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gdal_crs.cpp
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/******************************************************************************
*
* Project: Mapinfo Image Warper
* Purpose: Implementation of the GDALTransformer wrapper around CRS.C
functions
* to build a polynomial transformation based on ground control
* points.
* Author: Frank Warmerdam, warmerdam@pobox.com
*
***************************************************************************
CRS.C - Center for Remote Sensing rectification routines
Written By: Brian J. Buckley
At: The Center for Remote Sensing
Michigan State University
302 Berkey Hall
East Lansing, MI 48824
(517)353-7195
Written: 12/19/91
Last Update: 12/26/91 Brian J. Buckley
Last Update: 1/24/92 Brian J. Buckley
Added printout of trnfile. Triggered by BDEBUG.
Last Update: 1/27/92 Brian J. Buckley
Fixed bug so that only the active control points were used.
Last Update: 6/29/2011 C. F. Stallmann & R. van den Dool (South African
National Space Agency) GCP refinement added
Copyright (c) 1992, Michigan State University
* Copyright (c) 2008-2013, Even Rouault <even dot rouault at spatialys.com>
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 "gdal_alg.h"
#include "gdal_priv.h"
#include "cpl_conv.h"
#include "cpl_minixml.h"
#include "cpl_string.h"
#include "cpl_atomic_ops.h"
#include <math.h>
#include <stdlib.h>
#include <string.h>
#define MAXORDER 3
namespace
{
struct Control_Points
{
int count;
double *e1;
double *n1;
double *e2;
double *n2;
int *status;
};
} // namespace
struct GCPTransformInfo
{
GDALTransformerInfo sTI{};
double adfToGeoX[20]{};
double adfToGeoY[20]{};
double adfFromGeoX[20]{};
double adfFromGeoY[20]{};
double x1_mean{};
double y1_mean{};
double x2_mean{};
double y2_mean{};
int nOrder{};
int bReversed{};
std::vector<gdal::GCP> asGCPs{};
int bRefine{};
int nMinimumGcps{};
double dfTolerance{};
volatile int nRefCount{};
};
CPL_C_START
CPLXMLNode *GDALSerializeGCPTransformer(void *pTransformArg);
void *GDALDeserializeGCPTransformer(CPLXMLNode *psTree);
CPL_C_END
/* crs.c */
static int CRS_georef(double, double, double *, double *, double[], double[],
int);
static int CRS_compute_georef_equations(GCPTransformInfo *psInfo,
struct Control_Points *, double[],
double[], double[], double[], int);
static int remove_outliers(GCPTransformInfo *);
#define MSUCCESS 1 /* SUCCESS */
#define MNPTERR 0 /* NOT ENOUGH POINTS */
#define MUNSOLVABLE -1 /* NOT SOLVABLE */
#define MMEMERR -2 /* NOT ENOUGH MEMORY */
#define MPARMERR -3 /* PARAMETER ERROR */
#define MINTERR -4 /* INTERNAL ERROR */
static const char *const CRS_error_message[] = {
"Failed to compute GCP transform: Not enough points available",
"Failed to compute GCP transform: Transform is not solvable",
"Failed to compute GCP transform: Not enough memory",
"Failed to compute GCP transform: Parameter error",
"Failed to compute GCP transform: Internal error"};
/************************************************************************/
/* GDALCreateSimilarGCPTransformer() */
/************************************************************************/
static void *GDALCreateSimilarGCPTransformer(void *hTransformArg,
double dfRatioX, double dfRatioY)
{
