

if( psTransform->eResampleAlg == DRA_Cubic )
    {
        // Convert from upper left corner of pixel coordinates to center of
        // pixel coordinates:
        const double dfX = dfXIn - 0.5;
        const double dfY = dfYIn - 0.5;
        const int dX = int(dfX);
        const int dY = int(dfY);
        const double dfDeltaX = dfX - dX;
        const double dfDeltaY = dfY - dY;

const int dXNew = dX - 1;
        const int dYNew = dY - 1;
        if( !(dXNew >= 0 && dYNew >= 0 &&
              dXNew + 4 <= nRasterXSize && dYNew + 4 <= nRasterYSize) )
        {
            goto bilinear_fallback;
        }
        // Cubic interpolation.
        double adfElevData[16] = { 0.0 };
        if( !GDALRPCExtractDEMWindow( psTransform, dXNew, dYNew,
                                      4, 4, adfElevData ) )
        {
            return FALSE;
        }

double dfSumH = 0.0;
        double dfSumWeight = 0.0;
        for( int k_i = 0; k_i < 4; k_i++ )
        {
            // Loop across the X axis.
            for( int k_j = 0; k_j < 4; k_j++ )
            {
                // Calculate the weight for the specified pixel according
                // to the bicubic b-spline kernel we're using for
                // interpolation.
                const int dKernIndX = k_j - 1;
                const int dKernIndY = k_i - 1;
                const double dfPixelWeight =
                    BiCubicKernel(dKernIndX - dfDeltaX) *
                    BiCubicKernel(dKernIndY - dfDeltaY);

// Create a sum of all values
                // adjusted for the pixel's calculated weight.
                const double dfElev = adfElevData[k_j + k_i * 4];
                if( bGotNoDataValue && ARE_REAL_EQUAL(dfNoDataValue, dfElev) )
                    continue;

dfSumH += dfElev * dfPixelWeight;
                dfSumWeight += dfPixelWeight;
            }
        }
        if( dfSumWeight == 0.0 )
        {
            return FALSE;
        }

*pdfDEMH = dfSumH / dfSumWeight;

return TRUE;
    }
    else if( psTransform->eResampleAlg == DRA_Bilinear )
    {
bilinear_fallback:
        // Convert from upper left corner of pixel coordinates to center of
        // pixel coordinates:
        const double dfX = dfXIn - 0.5;
        const double dfY = dfYIn - 0.5;
        const int dX = static_cast<int>(dfX);
        const int dY = static_cast<int>(dfY);
        const double dfDeltaX = dfX - dX;
        const double dfDeltaY = dfY - dY;

if( !(dX >= 0 && dY >= 0 &&
              dX + 2 <= nRasterXSize && dY + 2 <= nRasterYSize) )
        {
            goto near_fallback;
        }

// Bilinear interpolation.
        double adfElevData[4] = { 0.0, 0.0, 0.0, 0.0 };
        if( !GDALRPCExtractDEMWindow( psTransform, dX, dY, 2, 2, adfElevData ) )
        {
            return FALSE;
        }

if( bGotNoDataValue )
        {
            // TODO: We could perhaps use a valid sample if there's one.
            bool bFoundNoDataElev = false;
            for( int k_i = 0; k_i < 4; k_i++ )
            {
                if( ARE_REAL_EQUAL(dfNoDataValue, adfElevData[k_i]) )
                    bFoundNoDataElev = true;
            }
            if( bFoundNoDataElev )
            {
                return FALSE;
            }
        }
        const double dfDeltaX1 = 1.0 - dfDeltaX;
        const double dfDeltaY1 = 1.0 - dfDeltaY;

