** Date Started: Aug 84
**
** This is part of the CTSim program
-** Copyright (C) 1983-2000 Kevin Rosenberg
+** Copyright (c) 1983-2001 Kevin Rosenberg
**
-** $Id: projections.cpp,v 1.44 2001/01/13 22:30:01 kevin Exp $
+** $Id: projections.cpp,v 1.57 2001/03/11 06:34:37 kevin Exp $
**
** This program is free software; you can redistribute it and/or modify
** it under the terms of the GNU General Public License (version 2) as
const int Projections::POLAR_INTERP_BILINEAR = 1;
const int Projections::POLAR_INTERP_BICUBIC = 2;
-const char* Projections::s_aszInterpName[] =
+const char* const Projections::s_aszInterpName[] =
{
{"nearest"},
{"bilinear"},
// {"bicubic"},
};
-const char* Projections::s_aszInterpTitle[] =
+const char* const Projections::s_aszInterpTitle[] =
{
{"Nearest"},
{"Bilinear"},
deleteProjData();
init (scanner.nView(), scanner.nDet());
- m_phmLen = scanner.phmLen();
m_rotInc = scanner.rotInc();
m_detInc = scanner.detInc();
+ m_detStart = scanner.detStart();
m_geometry = scanner.geometry();
- m_focalLength = scanner.focalLength();
- m_fieldOfView = scanner.fieldOfView();
+ m_dFocalLength = scanner.focalLength();
+ m_dSourceDetectorLength = scanner.sourceDetectorLength();
+ m_dViewDiameter = scanner.viewDiameter();
m_rotStart = 0;
- m_detStart = -(scanner.detLen() / 2);
+ m_dFanBeamAngle = scanner.fanBeamAngle();
}
void
kfloat64 _rotInc = m_rotInc;
kfloat64 _detStart = m_detStart;
kfloat64 _detInc = m_detInc;
- kfloat64 _phmLen = m_phmLen;
- kfloat64 _fieldOfView = m_fieldOfView;
- kfloat64 _focalLength = m_focalLength;
-
+ kfloat64 _viewDiameter = m_dViewDiameter;
+ kfloat64 _focalLength = m_dFocalLength;
+ kfloat64 _sourceDetectorLength = m_dSourceDetectorLength;
+ kfloat64 _fanBeamAngle = m_dFanBeamAngle;
+
fs.seekp(0);
if (! fs)
return false;
fs.writeFloat64 (_rotInc);
fs.writeFloat64 (_detStart);
fs.writeFloat64 (_detInc);
- fs.writeFloat64 (_phmLen);
+ fs.writeFloat64 (_viewDiameter);
fs.writeFloat64 (_focalLength);
- fs.writeFloat64 (_fieldOfView);
+ fs.writeFloat64 (_sourceDetectorLength);
+ fs.writeFloat64 (_fanBeamAngle);
fs.writeInt16 (_year);
fs.writeInt16 (_month);
fs.writeInt16 (_day);
{
kuint16 _hsize, _signature, _year, _month, _day, _hour, _minute, _second, _remarksize = 0;
kuint32 _nView, _nDet, _geom;
- kfloat64 _calcTime, _rotStart, _rotInc, _detStart, _detInc, _phmLen, _focalLength, _fieldOfView;
+ kfloat64 _calcTime, _rotStart, _rotInc, _detStart, _detInc, _focalLength, _sourceDetectorLength, _viewDiameter, _fanBeamAngle;
fs.seekg(0);
if (! fs)
fs.readFloat64 (_rotInc);
fs.readFloat64 (_detStart);
fs.readFloat64 (_detInc);
- fs.readFloat64 (_phmLen);
+ fs.readFloat64 (_viewDiameter);
fs.readFloat64 (_focalLength);
- fs.readFloat64 (_fieldOfView);
+ fs.readFloat64 (_sourceDetectorLength);
+ fs.readFloat64 (_fanBeamAngle);
fs.readInt16 (_year);
fs.readInt16 (_month);
fs.readInt16 (_day);
m_rotInc = _rotInc;
m_detStart = _detStart;
m_detInc = _detInc;
- m_phmLen = _phmLen;
- m_focalLength = _focalLength;
- m_fieldOfView = _fieldOfView;
+ m_dFocalLength = _focalLength;