GCPTransformInfo *psInfo = static_cast<GCPTransformInfo *>(hTransformArg);
VALIDATE_POINTER1(hTransformArg, "GDALCreateSimilarGCPTransformer",
nullptr);
if (dfRatioX == 1.0 && dfRatioY == 1.0)
{
/* We can just use a ref count, since using the source transformation */
/* is thread-safe */
CPLAtomicInc(&(psInfo->nRefCount));
}
else
{
auto newGCPs = psInfo->asGCPs;
for (auto &gcp : newGCPs)
{
gcp.Pixel() /= dfRatioX;
gcp.Line() /= dfRatioY;
}
/* As remove_outliers modifies the provided GCPs we don't need to
* reapply it */
psInfo = static_cast<GCPTransformInfo *>(GDALCreateGCPTransformer(
static_cast<int>(newGCPs.size()), gdal::GCP::c_ptr(newGCPs),
psInfo->nOrder, psInfo->bReversed));
}
return psInfo;
}
/************************************************************************/
/* GDALCreateGCPTransformer() */
/************************************************************************/
static void *GDALCreateGCPTransformerEx(int nGCPCount,
const GDAL_GCP *pasGCPList,
int nReqOrder, bool bReversed,
bool bRefine, double dfTolerance,
int nMinimumGcps)
{
// If no minimumGcp parameter was passed, we use the default value
// according to the model
if (bRefine && nMinimumGcps == -1)
{
nMinimumGcps = ((nReqOrder + 1) * (nReqOrder + 2)) / 2 + 1;
}
GCPTransformInfo *psInfo = nullptr;
double *padfGeoX = nullptr;
double *padfGeoY = nullptr;
double *padfRasterX = nullptr;
double *padfRasterY = nullptr;
int *panStatus = nullptr;
int iGCP = 0;
int nCRSresult = 0;
struct Control_Points sPoints;
double x1_sum = 0;
double y1_sum = 0;
double x2_sum = 0;
double y2_sum = 0;
memset(&sPoints, 0, sizeof(sPoints));
if (nReqOrder == 0)
{
if (nGCPCount >= 10)
nReqOrder = 2; /*for now we avoid 3rd order since it is unstable*/
else if (nGCPCount >= 6)
nReqOrder = 2;
else
nReqOrder = 1;
}
psInfo = new GCPTransformInfo();
psInfo->bReversed = bReversed;
psInfo->nOrder = nReqOrder;
psInfo->bRefine = bRefine;
psInfo->dfTolerance = dfTolerance;
psInfo->nMinimumGcps = nMinimumGcps;
psInfo->nRefCount = 1;
psInfo->asGCPs = gdal::GCP::fromC(pasGCPList, nGCPCount);
if (nGCPCount == 2 && nReqOrder == 1 &&
psInfo->asGCPs[0].X() != psInfo->asGCPs[1].X() &&
psInfo->asGCPs[0].Y() != psInfo->asGCPs[1].Y())
{
// Assumes that the 2 GCPs form opposite corners of a rectangle,
// and synthetize a 3rd corner
gdal::GCP newGCP;
newGCP.X() = psInfo->asGCPs[1].X();
newGCP.Y() = psInfo->asGCPs[0].Y();
newGCP.Pixel() = psInfo->asGCPs[1].Pixel();
newGCP.Line() = psInfo->asGCPs[0].Line();
psInfo->asGCPs.emplace_back(std::move(newGCP));
nGCPCount = 3;
pasGCPList = gdal::GCP::c_ptr(psInfo->asGCPs);
}
memcpy(psInfo->sTI.abySignature, GDAL_GTI2_SIGNATURE,
strlen(GDAL_GTI2_SIGNATURE));
psInfo->sTI.pszClassName = "GDALGCPTransformer";
psInfo->sTI.pfnTransform = GDALGCPTransform;
psInfo->sTI.pfnCleanup = GDALDestroyGCPTransformer;
psInfo->sTI.pfnSerialize = GDALSerializeGCPTransformer;
psInfo->sTI.pfnCreateSimilar = GDALCreateSimilarGCPTransformer;
/* -------------------------------------------------------------------- */
/* Compute the forward and reverse polynomials. */
/* -------------------------------------------------------------------- */
if (nGCPCount == 0)
{
nCRSresult = MNPTERR;
}
else if (bRefine)
{
nCRSresult = remove_outliers(psInfo);
}
else
{