*pdfDEMH = dfYZ;

return TRUE;
    }
    else
    {
near_fallback:
        const int dX = static_cast<int>(dfXIn);
        const int dY = static_cast<int>(dfYIn);
        if( !(dX >= 0 && dY >= 0 && dX < nRasterXSize && dY < nRasterYSize) )
        {
            return FALSE;
        }
        double dfDEMH = 0.0;
        if( !GDALRPCExtractDEMWindow( psTransform, dX, dY, 1, 1, &dfDEMH ) ||
            (bGotNoDataValue && ARE_REAL_EQUAL(dfNoDataValue, dfDEMH)) )
        {
            return FALSE;
        }

*pdfDEMH = dfDEMH;

return TRUE;
    }
}

/************************************************************************/
/*                    GDALRPCTransformWholeLineWithDEM()                */
/************************************************************************/

static int
GDALRPCTransformWholeLineWithDEM( const GDALRPCTransformInfo *psTransform,
                                  int nPointCount,
                                  double *padfX, double *padfY, double *padfZ,
                                  int *panSuccess,
                                  int nXLeft, int nXWidth,
                                  int nYTop, int nYHeight )
{
    double* padfDEMBuffer = static_cast<double *>(
        VSI_MALLOC2_VERBOSE(sizeof(double), nXWidth * nYHeight));
    if( padfDEMBuffer == nullptr )
    {
        for( int i = 0; i < nPointCount; i++ )
            panSuccess[i] = FALSE;
        return FALSE;
    }
    CPLErr eErr = psTransform->poDS->GetRasterBand(1)->
        RasterIO(GF_Read, nXLeft, nYTop, nXWidth, nYHeight,
                 padfDEMBuffer, nXWidth, nYHeight,
                 GDT_Float64, 0, 0, nullptr);
    if( eErr != CE_None )
    {
        for( int i = 0; i < nPointCount; i++ )
            panSuccess[i] = FALSE;
        VSIFree(padfDEMBuffer);
        return FALSE;
    }

int bGotNoDataValue = FALSE;
    const double dfNoDataValue =
        psTransform->poDS->GetRasterBand(1)->GetNoDataValue( &bGotNoDataValue );

// dfY in pixel center convention.
    const double dfY =
        psTransform->adfDEMReverseGeoTransform[3] +
        padfY[0] * psTransform->adfDEMReverseGeoTransform[5] - 0.5;
    const int nY = static_cast<int>(dfY);
    const double dfDeltaY = dfY - nY;

for( int i = 0; i < nPointCount; i++ )
    {
        double dfDEMH = 0.0;
        const double dfZ_i = padfZ ? padfZ[i] : 0.0;

if( psTransform->eResampleAlg == DRA_Cubic )
        {
            // dfX in pixel center convention.
            const double dfX =
                psTransform->adfDEMReverseGeoTransform[0] +
                padfX[i] * psTransform->adfDEMReverseGeoTransform[1] - 0.5;
            const int nX = static_cast<int>(dfX);
            const double dfDeltaX = dfX - nX;

const int nXNew = nX - 1;

double dfSumH = 0.0;
            double dfSumWeight = 0.0;
            for( int k_i = 0; k_i < 4; k_i++ )
            {
                // Loop across the X axis.
                for( int k_j = 0; k_j < 4; k_j++ )
                {
                    // Calculate the weight for the specified pixel according
                    // to the bicubic b-spline kernel we're using for
                    // interpolation.
                    const int dKernIndX = k_j - 1;
                    const int dKernIndY = k_i - 1;
                    const double dfPixelWeight =
                        BiCubicKernel(dKernIndX - dfDeltaX) *
                        BiCubicKernel(dKernIndY - dfDeltaY);