+ m_dSourceDetectorLength = _sourceDetectorLength;
+ m_dViewDiameter = _viewDiameter;
+ m_dFanBeamAngle = _fanBeamAngle;
m_year = _year;
m_month = _month;
m_day = _day;
printf("Projections Data\n\n");
printf("Description: %s\n", m_remark.c_str());
printf("Geometry: %s\n", Scanner::convertGeometryIDToName (m_geometry));
- printf("nView = %8d nDet = %8d\n", m_nView, m_nDet);
- printf("focalLength = %8.4f fieldOfView = %8.4f\n", m_focalLength, m_fieldOfView);
- printf("rotStart = %8.4f rotInc = %8.4f\n", m_rotStart, m_rotInc);
- printf("detStart = %8.4f detInc = %8.4f\n", m_detStart, m_detInc);
+ printf("nView = %8d nDet = %8d\n", m_nView, m_nDet);
+ printf("focalLength = %8.4f ViewDiameter = %8.4f\n", m_dFocalLength, m_dViewDiameter);
+ printf("fanBeamAngle= %8.4f SourceDetector = %8.4f\n", convertRadiansToDegrees(m_dFanBeamAngle), m_dSourceDetectorLength);
+ printf("rotStart = %8.4f rotInc = %8.4f\n", m_rotStart, m_rotInc);
+ printf("detStart = %8.4f detInc = %8.4f\n", m_detStart, m_detInc);
if (m_projData != NULL) {
if (startView < 0)
startView = 0;
+ if (endView < 0)
+ endView = m_nView - 1;
if (startView > m_nView - 1)
startView = m_nView - 1;
if (endView > m_nView - 1)
Projections::printScanInfo (std::ostringstream& os) const
{
os << "Number of detectors: " << m_nDet << "\n";
- os << " Number of views: " << m_nView<< "\n";
- os << " Remark: " << m_remark.c_str()<< "\n";
- os << " Geometry: " << Scanner::convertGeometryIDToName (m_geometry)<< "\n";
- os << " Focal Length: " << m_focalLength<< "\n";
- os << " Field Of View: " << m_fieldOfView<< "\n";
- os << " phmLen: " << m_phmLen<< "\n";
- os << " detStart: " << m_detStart<< "\n";
- os << " detInc: " << m_detInc<< "\n";
- os << " rotStart: " << m_rotStart<< "\n";
- os << " rotInc: " << m_rotInc<< "\n";
+ os << "Number of views: " << m_nView<< "\n";
+ os << "Description: " << m_remark.c_str()<< "\n";
+ os << "Geometry: " << Scanner::convertGeometryIDToName (m_geometry)<< "\n";
+ os << "Focal Length: " << m_dFocalLength<< "\n";
+ os << "Source Detector Length: " << m_dSourceDetectorLength << "\n";
+ os << "View Diameter: " << m_dViewDiameter<< "\n";
+ os << "Fan Beam Angle: " << convertRadiansToDegrees(m_dFanBeamAngle) << "\n";
+ os << "detStart: " << m_detStart<< "\n";
+ os << "detInc: " << m_detInc<< "\n";
+ os << "rotStart: " << m_rotStart<< "\n";
+ os << "rotInc: " << m_rotInc<< "\n";
}
if (! v || nx == 0 || ny == 0)
return false;
+
+ if (m_geometry != Scanner::GEOMETRY_PARALLEL) {
+ sys_error (ERR_WARNING, "convertPolar supports Parallel only");
+ return false;
+ }
Array2d<double> adView (nx, ny);
Array2d<double> adDet (nx, ny);
double** ppdView = adView.getArray();
double** ppdDet = adDet.getArray();
- calcArrayPolarCoordinates (nx, ny, ppdView, ppdDet);
+ if (! calcArrayPolarCoordinates (nx, ny, ppdView, ppdDet))
+ return false;
std::complex<double>** ppcDetValue = new std::complex<double>* [m_nView];
unsigned int iView;
if (! v || nx == 0 || ny == 0)
return false;
+ if (m_geometry != Scanner::GEOMETRY_PARALLEL) {