/* --------------------------------------------------------------------
*/
/* Allocate and initialize the working points list. */
/* --------------------------------------------------------------------
*/
try
{
padfGeoX = new double[nGCPCount];
padfGeoY = new double[nGCPCount];
padfRasterX = new double[nGCPCount];
padfRasterY = new double[nGCPCount];
panStatus = new int[nGCPCount];
for (iGCP = 0; iGCP < nGCPCount; iGCP++)
{
panStatus[iGCP] = 1;
padfGeoX[iGCP] = pasGCPList[iGCP].dfGCPX;
padfGeoY[iGCP] = pasGCPList[iGCP].dfGCPY;
padfRasterX[iGCP] = pasGCPList[iGCP].dfGCPPixel;
padfRasterY[iGCP] = pasGCPList[iGCP].dfGCPLine;
x1_sum += pasGCPList[iGCP].dfGCPPixel;
y1_sum += pasGCPList[iGCP].dfGCPLine;
x2_sum += pasGCPList[iGCP].dfGCPX;
y2_sum += pasGCPList[iGCP].dfGCPY;
}
psInfo->x1_mean = x1_sum / nGCPCount;
psInfo->y1_mean = y1_sum / nGCPCount;
psInfo->x2_mean = x2_sum / nGCPCount;
psInfo->y2_mean = y2_sum / nGCPCount;
sPoints.count = nGCPCount;
sPoints.e1 = padfRasterX;
sPoints.n1 = padfRasterY;
sPoints.e2 = padfGeoX;
sPoints.n2 = padfGeoY;
sPoints.status = panStatus;
nCRSresult = CRS_compute_georef_equations(
psInfo, &sPoints, psInfo->adfToGeoX, psInfo->adfToGeoY,
psInfo->adfFromGeoX, psInfo->adfFromGeoY, nReqOrder);
}
catch (const std::exception &e)
{
CPLError(CE_Failure, CPLE_OutOfMemory, "%s", e.what());
nCRSresult = MINTERR;
}
delete[] padfGeoX;
delete[] padfGeoY;
delete[] padfRasterX;
delete[] padfRasterY;
delete[] panStatus;
}
if (nCRSresult != 1)
{
CPLError(CE_Failure, CPLE_AppDefined, "%s",
CRS_error_message[-nCRSresult]);
GDALDestroyGCPTransformer(psInfo);
return nullptr;
}
else
{
return psInfo;
}
}
/**
* Create GCP based polynomial transformer.
*
* Computes least squares fit polynomials from a provided set of GCPs,
* and stores the coefficients for later transformation of points between
* pixel/line and georeferenced coordinates.
*
* The return value should be used as a TransformArg in combination with
* the transformation function GDALGCPTransform which fits the
* GDALTransformerFunc signature. The returned transform argument should
* be deallocated with GDALDestroyGCPTransformer when no longer needed.
*
* This function may fail (returning nullptr) if the provided set of GCPs
* are inadequate for the requested order, the determinate is zero or they
* are otherwise "ill conditioned".
*
* Note that 2nd order requires at least 6 GCPs, and 3rd order requires at
* least 10 gcps. If nReqOrder is 0 the highest order possible (limited to 2)
* with the provided gcp count will be used.
*
* @param nGCPCount the number of GCPs in pasGCPList.
* @param pasGCPList an array of GCPs to be used as input.
* @param nReqOrder the requested polynomial order. It should be 1, 2 or 3.
* Using 3 is not recommended due to potential numeric instabilities issues.
* @param bReversed set it to TRUE to compute the reversed transformation.
*
* @return the transform argument or nullptr if creation fails.
*/
void *GDALCreateGCPTransformer(int nGCPCount, const GDAL_GCP *pasGCPList,
int nReqOrder, int bReversed)
{
return GDALCreateGCPTransformerEx(nGCPCount, pasGCPList, nReqOrder,
CPL_TO_BOOL(bReversed), false, -1, -1);
}
/** Create GCP based polynomial transformer, with a tolerance threshold to
* discard GCPs that transform badly.