// Create a sum of all values
                    // adjusted for the pixel's calculated weight.
                    const double dfElev =
                        padfDEMBuffer[k_i * nXWidth + nXNew - nXLeft + k_j];
                    if( bGotNoDataValue &&
                        ARE_REAL_EQUAL(dfNoDataValue, dfElev) )
                        continue;

dfSumH += dfElev * dfPixelWeight;
                    dfSumWeight += dfPixelWeight;
                }
            }
            if( dfSumWeight == 0.0 )
            {
                if( psTransform->bHasDEMMissingValue )
                    dfDEMH = psTransform->dfDEMMissingValue;
                else
                {
                    panSuccess[i] = FALSE;
                    continue;
                }
            }
            else
                dfDEMH = dfSumH / dfSumWeight;
        }
        else if( psTransform->eResampleAlg == DRA_Bilinear )
        {
            // dfX in pixel center convention.
            const double dfX =
                psTransform->adfDEMReverseGeoTransform[0] +
                padfX[i] * psTransform->adfDEMReverseGeoTransform[1] - 0.5;
            const int nX = static_cast<int>(dfX);
            const double dfDeltaX = dfX - nX;

// Bilinear interpolation.
            double adfElevData[4] = {};
            memcpy(adfElevData,
                   padfDEMBuffer + nX - nXLeft,
                   2 * sizeof(double));
            memcpy(adfElevData + 2,
                   padfDEMBuffer + nXWidth + nX - nXLeft,
                   2 * sizeof(double));

int bFoundNoDataElev = FALSE;
            if( bGotNoDataValue )
            {
                int k_valid_sample = -1;
                for( int k_i = 0; k_i < 4; k_i++ )
                {
                    if( ARE_REAL_EQUAL(dfNoDataValue, adfElevData[k_i]) )
                    {
                        bFoundNoDataElev = TRUE;
                    }
                    else if( k_valid_sample < 0 )
                    {
                        k_valid_sample = k_i;
                    }
                }
                if( bFoundNoDataElev )
                {
                    if( k_valid_sample >= 0 )
                    {
                        dfDEMH = adfElevData[k_valid_sample];
                        RPCTransformPoint( psTransform, padfX[i], padfY[i],
                            dfZ_i + (psTransform->dfHeightOffset + dfDEMH) *
                                        psTransform->dfHeightScale,
                            padfX + i, padfY + i );

panSuccess[i] = TRUE;
                        continue;
                    }
                    else if( psTransform->bHasDEMMissingValue )
                    {
                        dfDEMH = psTransform->dfDEMMissingValue;
                        RPCTransformPoint( psTransform, padfX[i], padfY[i],
                            dfZ_i + (psTransform->dfHeightOffset + dfDEMH) *
                                        psTransform->dfHeightScale,
                            padfX + i, padfY + i );

panSuccess[i] = TRUE;
                        continue;
                    }
                    else
                    {
                        panSuccess[i] = FALSE;
                        continue;
                    }
                }
            }
            const double dfDeltaX1 = 1.0 - dfDeltaX;
            const double dfDeltaY1 = 1.0 - dfDeltaY;

const double dfXZ1 =
                adfElevData[0] * dfDeltaX1 + adfElevData[1] * dfDeltaX;
            const double dfXZ2 =
                adfElevData[2] * dfDeltaX1 + adfElevData[3] * dfDeltaX;
            const double dfYZ = dfXZ1 * dfDeltaY1 + dfXZ2 * dfDeltaY;
            dfDEMH = dfYZ;
        }
        else
        {
            const double dfX =
                psTransform->adfDEMReverseGeoTransform[0] +
                padfX[i] * psTransform->adfDEMReverseGeoTransform[1];
            const int nX = int(dfX);

dfDEMH = padfDEMBuffer[nX - nXLeft];
            if( bGotNoDataValue && ARE_REAL_EQUAL(dfNoDataValue, dfDEMH) )
            {
                if( psTransform->bHasDEMMissingValue )
                    dfDEMH = psTransform->dfDEMMissingValue;
                else
                {
                    panSuccess[i] = FALSE;
                    continue;
                }
            }
        }

RPCTransformPoint( psTransform, padfX[i], padfY[i],
                            dfZ_i + (psTransform->dfHeightOffset + dfDEMH) *
                                        psTransform->dfHeightScale,
                            padfX + i, padfY + i );

panSuccess[i] = TRUE;
    }

VSIFree(padfDEMBuffer);

return TRUE;
}

/************************************************************************/
/*                           GDALRPCOpenDEM()                           */
/************************************************************************/

static bool GDALRPCOpenDEM( GDALRPCTransformInfo* psTransform )
{
    CPLAssert( psTransform->pszDEMPath != nullptr );

bool bIsValid = false;