+ sys_error (ERR_WARNING, "convertFFTPolar supports Parallel only");
+ return false;
+ }
+
#ifndef HAVE_FFT
return false;
#else
fftw_destroy_plan (plan);
delete [] pcIn;
- calcArrayPolarCoordinates (nx, ny, ppdView, ppdDet);
+ bool bError = calcArrayPolarCoordinates (nx, ny, ppdView, ppdDet);
- interpolatePolar (v, vImag, nx, ny, ppcDetValue, ppdView, ppdDet, m_nView, m_nDet, iInterpolationID);
+ if (! bError)
+ interpolatePolar (v, vImag, nx, ny, ppcDetValue, ppdView, ppdDet, m_nView, m_nDet, iInterpolationID);
for (iView = 0; iView < m_nView; iView++)
delete [] ppcDetValue[iView];
delete [] ppcDetValue;
- return true;
+ return bError;
#endif
}
-void
+bool
Projections::calcArrayPolarCoordinates (unsigned int nx, unsigned int ny, double** ppdView, double** ppdDet)
{
- double xMin = -m_phmLen / 2;
- double xMax = xMin + m_phmLen;
- double yMin = -m_phmLen / 2;
- double yMax = yMin + m_phmLen;
+ double xMin = -phmLen() / 2;
+ double xMax = xMin + phmLen();
+ double yMin = -phmLen() / 2;
+ double yMax = yMin + phmLen();
double xInc = (xMax - xMin) / nx; // size of cells
double yInc = (yMax - yMin) / ny;
int iDetCenter = (m_nDet - 1) / 2; // index refering to L=0 projection
- if (m_geometry != Scanner::GEOMETRY_PARALLEL) {
- sys_error (ERR_WARNING, "convertPolar supports Parallel only");
- return;
- }
-
// Calculates polar coordinates (view#, det#) for each point on phantom grid
double x = xMin + xInc / 2; // Rectang coords of center of pixel
for (unsigned int ix = 0; ix < nx; x += xInc, ix++) {
ppdDet[ix][iy] = (r / m_detInc) + iDetCenter;
}
}
+
+ return true;
}
void
for (unsigned int ix = 0; ix < ny; ix++) {
for (unsigned int iy = 0; iy < ny; iy++) {
if (iInterpolationID == POLAR_INTERP_NEAREST) {
- int iView = nearest<int> (ppdView[ix][iy]);
- int iDet = nearest<int> (ppdDet[ix][iy]);
+ unsigned int iView = nearest<int> (ppdView[ix][iy]);
+ unsigned int iDet = nearest<int> (ppdDet[ix][iy]);
if (iView == nView) {
iView = 0;
// iDet = m_nDet - iDet;
v[ix][iy] = 0;
}
} else if (iInterpolationID == POLAR_INTERP_BILINEAR) {
- int iFloorView = static_cast<int>(ppdView[ix][iy]);
+ unsigned int iFloorView = static_cast<int>(ppdView[ix][iy]);
double dFracView = ppdView[ix][iy] - iFloorView;
- int iFloorDet = static_cast<int>(ppdDet[ix][iy]);
+ unsigned int iFloorDet = static_cast<int>(ppdDet[ix][iy]);
double dFracDet = ppdDet[ix][iy] - iFloorDet;
if (iFloorDet >= 0 && iFloorView >= 0) {
}
+bool
+Projections::initFromSomatomAR_STAR (int iNViews, int iNDets, unsigned char* pData, unsigned long lDataLength)
+{
+ init (iNViews, iNDets);
+ m_geometry = Scanner::GEOMETRY_EQUIANGULAR;
+ m_dFanBeamAngle = iNDets * convertDegreesToRadians (3.06976 / 60);
+ m_dFocalLength = 51;
+ m_dSourceDetectorLength = 89;
+ m_detInc = convertDegreesToRadians (3.06976 / 60);
+ m_detStart = -m_dFanBeamAngle / 2;
+ m_rotInc = TWOPI / static_cast<double>(iNViews);
+ m_rotStart = HALFPI;
+ m_dViewDiameter = sin (m_dFanBeamAngle / 2) * m_dFocalLength * 2;
+
+ if (iNDets != 1024)
+ return false;