*/
void *GDALCreateGCPRefineTransformer(int nGCPCount, const GDAL_GCP *pasGCPList,
int nReqOrder, int bReversed,
double dfTolerance, int nMinimumGcps)
{
return GDALCreateGCPTransformerEx(nGCPCount, pasGCPList, nReqOrder,
CPL_TO_BOOL(bReversed), true, dfTolerance,
nMinimumGcps);
}
/************************************************************************/
/* GDALDestroyGCPTransformer() */
/************************************************************************/
/**
* Destroy GCP transformer.
*
* This function is used to destroy information about a GCP based
* polynomial transformation created with GDALCreateGCPTransformer().
*
* @param pTransformArg the transform arg previously returned by
* GDALCreateGCPTransformer().
*/
void GDALDestroyGCPTransformer(void *pTransformArg)
{
if (pTransformArg == nullptr)
return;
GCPTransformInfo *psInfo = static_cast<GCPTransformInfo *>(pTransformArg);
if (CPLAtomicDec(&(psInfo->nRefCount)) == 0)
{
delete psInfo;
}
}
/************************************************************************/
/* GDALGCPTransform() */
/************************************************************************/
/**
* Transforms point based on GCP derived polynomial model.
*
* This function matches the GDALTransformerFunc signature, and can be
* used to transform one or more points from pixel/line coordinates to
* georeferenced coordinates (SrcToDst) or vice versa (DstToSrc).
*
* @param pTransformArg return value from GDALCreateGCPTransformer().
* @param bDstToSrc TRUE if transformation is from the destination
* (georeferenced) coordinates to pixel/line or FALSE when transforming
* from pixel/line to georeferenced coordinates.
* @param nPointCount the number of values in the x, y and z arrays.
* @param x array containing the X values to be transformed.
* @param y array containing the Y values to be transformed.
* @param z array containing the Z values to be transformed.
* @param panSuccess array in which a flag indicating success (TRUE) or
* failure (FALSE) of the transformation are placed.
*
* @return TRUE if all points have been successfully transformed.
*/
int GDALGCPTransform(void *pTransformArg, int bDstToSrc, int nPointCount,
double *x, double *y, CPL_UNUSED double *z,
int *panSuccess)
{
int i = 0;
GCPTransformInfo *psInfo = static_cast<GCPTransformInfo *>(pTransformArg);
if (psInfo->bReversed)
bDstToSrc = !bDstToSrc;
int bRet = TRUE;
for (i = 0; i < nPointCount; i++)
{
if (x[i] == HUGE_VAL || y[i] == HUGE_VAL)
{
bRet = FALSE;
panSuccess[i] = FALSE;
continue;
}
if (bDstToSrc)
{
CRS_georef(x[i] - psInfo->x2_mean, y[i] - psInfo->y2_mean, x + i,
y + i, psInfo->adfFromGeoX, psInfo->adfFromGeoY,
psInfo->nOrder);
}
else
{
CRS_georef(x[i] - psInfo->x1_mean, y[i] - psInfo->y1_mean, x + i,
y + i, psInfo->adfToGeoX, psInfo->adfToGeoY,
psInfo->nOrder);
}
panSuccess[i] = TRUE;
}
return bRet;
}
/************************************************************************/
/* GDALSerializeGCPTransformer() */
/************************************************************************/
CPLXMLNode *GDALSerializeGCPTransformer(void *pTransformArg)
{
CPLXMLNode *psTree = nullptr;
GCPTransformInfo *psInfo = static_cast<GCPTransformInfo *>(pTransformArg);
VALIDATE_POINTER1(pTransformArg, "GDALSerializeGCPTransformer", nullptr);
psTree = CPLCreateXMLNode(nullptr, CXT_Element, "GCPTransformer");
/* -------------------------------------------------------------------- */
/* Serialize Order and bReversed. */
/* -------------------------------------------------------------------- */
CPLCreateXMLElementAndValue(psTree, "Order",
CPLSPrintf("%d", psInfo->nOrder));
CPLCreateXMLElementAndValue(psTree, "Reversed",
CPLSPrintf("%d", psInfo->bReversed));
if (psInfo->bRefine)
{
CPLCreateXMLElementAndValue(psTree, "Refine",