CPLString osPrevValueConfigOption;
    if( psTransform->bApplyDEMVDatumShift )
    {
        osPrevValueConfigOption
            = CPLGetThreadLocalConfigOption("GTIFF_REPORT_COMPD_CS", "");
        CPLSetThreadLocalConfigOption("GTIFF_REPORT_COMPD_CS", "YES");
    }
    CPLConfigOptionSetter oSetter("CPL_ALLOW_VSISTDIN", "NO", true);
    psTransform->poDS = reinterpret_cast<GDALDataset *>(
        GDALOpen(psTransform->pszDEMPath, GA_ReadOnly));
    if( psTransform->poDS != nullptr &&
        psTransform->poDS->GetRasterCount() >= 1 )
    {
        psTransform->nBufferMaxRadius =
            atoi(CPLGetConfigOption("GDAL_RPC_DEM_BUFFER_MAX_RADIUS", "2"));
        psTransform->nHitsInBuffer = 0;
        const int nMaxWindowSize = 4;
        psTransform->padfDEMBuffer = static_cast<double*>(VSIMalloc(
            (nMaxWindowSize + 2 * psTransform->nBufferMaxRadius) *
            (nMaxWindowSize + 2 * psTransform->nBufferMaxRadius) *
            sizeof(double) ));
        psTransform->nBufferX = -1;
        psTransform->nBufferY = -1;
        psTransform->nBufferWidth = -1;
        psTransform->nBufferHeight = -1;
        psTransform->nLastQueriedX = -1;
        psTransform->nLastQueriedY = -1;
        const char* pszSpatialRef = psTransform->poDS->GetProjectionRef();
        if( pszSpatialRef != nullptr && pszSpatialRef[0] != '\0' )
        {
            OGRSpatialReference* poWGSSpaRef =
                    new OGRSpatialReference(SRS_WKT_WGS84);

OGRSpatialReference* poDSSpaRef =
                    new OGRSpatialReference(pszSpatialRef);
            if( !psTransform->bApplyDEMVDatumShift )
                poDSSpaRef->StripVertical();

if( !poWGSSpaRef->IsSame(poDSSpaRef) )
                psTransform->poCT =
                    OGRCreateCoordinateTransformation(poWGSSpaRef,
                                                        poDSSpaRef);

if( psTransform->poCT != nullptr && !poDSSpaRef->IsCompound() )
            {
                // Empiric attempt to guess if the coordinate transformation
                // to WGS84 is a no-op. For example for NED13 datasets in
                // NAD83.
                double adfX[] = { -179.0, 179.0, 179.0, -179.0, 0.0, 0.0 };
                double adfY[] = { 89.0, 89.0, -89.0, -89.0, 0.0, 0.0 };
                double adfZ[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

// Also test with a "reference point" from the RPC values.
                double dfRefLong = 0.0;
                double dfRefLat = 0.0;
                if( psTransform->sRPC.dfMIN_LONG != -180 ||
                    psTransform->sRPC.dfMAX_LONG != 180 )
                {
                    dfRefLong = (psTransform->sRPC.dfMIN_LONG +
                                    psTransform->sRPC.dfMAX_LONG) * 0.5;
                    dfRefLat  = (psTransform->sRPC.dfMIN_LAT +
                                    psTransform->sRPC.dfMAX_LAT ) * 0.5;
                }
                else
                {
                    dfRefLong = psTransform->sRPC.dfLONG_OFF;
                    dfRefLat  = psTransform->sRPC.dfLAT_OFF;
                }
                adfX[5] = dfRefLong;
                adfY[5] = dfRefLat;