+ bool bValid = (iNViews == 750 && lDataLength == 1560000L) || (iNViews == 950 && lDataLength == 1976000L) || (iNViews == 1500 && lDataLength == 3120000);
+ if (! bValid)
+ return false;
+
+ long lDataPos = 0;
+ for (int iv = 0; iv < iNViews; iv++) {
+ unsigned char* pArgBase = pData + lDataPos;
+ unsigned char* p = pArgBase+0;
+#ifndef WORDS_BIGENDIAN
+ SwapBytes4 (p);
+#endif
+ long lProjNumber = *reinterpret_cast<long*>(p);
+
+ p = pArgBase+20;
+#ifndef WORDS_BIGENDIAN
+ SwapBytes4 (p);
+#endif
+ long lEscale = *reinterpret_cast<long*>(p);
+
+ p = pArgBase+28;
+#ifndef WORDS_BIGENDIAN
+ SwapBytes4 (p);
+#endif
+ long lTime = *reinterpret_cast<long*>(p);
+
+ p = pArgBase + 4;
+#ifndef WORDS_BIGENDIAN
+ SwapBytes4 (p);
+#endif
+ double dAlpha = *reinterpret_cast<float*>(p) + HALFPI;
+
+ p = pArgBase+12;
+#ifndef WORDS_BIGENDIAN
+ SwapBytes4 (p);
+#endif
+ double dAlign = *reinterpret_cast<float*>(p);
+
+ p = pArgBase + 16;
+#ifndef WORDS_BIGENDIAN
+ SwapBytes4 (p);
+#endif
+ double dMaxValue = *reinterpret_cast<float*>(p);
+
+ lDataPos += 32;
+ double dEScale = pow (2.0, -lEscale);
+ double dBetaInc = convertDegreesToRadians (3.06976 / 60);
+ int iCenter = (iNDets + 1) / 2;
+
+ DetectorArray& detArray = getDetectorArray( iv );
+ detArray.setViewAngle (dAlpha);
+ DetectorValue* detval = detArray.detValues();
+
+ double dTempScale = 2294.4871 * dEScale;
+ for (int id = 0; id < iNDets; id++) {
+ int iV = pData[lDataPos+1] + 256 * pData[lDataPos];
+ if (iV > 32767) // two's complement signed conversion
+ iV = iV - 65536;
+ double dCosScale = cos ((id + 1 - iCenter) * dBetaInc);
+ detval[id] = iV / (dTempScale * dCosScale);
+ lDataPos += 2;
+ }
+ }
+
+ return true;
+}
+
+Projections*
+Projections::interpolateToParallel ()
+{
+ if (m_geometry == Scanner::GEOMETRY_PARALLEL)
+ return this;
+
+ int nDet = m_nDet;
+ int nView = m_nView;
+ Projections* pProjNew = new Projections (nView, nDet);
+ pProjNew->m_geometry = Scanner::GEOMETRY_PARALLEL;
+ pProjNew->m_dFocalLength = m_dFocalLength;
+ pProjNew->m_dSourceDetectorLength = m_dSourceDetectorLength;
+ pProjNew->m_dViewDiameter = m_dViewDiameter;
+ pProjNew->m_dFanBeamAngle = m_dFanBeamAngle;
+ pProjNew->m_calcTime = 0;
+ pProjNew->m_remark = m_remark;
+ pProjNew->m_remark += "; Interpolate to Parallel";
+ pProjNew->m_label.setLabelType (Array2dFileLabel::L_HISTORY);
+ pProjNew->m_label.setLabelString (pProjNew->m_remark);
+ pProjNew->m_label.setCalcTime (pProjNew->m_calcTime);
+ pProjNew->m_label.setDateTime (pProjNew->m_year, pProjNew->m_month, pProjNew->m_day, pProjNew->m_hour, pProjNew->m_minute, pProjNew->m_second);
+
+ pProjNew->m_rotStart = 0;
+ pProjNew->m_rotInc = PI / nView;;
+ pProjNew->m_detStart = -m_dViewDiameter / 2;
+ pProjNew->m_detInc = m_dViewDiameter / nDet;
+ if (nDet % 2 == 0) // even
+ pProjNew->m_detInc = m_dViewDiameter / (nDet - 1);
+
+ ParallelRaysums parallel (this);
+
+ double* pdThetaValuesForT = new double [pProjNew->nView()];
+ double* pdRaysumsForT = new double [pProjNew->nView()];
+
+ // interpolate to evenly spaced theta (views)
+ double dDetPos = pProjNew->m_detStart;
