// =================
// || Worksheet 11
// || In this exercise, we are going be solving the 2d wave equation using smoother spatial derivatives.
//    d^2/dt^2 f(x,y,t) = - k (d^2/dx^2+d^2/dy^2) f(x,y,t)
// =================

// see also, e.g. http://www.mtnmath.com/whatrh/node66.html

#include "program.h"

using namespace std;
using namespace cv;

int worksheettwelve(Mat& src)
{
    Mat input = Mat::zeros(200,200, CV_32F );
    
    // draw a little circle in the middle of our image.
    circle(input, Point(input.rows/2, input.cols/2), 25.0f, Scalar( 1.0, 1.0, 1.0 ),CV_FILLED);
    
    // a window to show our outputs
    cv::namedWindow( "current frame", WINDOW_AUTOSIZE );
    
    int MAX_NUMBER_OF_FRAMES = 5000;
    
    // dissipation factor.
    float k = 0.003f;
    
    // this is of the initial data
    Mat prev_frame = input.clone() ;
    Mat prev_prev_frame = input.clone();
    
    // this is going to be our Laplacian kernel.
    int krn_sz = 9;
    cv::Mat kernel = (cv::Mat::zeros(krn_sz, krn_sz, CV_32F));
    float T = 1.0f;
    // set up the kernel
    for(int i =0; i <krn_sz;i++)
    {
        for(int j=0;j<krn_sz;j++)
        {
            kernel.at<float>(i,j) = (1.0/(T*T))*exp( - ((i-4)*(i-4) + (j-4)*(j-4))/T)*(-T + ((i-4)*(i-4) + (j-4)*(j-4)));
        }
    }
    cv::imshow( "current frame", kernel);
    cv::waitKey();
    
    Mat colorized_frame;
    
    // repeat this for each of the frames.
    for (int n = 0; n < MAX_NUMBER_OF_FRAMES; n++)
    {
        // compute kernel convolution;
        Mat Lframe;// = kernel * prev_frame;
        cv::filter2D(prev_frame, Lframe, prev_frame.depth(), kernel);
        
        // f(t+1) =   -f(t-1)        +   2 * f(t)      - k * L f(t)
        Mat frame = -prev_prev_frame + 2.0f*prev_frame + k * Lframe;
        
        // 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 PREVIOUS two frames. !!!!!
        prev_prev_frame = prev_frame.clone();
        prev_frame = frame.clone();
    }
    
    return 0;
}