CPLSPrintf("%d", psInfo->bRefine));
CPLCreateXMLElementAndValue(psTree, "MinimumGcps",
CPLSPrintf("%d", psInfo->nMinimumGcps));
CPLCreateXMLElementAndValue(psTree, "Tolerance",
CPLSPrintf("%f", psInfo->dfTolerance));
}
/* -------------------------------------------------------------------- */
/* Attach GCP List. */
/* -------------------------------------------------------------------- */
if (!psInfo->asGCPs.empty())
{
if (psInfo->bRefine)
{
remove_outliers(psInfo);
}
GDALSerializeGCPListToXML(psTree, psInfo->asGCPs, nullptr);
}
return psTree;
}
/************************************************************************/
/* GDALDeserializeReprojectionTransformer() */
/************************************************************************/
void *GDALDeserializeGCPTransformer(CPLXMLNode *psTree)
{
std::vector<gdal::GCP> asGCPs;
void *pResult = nullptr;
int nReqOrder = 0;
int bReversed = 0;
int bRefine = 0;
int nMinimumGcps = 0;
double dfTolerance = 0.0;
/* -------------------------------------------------------------------- */
/* Check for GCPs. */
/* -------------------------------------------------------------------- */
CPLXMLNode *psGCPList = CPLGetXMLNode(psTree, "GCPList");
if (psGCPList != nullptr)
{
GDALDeserializeGCPListFromXML(psGCPList, asGCPs, nullptr);
}
/* -------------------------------------------------------------------- */
/* Get other flags. */
/* -------------------------------------------------------------------- */
nReqOrder = atoi(CPLGetXMLValue(psTree, "Order", "3"));
bReversed = atoi(CPLGetXMLValue(psTree, "Reversed", "0"));
bRefine = atoi(CPLGetXMLValue(psTree, "Refine", "0"));
nMinimumGcps = atoi(CPLGetXMLValue(psTree, "MinimumGcps", "6"));
dfTolerance = CPLAtof(CPLGetXMLValue(psTree, "Tolerance", "1.0"));
/* -------------------------------------------------------------------- */
/* Generate transformation. */
/* -------------------------------------------------------------------- */
if (bRefine)
{
pResult = GDALCreateGCPRefineTransformer(
static_cast<int>(asGCPs.size()), gdal::GCP::c_ptr(asGCPs),
nReqOrder, bReversed, dfTolerance, nMinimumGcps);
}
else
{
pResult = GDALCreateGCPTransformer(static_cast<int>(asGCPs.size()),
gdal::GCP::c_ptr(asGCPs), nReqOrder,
bReversed);
}
return pResult;
}
/************************************************************************/
/* ==================================================================== */
/* Everything below this point derived from the CRS.C from GRASS. */
/* ==================================================================== */
/************************************************************************/
/* STRUCTURE FOR USE INTERNALLY WITH THESE FUNCTIONS. THESE FUNCTIONS EXPECT
SQUARE MATRICES SO ONLY ONE VARIABLE IS GIVEN (N) FOR THE MATRIX SIZE */
struct MATRIX
{
int n; /* SIZE OF THIS MATRIX (N x N) */
double *v;
};
/* CALCULATE OFFSET INTO ARRAY BASED ON R/C */
#define M(row, col) m->v[(((row)-1) * (m->n)) + (col)-1]
/***************************************************************************/
/*
FUNCTION PROTOTYPES FOR STATIC (INTERNAL) FUNCTIONS
*/
/***************************************************************************/
static int calccoef(struct Control_Points *, double, double, double *, double *,
int);
static int calcls(struct Control_Points *, struct MATRIX *, double, double,
double *, double *, double *, double *);
static int exactdet(struct Control_Points *, struct MATRIX *, double, double,
double *, double *, double *, double *);
static int solvemat(struct MATRIX *, double *, double *, double *, double *);
static double term(int, double, double);
/***************************************************************************/
/*
TRANSFORM A SINGLE COORDINATE PAIR.