+ for (int iD = 0; iD < pProjNew->nDet(); iD++, dDetPos += pProjNew->m_detInc) {
+ parallel.getThetaAndRaysumsForT (iD, pdThetaValuesForT, pdRaysumsForT);
+
+ double dViewAngle = m_rotStart;
+ for (int iV = 0; iV < pProjNew->nView(); iV++, dViewAngle += pProjNew->m_rotInc) {
+ DetectorValue* detValues = pProjNew->getDetectorArray (iV).detValues();
+
+ detValues[iD] = parallel.interpolate (pdThetaValuesForT, pdRaysumsForT, pProjNew->nView(), dViewAngle);
+ }
+ }
+ delete pdThetaValuesForT;
+ delete pdRaysumsForT;
+
+ // interpolate to evenly space t (detectors)
+ double* pdOriginalDetPositions = new double [pProjNew->nDet()];
+ parallel.getDetPositions (pdOriginalDetPositions);
+
+ double* pdDetValueCopy = new double [pProjNew->nDet()];
+ double dViewAngle = m_rotStart;
+ for (int iV = 0; iV < pProjNew->nView(); iV++, dViewAngle += pProjNew->m_rotInc) {
+ DetectorArray& detArray = pProjNew->getDetectorArray (iV);
+ DetectorValue* detValues = detArray.detValues();
+ detArray.setViewAngle (dViewAngle);
+
+ for (int i = 0; i < pProjNew->nDet(); i++)
+ pdDetValueCopy[i] = detValues[i];
+
+ double dDetPos = pProjNew->m_detStart;
+ for (int iD = 0; iD < pProjNew->nDet(); iD++, dDetPos += pProjNew->m_detInc) {
+ detValues[iD] = parallel.interpolate (pdOriginalDetPositions, pdDetValueCopy, pProjNew->nDet(), dDetPos);
+ }
+ }
+ delete pdDetValueCopy;
+ delete pdOriginalDetPositions;
+
+ return pProjNew;
+}
+
+
+///////////////////////////////////////////////////////////////////////////////
+//
+// Class ParallelRaysums
+//
+// Used for converting divergent beam raysums into Parallel raysums
+//
+///////////////////////////////////////////////////////////////////////////////
+
+ParallelRaysums::ParallelRaysums (Projections* pProjections)
+: m_iNumCoordinates(0), m_iNumView(pProjections->nView()), m_iNumDet(pProjections->nDet())
+{
+ int iGeometry = pProjections->geometry();
+ double dDetInc = pProjections->detInc();
+ double dDetStart = pProjections->detStart();
+ double dFocalLength = pProjections->focalLength();
+
+ m_iNumCoordinates = m_iNumView * m_iNumDet;
+ m_vecpCoordinates.reserve (m_iNumCoordinates);
+ for (int i = 0; i < m_iNumCoordinates; i++)
+ m_vecpCoordinates[i] = new ParallelRaysumCoordinate;
+
+ int iCoordinate = 0;
+ for (int iV = 0; iV < m_iNumView; iV++) {
+ double dViewAngle = pProjections->getDetectorArray(iV).viewAngle();
+ const DetectorValue* detValues = pProjections->getDetectorArray(iV).detValues();
+
+ double dDetPos = dDetStart;
+ for (int iD = 0; iD < m_iNumDet; iD++) {
+ ParallelRaysumCoordinate* pC = m_vecpCoordinates[iCoordinate++];
+
+ if (iGeometry == Scanner::GEOMETRY_PARALLEL) {
+ pC->m_dTheta = normalizeAngle (dViewAngle);
+ pC->m_dT = dDetPos;
+ } else if (iGeometry == Scanner::GEOMETRY_EQUILINEAR) {
+ double dFanAngle = atan (dDetPos / pProjections->sourceDetectorLength());
+ pC->m_dTheta = normalizeAngle (dViewAngle + dFanAngle);
+ pC->m_dT = dFocalLength * sin(dFanAngle);
+
+ } else if (iGeometry == Scanner::GEOMETRY_EQUIANGULAR) {
+ // fan angle is same as dDetPos