if( psTransform->poCT->Transform(
                                            6, adfX, adfY, adfZ) &&
                    fabs(adfX[0] - -179.0) < 1.0e-12 &&
                    fabs(adfY[0] -   89.0) < 1.0e-12 &&
                    fabs(adfX[1] -  179.0) < 1.0e-12 &&
                    fabs(adfY[1] -   89.0) < 1.0e-12 &&
                    fabs(adfX[2] -  179.0) < 1.0e-12 &&
                    fabs(adfY[2] -  -89.0) < 1.0e-12 &&
                    fabs(adfX[3] - -179.0) < 1.0e-12 &&
                    fabs(adfY[3] -  -89.0) < 1.0e-12 &&
                    fabs(adfX[4] -    0.0) < 1.0e-12 &&
                    fabs(adfY[4] -    0.0) < 1.0e-12 &&
                    fabs(adfX[5] - dfRefLong) < 1.0e-12 &&
                    fabs(adfY[5] - dfRefLat) < 1.0e-12 )
                {
                    CPLDebug("RPC",
                                "Short-circuiting coordinate transformation "
                                "from DEM SRS to WGS 84 due to apparent nop");
                    delete psTransform->poCT;
                    psTransform->poCT = nullptr;
                }
            }

delete poWGSSpaRef;
            delete poDSSpaRef;
        }

if( psTransform->poDS->GetGeoTransform(
                            psTransform->adfDEMGeoTransform) == CE_None &&
            GDALInvGeoTransform( psTransform->adfDEMGeoTransform,
                                    psTransform->adfDEMReverseGeoTransform ) )
        {
            bIsValid = true;
        }
    }

if( psTransform->bApplyDEMVDatumShift )
    {
        CPLSetThreadLocalConfigOption("GTIFF_REPORT_COMPD_CS",
                                        !osPrevValueConfigOption.empty()
                                            ? osPrevValueConfigOption.c_str()
                                            : nullptr);
    }

return bIsValid;
}

/************************************************************************/
/*                          GDALRPCTransform()                          */
/************************************************************************/

/** RPC transform */
int GDALRPCTransform( void *pTransformArg, int bDstToSrc,
                      int nPointCount,
                      double *padfX, double *padfY, double *padfZ,
                      int *panSuccess )

{
    VALIDATE_POINTER1( pTransformArg, "GDALRPCTransform", 0 );

GDALRPCTransformInfo *psTransform =
        static_cast<GDALRPCTransformInfo *>(pTransformArg);

if( psTransform->bReversed )
        bDstToSrc = !bDstToSrc;

/* -------------------------------------------------------------------- */
/*      The simple case is transforming from lat/long to pixel/line.    */
/*      Just apply the equations directly.                              */
/* -------------------------------------------------------------------- */
    if( bDstToSrc )
    {
        // Optimization to avoid doing too many picking in DEM in the particular
        // case where each point to transform is on a single line of the DEM.
        // To make it simple and fast we check that all input latitudes are
        // identical, that the DEM is in WGS84 geodetic and that it has no
        // rotation.  Such case is for example triggered when doing gdalwarp
        // with a target SRS of EPSG:4326 or EPSG:3857.
        if( nPointCount >= 10 && psTransform->poDS != nullptr &&
            psTransform->poCT == nullptr && padfY[0] == padfY[nPointCount-1] &&
            padfY[0] == padfY[nPointCount/ 2] &&
            psTransform->adfDEMReverseGeoTransform[1] > 0.0 &&
            psTransform->adfDEMReverseGeoTransform[2] == 0.0 &&
            psTransform->adfDEMReverseGeoTransform[4] == 0.0 &&
            CPLTestBool(CPLGetConfigOption("GDAL_RPC_DEM_OPTIM", "YES")) )
        {
            bool bUseOptimized = true;
            double dfMinX = padfX[0];
            double dfMaxX = padfX[0];
            for( int i = 1; i < nPointCount; i++ )
            {
                if( padfY[i] != padfY[0] )
                {
                    bUseOptimized = false;
                    break;
                }
                if( padfX[i] < dfMinX ) dfMinX = padfX[i];
                if( padfX[i] > dfMaxX ) dfMaxX = padfX[i];
            }
            if( bUseOptimized )
            {
                double dfX1 = 0.0;
                double dfY1 = 0.0;
                double dfX2 = 0.0;
                double dfY2 = 0.0;
                GDALApplyGeoTransform( psTransform->adfDEMReverseGeoTransform,
                                    dfMinX, padfY[0], &dfX1, &dfY1 );
                GDALApplyGeoTransform( psTransform->adfDEMReverseGeoTransform,
                                    dfMaxX, padfY[0], &dfX2, &dfY2 );