*/
/***************************************************************************/
static int
CRS_georef(double e1, /* EASTINGS TO BE TRANSFORMED */
double n1, /* NORTHINGS TO BE TRANSFORMED */
double *e, /* EASTINGS TO BE TRANSFORMED */
double *n, /* NORTHINGS TO BE TRANSFORMED */
double E[], /* EASTING COEFFICIENTS */
double N[], /* NORTHING COEFFICIENTS */
int order /* ORDER OF TRANSFORMATION TO BE PERFORMED, MUST MATCH THE
ORDER USED TO CALCULATE THE COEFFICIENTS */
)
{
double e3 = 0.0;
double e2n = 0.0;
double en2 = 0.0;
double n3 = 0.0;
double e2 = 0.0;
double en = 0.0;
double n2 = 0.0;
switch (order)
{
case 1:
*e = E[0] + E[1] * e1 + E[2] * n1;
*n = N[0] + N[1] * e1 + N[2] * n1;
break;
case 2:
e2 = e1 * e1;
n2 = n1 * n1;
en = e1 * n1;
*e = E[0] + E[1] * e1 + E[2] * n1 + E[3] * e2 + E[4] * en +
E[5] * n2;
*n = N[0] + N[1] * e1 + N[2] * n1 + N[3] * e2 + N[4] * en +
N[5] * n2;
break;
case 3:
e2 = e1 * e1;
en = e1 * n1;
n2 = n1 * n1;
e3 = e1 * e2;
e2n = e2 * n1;
en2 = e1 * n2;
n3 = n1 * n2;
*e = E[0] + E[1] * e1 + E[2] * n1 + E[3] * e2 + E[4] * en +
E[5] * n2 + E[6] * e3 + E[7] * e2n + E[8] * en2 + E[9] * n3;
*n = N[0] + N[1] * e1 + N[2] * n1 + N[3] * e2 + N[4] * en +
N[5] * n2 + N[6] * e3 + N[7] * e2n + N[8] * en2 + N[9] * n3;
break;
default:
return (MPARMERR);
}
return (MSUCCESS);
}
/***************************************************************************/
/*
COMPUTE THE GEOREFFERENCING COEFFICIENTS BASED ON A SET OF CONTROL POINTS
*/
/***************************************************************************/
static int CRS_compute_georef_equations(GCPTransformInfo *psInfo,
struct Control_Points *cp, double E12[],
double N12[], double E21[],
double N21[], int order)
{
double *tempptr = nullptr;
int status = 0;
if (order < 1 || order > MAXORDER)
return (MPARMERR);
/* CALCULATE THE FORWARD TRANSFORMATION COEFFICIENTS */
status = calccoef(cp, psInfo->x1_mean, psInfo->y1_mean, E12, N12, order);
if (status != MSUCCESS)
return (status);
/* SWITCH THE 1 AND 2 EASTING AND NORTHING ARRAYS */
tempptr = cp->e1;
cp->e1 = cp->e2;
cp->e2 = tempptr;
tempptr = cp->n1;
cp->n1 = cp->n2;
cp->n2 = tempptr;
/* CALCULATE THE BACKWARD TRANSFORMATION COEFFICIENTS */
status = calccoef(cp, psInfo->x2_mean, psInfo->y2_mean, E21, N21, order);
/* SWITCH THE 1 AND 2 EASTING AND NORTHING ARRAYS BACK */
tempptr = cp->e1;
cp->e1 = cp->e2;
cp->e2 = tempptr;
tempptr = cp->n1;
cp->n1 = cp->n2;
cp->n2 = tempptr;
return (status);
}
/***************************************************************************/
/*
