interpolate.cpp

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/*===============================================================================================================================
 
This file is part of CoastalME, the Coastal Modelling Environment.
 
CoastalME is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
 
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
 
You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 
===============================================================================================================================*/
#include <assert.h>
#include <cfloat>
#include <iostream>
#include <iomanip>
#include <vector>
using namespace std;
 
#include "cme.h"
 
//===============================================================================================================================
//===============================================================================================================================
double dGetInterpolatedValue(vector<double> const* pVdXdata, vector<double> const* pVdYdata, double dX, bool bExtrapolate)
{
   int size = static_cast<int>(pVdXdata->size());
 
   int i = 0;                                   // Find left end of interval for interpolation
   if (dX >= pVdXdata->at(size - 2))            // Special case: beyond right end
   {
      i = size - 2;
   }
   else
   {
      while (dX > pVdXdata->at(i+1)) i++;
   }
   
   double dXL = pVdXdata->at(i);
   double dYL = pVdYdata->at(i);
   double dXR = pVdXdata->at(i+1);
   double dYR = pVdYdata->at(i+1);              // Points on either side (unless beyond ends)
      
   if (! bExtrapolate)                          // If beyond ends of array and not extrapolating
   {
      if (dX < dXL)
         dYR = dYL;
 
      if (dX > dXR)
         dYL = dYR;
   }
 
   double ddYdX = (dYR - dYL) / (dXR - dXL);    // Gradient
 
   return (dYL + ddYdX * (dX - dXL));           // Linear interpolation
}
 
//===============================================================================================================================
//===============================================================================================================================
double dGetInterpolatedValue(vector<int> const* pVnXdata, vector<double> const* pVdYdata, int nX, bool bExtrapolate )
{
   unsigned int nSize = static_cast<unsigned int>(pVnXdata->size());
 
   int i = 0;                                   // Find left end of interval for interpolation
   if (nX >= pVnXdata->at(nSize - 2))           // Special case: beyond right end
   {
      i = nSize - 2;
   }
   else
   {
      while (nX > pVnXdata->at(i+1)) i++;
   }
   
   int nXL = pVnXdata->at(i);
   int nXR = pVnXdata->at(i+1);
      
   double dYL = pVdYdata->at(i);
   double dYR = pVdYdata->at(i+1);                  // Points on either side (unless beyond ends)
      
   if (! bExtrapolate)                          // If beyond ends of array and not extrapolating
   {
      if (nX < nXL) dYR = dYL;
      if (nX > nXR) dYL = dYR;
   }
 
   double ddYdX = (dYR - dYL) / static_cast<double>(nXR - nXL);      // Gradient
 
   return dYL + ddYdX * static_cast<double>(nX - nXL);               // Linear interpolation
}
 
//===============================================================================================================================
//===============================================================================================================================
int nFindIndex(vector<double> const* pVdX, double const dValueIn)
{
   double dLastValue = DBL_MAX;
   int nIndexFound = 0;
 
   for (unsigned int i = 0; i < pVdX->size(); ++i)
   {
      double dThisValue = tAbs(dValueIn - pVdX->at(i));
 
      if (dThisValue <= dLastValue)
      {
         dLastValue = dThisValue;
         nIndexFound = i;
      }
   }
 
   return nIndexFound;
}
 
//===============================================================================================================================
//===============================================================================================================================
vector<double> VdInterpolateCShoreProfileOutput(vector<double> const* pVdX, vector<double> const* pVdY, vector<double> const* pVdXNew)
{
   int nXSize = static_cast<int>(pVdX->size());
   int nXNewSize = static_cast<int>(pVdXNew->size());
 
   // assert(nXSize > 0);
   // assert(nXNewSize > 0);
 
   double dX;
   double dY;
   vector<double> VdYNew(nXNewSize, 0.0);
 
   for (int i = 0; i < nXNewSize; ++i)
   {
      int idx = nFindIndex(pVdX, pVdXNew->at(i));
 
      if (pVdX->at(idx) > pVdXNew->at(i))
      {
         if (idx > 0)
         {
            dX = pVdX->at(idx) - pVdX->at(idx-1);
            dY = pVdY->at(idx) - pVdY->at(idx-1);
         }
         else
         {
            dX = pVdX->at(idx+1) - pVdX->at(idx);
            dY = pVdY->at(idx+1) - pVdY->at(idx);
         }
      }
      else
      {
         if (idx < nXSize-1)
         {
            dX = pVdX->at(idx+1) - pVdX->at(idx);
            dY = pVdY->at(idx+1) - pVdY->at(idx);
         }
         else
         {
            dX = pVdX->at(idx) - pVdX->at(idx-1);
            dY = pVdY->at(idx) - pVdY->at(idx-1);
         }
      }
 
      // Safety check: this crashes (divide by zero) if there are identical consecutive values in pVdX, and thus if dX becomes 0. To prevent this, if dX is near zero, set to a small non-zero number
      if (bFPIsEqual(dX, 0.0, TOLERANCE))
         dX = 1e-10;
 
      double dM = dY / dX;
      double dB = pVdY->at(idx) - pVdX->at(idx) * dM;
 
      // VdYNew[i] = (pVdXNew->at(i) * dM) + dB;
      VdYNew[nXNewSize-1 - i] = (pVdXNew->at(i) * dM) + dB;
   }
 
   return VdYNew;
}