// Convert to center of pixel convention for reading the image
                // data.
                if( psTransform->eResampleAlg != DRA_NearestNeighbour )
                {
                    dfX1 -= 0.5;
                    dfY1 -= 0.5;
                    dfX2 -= 0.5;
                    // dfY2 -= 0.5;
                }
                int nXLeft = static_cast<int>(floor(dfX1));
                int nXRight = static_cast<int>(floor(dfX2));
                int nXWidth = nXRight - nXLeft + 1;
                int nYTop = static_cast<int>(floor(dfY1));
                int nYHeight;
                if( psTransform->eResampleAlg == DRA_Cubic )
                {
                    nXLeft--;
                    nXWidth += 3;
                    nYTop--;
                    nYHeight = 4;
                }
                else if( psTransform->eResampleAlg == DRA_Bilinear )
                {
                    nXWidth++;
                    nYHeight = 2;
                }
                else
                {
                    nYHeight = 1;
                }
                if( nXLeft >= 0 &&
                    nXLeft + nXWidth <= psTransform->poDS->GetRasterXSize() &&
                    nYTop >= 0 &&
                    nYTop + nYHeight <= psTransform->poDS->GetRasterYSize() )
                {
                    static bool bOnce = false;
                    if( !bOnce )
                    {
                        bOnce = true;
                        CPLDebug("RPC",
                                 "Using GDALRPCTransformWholeLineWithDEM");
                    }
                    return GDALRPCTransformWholeLineWithDEM(psTransform,
                                                            nPointCount,
                                                            padfX, padfY, padfZ,
                                                            panSuccess,
                                                            nXLeft, nXWidth,
                                                            nYTop, nYHeight);
                }
            }
        }

for( int i = 0; i < nPointCount; i++ )
        {
            double dfHeight = 0.0;
            if( !GDALRPCGetHeightAtLongLat( psTransform, padfX[i], padfY[i],
                                            &dfHeight ) )
            {
                panSuccess[i] = FALSE;
                padfX[i] = HUGE_VAL;
                padfY[i] = HUGE_VAL;
                continue;
            }

RPCTransformPoint( psTransform, padfX[i], padfY[i],
                               (padfZ ? padfZ[i] : 0.0) + dfHeight,
                                padfX + i, padfY + i );
            panSuccess[i] = TRUE;
        }

return TRUE;
    }

if( padfZ == nullptr )
    {
        CPLError(CE_Failure, CPLE_NotSupported,
                 "Z array should be provided for reverse RPC computation");
        return FALSE;
    }

/* -------------------------------------------------------------------- */
/*      Compute the inverse (pixel/line/height to lat/long).  This      */
/*      function uses an iterative method from an initial linear        */
/*      approximation.                                                  */
/* -------------------------------------------------------------------- */
    for( int i = 0; i < nPointCount; i++ )
    {
        double dfResultX = 0.0;
        double dfResultY = 0.0;

if( !RPCInverseTransformPoint( psTransform, padfX[i], padfY[i],
                    padfZ[i],
                    &dfResultX, &dfResultY ) )
        {
            panSuccess[i] = FALSE;
            padfX[i] = HUGE_VAL;
            padfY[i] = HUGE_VAL;
            continue;
        }

padfX[i] = dfResultX;
        padfY[i] = dfResultY;

panSuccess[i] = TRUE;
    }

return TRUE;
}

/************************************************************************/
/*                    GDALSerializeRPCTransformer()                     */
/************************************************************************/