COMPUTE THE GEOREFFERENCING COEFFICIENTS BASED ON A SET OF CONTROL POINTS
*/
/***************************************************************************/
static int calccoef(struct Control_Points *cp, double x_mean, double y_mean,
double E[], double N[], int order)
{
struct MATRIX m;
double *a = nullptr;
double *b = nullptr;
int numactive = 0; /* NUMBER OF ACTIVE CONTROL POINTS */
int status = 0;
int i = 0;
memset(&m, 0, sizeof(m));
/* CALCULATE THE NUMBER OF VALID CONTROL POINTS */
for (i = numactive = 0; i < cp->count; i++)
{
if (cp->status[i] > 0)
numactive++;
}
/* CALCULATE THE MINIMUM NUMBER OF CONTROL POINTS NEEDED TO DETERMINE
A TRANSFORMATION OF THIS ORDER */
m.n = ((order + 1) * (order + 2)) / 2;
if (numactive < m.n)
return (MNPTERR);
/* INITIALIZE MATRIX */
m.v = static_cast<double *>(
VSICalloc(cpl::fits_on<int>(m.n * m.n), sizeof(double)));
if (m.v == nullptr)
{
return (MMEMERR);
}
a = static_cast<double *>(VSICalloc(m.n, sizeof(double)));
if (a == nullptr)
{
CPLFree(m.v);
return (MMEMERR);
}
b = static_cast<double *>(VSICalloc(m.n, sizeof(double)));
if (b == nullptr)
{
CPLFree(m.v);
CPLFree(a);
return (MMEMERR);
}
if (numactive == m.n)
status = exactdet(cp, &m, x_mean, y_mean, a, b, E, N);
else
status = calcls(cp, &m, x_mean, y_mean, a, b, E, N);
CPLFree(m.v);
CPLFree(a);
CPLFree(b);
return (status);
}
/***************************************************************************/
/*
CALCULATE THE TRANSFORMATION COEFFICIENTS WITH EXACTLY THE MINIMUM
NUMBER OF CONTROL POINTS REQUIRED FOR THIS TRANSFORMATION.
*/
/***************************************************************************/
static int exactdet(struct Control_Points *cp, struct MATRIX *m, double x_mean,
double y_mean, double a[], double b[],
double E[], /* EASTING COEFFICIENTS */
double N[] /* NORTHING COEFFICIENTS */
)
{
int currow = 1;
for (int pntnow = 0; pntnow < cp->count; pntnow++)
{
if (cp->status[pntnow] > 0)
{
/* POPULATE MATRIX M */
for (int j = 1; j <= m->n; j++)
{
M(currow, j) =
term(j, cp->e1[pntnow] - x_mean, cp->n1[pntnow] - y_mean);
}
/* POPULATE MATRIX A AND B */
a[currow - 1] = cp->e2[pntnow];
b[currow - 1] = cp->n2[pntnow];
currow++;
}
}
if (currow - 1 != m->n)
return (MINTERR);
return (solvemat(m, a, b, E, N));
}
/***************************************************************************/
/*
CALCULATE THE TRANSFORMATION COEFFICIENTS WITH MORE THAN THE MINIMUM
NUMBER OF CONTROL POINTS REQUIRED FOR THIS TRANSFORMATION. THIS
ROUTINE USES THE LEAST SQUARES METHOD TO COMPUTE THE COEFFICIENTS.