+ pC->m_dTheta = normalizeAngle (dViewAngle + dDetPos);
+ pC->m_dT = dFocalLength * sin (dDetPos);
+ }
+ if (pC->m_dTheta >= PI) { // convert T/Theta to 0-PI interval
+ pC->m_dTheta -= PI;
+ pC->m_dT = -pC->m_dT - pProjections->detInc();
+ }
+ pC->m_dRaysum = detValues[iD];
+ dDetPos += dDetInc;
+ }
+ }
+}
+
+ParallelRaysums::~ParallelRaysums()
+{
+ for (int i = 0; i < m_iNumCoordinates; i++)
+ delete m_vecpCoordinates[i];
+}
+
+ParallelRaysums::CoordinateContainer&
+ParallelRaysums::getSortedByTheta()
+{
+ if (m_vecpSortedByTheta.size() == 0) {
+ m_vecpSortedByTheta.resize (m_iNumCoordinates);
+ for (int i = 0; i < m_iNumCoordinates; i++)
+ m_vecpSortedByTheta[i] = m_vecpCoordinates[i];
+ std::sort (m_vecpSortedByTheta.begin(), m_vecpSortedByTheta.end(), ParallelRaysumCoordinate::compareByTheta);
+ }
+
+ return m_vecpSortedByTheta;
+}
+
+ParallelRaysums::CoordinateContainer&
+ParallelRaysums::getSortedByT()
+{
+ if (m_vecpSortedByT.size() == 0) {
+ m_vecpSortedByT.resize (m_iNumCoordinates);
+ for (int i = 0; i < m_iNumCoordinates; i++)
+ m_vecpSortedByT[i] = m_vecpCoordinates[i];
+ std::sort (m_vecpSortedByT.begin(), m_vecpSortedByT.end(), ParallelRaysumCoordinate::compareByT);
+ }
+
+ return m_vecpSortedByT;
+}
+
+
+void
+ParallelRaysums::getLimits (double* dMinT, double* dMaxT, double* dMinTheta, double* dMaxTheta) const
+{
+ if (m_iNumCoordinates <= 0)
+ return;
+
+ *dMinT = *dMaxT = m_vecpCoordinates[0]->m_dT;
+ *dMinTheta = *dMaxTheta = m_vecpCoordinates[0]->m_dTheta;
+
+ for (int i = 0; i < m_iNumCoordinates; i++) {
+ double dT = m_vecpCoordinates[i]->m_dT;
+ double dTheta = m_vecpCoordinates[i]->m_dTheta;
+
+ if (dT < *dMinT)
+ *dMinT = dT;
+ else if (dT > *dMaxT)
+ *dMaxT = dT;
+
+ if (dTheta < *dMinTheta)
+ *dMinTheta = dTheta;
+ else if (dTheta > *dMaxTheta)
+ *dMaxTheta = dTheta;
+ }
+}
+
+void
+ParallelRaysums::getThetaAndRaysumsForT (int iTheta, double* pTheta, double* pRaysum)
+{
+ const CoordinateContainer& coordsT = getSortedByT();
+
+ int iBase = iTheta * m_iNumView;
+ for (int i = 0; i < m_iNumView; i++) {
+ int iPos = iBase + i;
+ pTheta[i] = coordsT[iPos]->m_dTheta;
+ pRaysum[i] = coordsT[iPos]->m_dRaysum;
+ }
+}
+
+void
+ParallelRaysums::getDetPositions (double* pdDetPos)
+{
+ const CoordinateContainer& coordsT = getSortedByT();
+
+ int iPos = 0;
+ for (int i = 0; i < m_iNumDet; i++) {
+ pdDetPos[i] = coordsT[iPos]->m_dT;
+ iPos += m_iNumView;
+ }
+}
+
+// locate by bisection, O(log2(n))
+double
+ParallelRaysums::interpolate (double* pdX, double* pdY, int n, double dX)
+{
+ int iLower = -1;
+ int iUpper = n;
+
+ while (iUpper - iLower > 1) {
+ int iMiddle = (iUpper + iLower) >> 1;
+ if (dX >= pdX[iMiddle])
+ iLower = iMiddle;
+ else
+ iUpper = iMiddle;
+ }
+ if (dX <= pdX[0])
+ return pdY[0];
+ else if (dX >= pdX[n-1])
+ return pdY[1];
+
+ if (iLower < 0 || iLower >= n) {
+ sys_error (ERR_SEVERE, "Coordinate out of range [locateThetaBase]");
+ return 0;
+ }
+
+ return pdY[iLower] + (pdY[iUpper] - pdY[iLower]) * ((dX - pdX[iLower]) / (pdX[iUpper] - pdX[iLower]));
+}
+