CPLXMLNode *GDALSerializeRPCTransformer( void *pTransformArg )

{
    VALIDATE_POINTER1( pTransformArg, "GDALSerializeRPCTransformer", nullptr );

GDALRPCTransformInfo *psInfo =
        static_cast<GDALRPCTransformInfo *>(pTransformArg);

CPLXMLNode *psTree = CPLCreateXMLNode(nullptr, CXT_Element, "RPCTransformer");

/* -------------------------------------------------------------------- */
/*      Serialize bReversed.                                            */
/* -------------------------------------------------------------------- */
    CPLCreateXMLElementAndValue(
        psTree, "Reversed",
        CPLString().Printf( "%d", psInfo->bReversed ) );

/* -------------------------------------------------------------------- */
/*      Serialize Height Offset.                                        */
/* -------------------------------------------------------------------- */
    CPLCreateXMLElementAndValue(
        psTree, "HeightOffset",
        CPLString().Printf( "%.15g", psInfo->dfHeightOffset ) );

/* -------------------------------------------------------------------- */
/*      Serialize Height Scale.                                         */
/* -------------------------------------------------------------------- */
    if( psInfo->dfHeightScale != 1.0 )
        CPLCreateXMLElementAndValue(
            psTree, "HeightScale",
            CPLString().Printf( "%.15g", psInfo->dfHeightScale ) );

/* -------------------------------------------------------------------- */
/*      Serialize DEM path.                                             */
/* -------------------------------------------------------------------- */
    if( psInfo->pszDEMPath != nullptr )
    {
        CPLCreateXMLElementAndValue(
            psTree, "DEMPath",
            CPLString().Printf( "%s", psInfo->pszDEMPath ) );

/* -------------------------------------------------------------------- */
/*      Serialize DEM interpolation                                     */
/* -------------------------------------------------------------------- */
        CPLCreateXMLElementAndValue(
            psTree, "DEMInterpolation",
            GDALSerializeRPCDEMResample(psInfo->eResampleAlg) );

if( psInfo->bHasDEMMissingValue )
        {
            CPLCreateXMLElementAndValue(
                psTree, "DEMMissingValue",
                CPLSPrintf("%.18g", psInfo->dfDEMMissingValue) );
        }

CPLCreateXMLElementAndValue(
                psTree, "DEMApplyVDatumShift",
                psInfo->bApplyDEMVDatumShift ? "true" : "false" );
    }

/* -------------------------------------------------------------------- */
/*      Serialize pixel error threshold.                                */
/* -------------------------------------------------------------------- */
    CPLCreateXMLElementAndValue(
        psTree, "PixErrThreshold",
        CPLString().Printf( "%.15g", psInfo->dfPixErrThreshold ) );

/* -------------------------------------------------------------------- */
/*      RPC metadata.                                                   */
/* -------------------------------------------------------------------- */
    char **papszMD = RPCInfoToMD( &(psInfo->sRPC) );
    CPLXMLNode *psMD= CPLCreateXMLNode( psTree, CXT_Element,
                                        "Metadata" );

for( int i = 0; papszMD != nullptr && papszMD[i] != nullptr; i++ )
    {
        char *pszKey = nullptr;

const char *pszRawValue = CPLParseNameValue( papszMD[i], &pszKey );

CPLXMLNode *psMDI = CPLCreateXMLNode( psMD, CXT_Element, "MDI" );
        CPLSetXMLValue( psMDI, "#key", pszKey );
        CPLCreateXMLNode( psMDI, CXT_Text, pszRawValue );

CPLFree( pszKey );
    }

CSLDestroy( papszMD );

return psTree;
}

/************************************************************************/
/*                   GDALDeserializeRPCTransformer()                    */
/************************************************************************/

void *GDALDeserializeRPCTransformer( CPLXMLNode *psTree )

