#include <iostream>
#include <math.h>
#include <fstream>

//#define _DEBUG_
//#define _INTERACTIVE_
//#define _SUPERPOSITIONEXAMPLE_

using namespace std;

const double PI = 4.0*atan(1.0);

double waveApprox( double position, double velocity, double time, int numTerms);

int main (int argc, char * const argv[]) {

#ifdef _SUPERPOSITIONEXAMPLE_
const string baseDirString = "/Users/rj/Desktop/";
const string fiveTerms = baseDirString + "fiveTerms.dat";
const string twentyTerms = baseDirString + "twentyTerms.dat";
const string twoHundredTerms = baseDirString + "twoHundredTerms.dat";

ofstream fiveTermsOut;
ofstream twentyTermsOut;
ofstream twoHundredTermsOut;

fiveTermsOut.open(fiveTerms.c_str());
twentyTermsOut.open(twentyTerms.c_str());
twoHundredTermsOut.open(twoHundredTerms.c_str());

ofstream* fileArray[] = {&fiveTermsOut, &twentyTermsOut, &twoHundredTermsOut};
#endif

int numTerms;
double position, finalPosition, initialTime, initialVelocity, stepSize;

//set some initial conditions that will work with _INTERACTIVE_ turned off
position = 2;
initialVelocity = 1;
stepSize = 0.1;
initialTime = 0;
numTerms = 5;
finalPosition = 20;

#ifdef _DEBUG_
    cout << waveApprox(2,1,1,5) << endl;
#endif

#ifdef _INTERACTIVE_
    cout << "Interactive wave motion data generator\n";
    cout << "Please enter the number of harmonics: ";
    cin >> numTerms;
    cout << "Please enter the initial position: ";
    cin >> position;
    cout << "Please enter the final position: ";
    cin >> finalPosition;
    cout << "Please enter the initial time: ";
    cin >> initialTime;
    cout << "Please enter the initial velocity: ";
    cin >> initialVelocity;
    cout << "Please enter the set size: ";
    cin >> stepSize;
#ifdef _DEBUG_
    cout << "Number of Terms: " << numTerms
        << " Initial Position: " << position
        << " Final Position: " << finalPosition
        << " Initial Time: " << initialTime
        << " Initial Velocity: " << initialVelocity
        << " Step size: " << stepSize;
#endif
#endif

#ifdef _SUPERPOSITIONEXAMPLE_
    double tempPos = 0;
    for(int i = 0; i <= finalPosition/stepSize; i++){
        tempPos = i*stepSize;
        for(int j = 0; j < 3; j++){
            if(0 == j) numTerms = 5; else if(1 == j) numTerms = 20; else numTerms = 100;
            *fileArray[j] << tempPos << " "
                     << waveApprox(tempPos, initialVelocity, initialTime, numTerms)
                     << endl;
        }
    }
#endif

#ifdef _PROPNONDISPERSIVE_
    

#endif

    cout << "That's all folks!\n";
    return 0;
}


double waveApprox( double position, double velocity, double time, int numTerms){

    double solution = 0;
    int termCount = 0;
    
    for (int i = 1; i <= 2*numTerms; i++){
        if( 0 == ((i+1) % 2)){
            solution += (1/(double)i) * sin(i * position - i * velocity * time);
            termCount++;
        }
    }// Don't forget to add the other term and multiply by the weight factor

    solution *= (4/PI);
    solution += (4/PI);

#ifdef _DEBUG_
    cout << "Number of terms: " << termCount << endl;
#endif

    return solution;
}