*/
/***************************************************************************/
static int calcls(struct Control_Points *cp, struct MATRIX *m, double x_mean,
double y_mean, double a[], double b[],
double E[], /* EASTING COEFFICIENTS */
double N[] /* NORTHING COEFFICIENTS */
)
{
int numactive = 0;
/* INITIALIZE THE UPPER HALF OF THE MATRIX AND THE TWO COLUMN VECTORS */
for (int i = 1; i <= m->n; i++)
{
for (int j = i; j <= m->n; j++)
M(i, j) = 0.0;
a[i - 1] = b[i - 1] = 0.0;
}
/* SUM THE UPPER HALF OF THE MATRIX AND THE COLUMN VECTORS ACCORDING TO
THE LEAST SQUARES METHOD OF SOLVING OVER DETERMINED SYSTEMS */
for (int n = 0; n < cp->count; n++)
{
if (cp->status[n] > 0)
{
numactive++;
for (int i = 1; i <= m->n; i++)
{
for (int j = i; j <= m->n; j++)
M(i, j) += term(i, cp->e1[n] - x_mean, cp->n1[n] - y_mean) *
term(j, cp->e1[n] - x_mean, cp->n1[n] - y_mean);
a[i - 1] +=
cp->e2[n] * term(i, cp->e1[n] - x_mean, cp->n1[n] - y_mean);
b[i - 1] +=
cp->n2[n] * term(i, cp->e1[n] - x_mean, cp->n1[n] - y_mean);
}
}
}
if (numactive <= m->n)
return (MINTERR);
/* TRANSPOSE VALUES IN UPPER HALF OF M TO OTHER HALF */
for (int i = 2; i <= m->n; i++)
{
for (int j = 1; j < i; j++)
M(i, j) = M(j, i);
}
return (solvemat(m, a, b, E, N));
}
/***************************************************************************/
/*
CALCULATE THE X/Y TERM BASED ON THE TERM NUMBER
ORDER\TERM 1 2 3 4 5 6 7 8 9 10
1 e0n0 e1n0 e0n1
2 e0n0 e1n0 e0n1 e2n0 e1n1 e0n2
3 e0n0 e1n0 e0n1 e2n0 e1n1 e0n2 e3n0 e2n1 e1n2 e0n3
*/
/***************************************************************************/
static double term(int nTerm, double e, double n)
{
switch (nTerm)
{
case 1:
return (1.0);
case 2:
return (e);
case 3:
return (n);
case 4:
return ((e * e));
case 5:
return ((e * n));
case 6:
return ((n * n));
case 7:
return ((e * e * e));
case 8:
return ((e * e * n));
case 9:
return ((e * n * n));
case 10:
return ((n * n * n));
}
return 0.0;
}
/***************************************************************************/
/*
SOLVE FOR THE 'E' AND 'N' COEFFICIENTS BY USING A SOMEWHAT MODIFIED
GAUSSIAN ELIMINATION METHOD.
| M11 M12 ... M1n | | E0 | | a0 |
| M21 M22 ... M2n | | E1 | = | a1 |
| . . . . | | . | | . |
| Mn1 Mn2 ... Mnn | | En-1 | | an-1 |
and
| M11 M12 ... M1n | | N0 | | b0 |
| M21 M22 ... M2n | | N1 | = | b1 |
| . . . . | | . | | . |
| Mn1 Mn2 ... Mnn | | Nn-1 | | bn-1 |
*/
/***************************************************************************/
static int solvemat(struct MATRIX *m, double a[], double b[], double E[],
double N[])
{
for (int i = 1; i <= m->n; i++)
{
int j = i;
/* find row with largest magnitude value for pivot value */
double pivot =
M(i, j); /* ACTUAL VALUE OF THE LARGEST PIVOT CANDIDATE */
int imark = i;
for (int i2 = i + 1; i2 <= m->n; i2++)
{
if (fabs(M(i2, j)) > fabs(pivot))
{
pivot = M(i2, j);
imark = i2;
}
}
/* if the pivot is very small then the points are nearly co-linear */
/* co-linear points result in an undefined matrix, and nearly */
/* co-linear points results in a solution with rounding error */
if (pivot == 0.0)
return (MUNSOLVABLE);
/* if row with highest pivot is not the current row, switch them */
if (imark != i)
{
for (int j2 = 1; j2 <= m->n; j2++)
{
std::swap(M(imark, j2), M(i, j2));
}
std::swap(a[imark - 1], a[i - 1]);
std::swap(b[imark - 1], b[i - 1]);
}
/* compute zeros above and below the pivot, and compute
values for the rest of the row as well */
for (int i2 = 1; i2 <= m->n; i2++)
{
if (i2 != i)
{
const double factor = M(i2, j) / pivot;
for (int j2 = j; j2 <= m->n; j2++)