{
    char **papszOptions = nullptr;

/* -------------------------------------------------------------------- */
/*      Collect metadata.                                               */
/* -------------------------------------------------------------------- */
    CPLXMLNode *psMetadata = CPLGetXMLNode( psTree, "Metadata" );

if( psMetadata == nullptr
        || psMetadata->eType != CXT_Element
        || !EQUAL(psMetadata->pszValue, "Metadata") )
        return nullptr;

char **papszMD = nullptr;
    for( CPLXMLNode *psMDI = psMetadata->psChild;
         psMDI != nullptr;
         psMDI = psMDI->psNext )
    {
        if( !EQUAL(psMDI->pszValue, "MDI")
            || psMDI->eType != CXT_Element
            || psMDI->psChild == nullptr
            || psMDI->psChild->psNext == nullptr
            || psMDI->psChild->eType != CXT_Attribute
            || psMDI->psChild->psChild == nullptr )
            continue;

papszMD =
            CSLSetNameValue( papszMD,
                             psMDI->psChild->psChild->pszValue,
                             psMDI->psChild->psNext->pszValue );
    }

GDALRPCInfo sRPC;
    if( !GDALExtractRPCInfo( papszMD, &sRPC ) )
    {
        CPLError( CE_Failure, CPLE_AppDefined,
                  "Failed to reconstitute RPC transformer." );
        CSLDestroy( papszMD );
        return nullptr;
    }

CSLDestroy( papszMD );

/* -------------------------------------------------------------------- */
/*      Get other flags.                                                */
/* -------------------------------------------------------------------- */
    const int bReversed = atoi(CPLGetXMLValue(psTree, "Reversed", "0"));

const double dfPixErrThreshold =
        CPLAtof(CPLGetXMLValue(psTree, "PixErrThreshold",
                               CPLSPrintf( "%f", DEFAULT_PIX_ERR_THRESHOLD )));

papszOptions = CSLSetNameValue(papszOptions,  "RPC_HEIGHT",
                                   CPLGetXMLValue(psTree, "HeightOffset", "0"));
    papszOptions = CSLSetNameValue(papszOptions, "RPC_HEIGHT_SCALE",
                                   CPLGetXMLValue(psTree, "HeightScale", "1"));
    const char* pszDEMPath = CPLGetXMLValue(psTree, "DEMPath", nullptr);
    if( pszDEMPath != nullptr )
        papszOptions = CSLSetNameValue( papszOptions, "RPC_DEM",
                                        pszDEMPath);

const char* pszDEMInterpolation =
        CPLGetXMLValue(psTree, "DEMInterpolation", "bilinear");
    if( pszDEMInterpolation != nullptr )
        papszOptions = CSLSetNameValue( papszOptions, "RPC_DEMINTERPOLATION",
                                        pszDEMInterpolation);

const char* pszDEMMissingValue =
        CPLGetXMLValue(psTree, "DEMMissingValue", nullptr);
    if( pszDEMMissingValue != nullptr )
        papszOptions = CSLSetNameValue( papszOptions, "RPC_DEM_MISSING_VALUE",
                                        pszDEMMissingValue);

const char* pszDEMApplyVDatumShift =
        CPLGetXMLValue(psTree, "DEMApplyVDatumShift", nullptr);
    if( pszDEMApplyVDatumShift != nullptr )
        papszOptions = CSLSetNameValue(papszOptions,
                                       "RPC_DEM_APPLY_VDATUM_SHIFT",
                                       pszDEMApplyVDatumShift);

/* -------------------------------------------------------------------- */
/*      Generate transformation.                                        */
/* -------------------------------------------------------------------- */
    void *pResult =
        GDALCreateRPCTransformer( &sRPC, bReversed, dfPixErrThreshold,
                                  papszOptions );

CSLDestroy( papszOptions );

return pResult;
}