// =================
// || Worksheet 14
// || In this exercise, we are going be solving the 1d KDV (Korteweg De Vries) equation.
//    d/dt f(x,t) = - d^3/dx^3 f(x,t) - 6 k f(x,t) d/dx f(x,t)
// =================

// see also, e.g. https://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation

#include "program.h"

using namespace std;
using namespace cv;

void INSERT_KDV_SOLITON(Mat img, float x0, float c)
{
    float val;
    for(int x =0; x < img.cols; x++)
    {
        val = 0.5*sqrt(c)*(x-x0);
        val = 0.5*c/(cosh(val)*cosh(val));
        
        for(int y =0; y < img.rows; y++)
        {
            img.at<float>(x,y) += val;
        }
    }
}


int worksheetfourteen(Mat& src)
{
    Mat input = Mat::zeros(200,200, CV_32F );
    
    // insert two solitons!
    INSERT_KDV_SOLITON(input,20,3);
    INSERT_KDV_SOLITON(input,60,1);
    
    // a window to show our outputs
    cv::namedWindow( "current frame", WINDOW_AUTOSIZE );
    imshow( "current frame", input);
    waitKey();
    
    int MAX_NUMBER_OF_FRAMES = 5000;
    
    // dissipation factor.
    float k = 0.01f;
    
    // this is of the initial data
    Mat prev_frame = input.clone() ;
    
    Mat colorized_frame;
    
    // repeat this for each of the frames.
    for (int n = 0; n < MAX_NUMBER_OF_FRAMES; n++)
    {
        // Do the numerical calculations here!
        
        // ???
        Mat frame;
        
        
        // lets colorize our image too, so that it looks better.
        frame.convertTo(colorized_frame,CV_8UC1, 127,127);
        applyColorMap(colorized_frame, colorized_frame,COLORMAP_AUTUMN);
        // lets also make it 4 times the size, so we dont strain our eyes.
        resize(colorized_frame,colorized_frame,Size(colorized_frame.cols*4,colorized_frame.rows*4 ) );
        
        // display the current frame.
        cv::imshow( "current frame", colorized_frame);
        
        //wait for 'esc' key press for 300ms. If 'esc' key is pressed, break loop
        if (waitKey(10) == 27)
        {
            cout << "esc key is pressed by user" << endl;
            break;
        }
        
        // need to update
        prev_frame = frame.clone();
    }
    
    return 0;
}