#include <cstdlib>
#include <iostream>
#include <math.h>
#include <graphics.h>
using namespace std;

const int optX = 800;
const int optY = 800;
const int halfX = (int)optX / 2;
const int dp = 1;
const double eps = 9e-16;

void ParabBrez(double aa, double bb, double cc, double dd);

int main(){
    initwindow(optX, optY);
    //ParabBrez(-0.0025, -3, 1, 1);
    //ParabBrez(0.0025, -3, 1, 1);
    ParabBrez(0.25, -3, 1, 1);
    //ParabBrez(0.025, -3, 1, 1);
    //ParabBrez(0.1, 0, 1,0);
    //ParabBrez(0.025, 434, 1, 1);
    //ParabBrez(6.25, 19, 4, -1);
    //ParabBrez(5, 43, 1, 1);
    getch();
    closegraph();
    return 0;
}

void draw_pixel(double x, double y, int where)
{
     double x_coord = halfX - (int)x * dp;
     double y_coord = where - (int)(y * dp);
     putpixel(x_coord, y_coord, WHITE);
}

void ParabBrez(double aa, double bb, double cc, double dd)
{

	//double a = aa / (cc * cc), b = -(2 * aa * dd) / (cc * cc) , c = (aa * dd * dd) / (cc * cc) + bb, d = dd;
	//cout<<aa / (cc * cc)<<" "<<-(2 * aa * dd) / (cc * cc)<<" "<<(aa * dd * dd) / (cc * cc) + bb<<endl;

	double a = aa / (cc * cc), b = bb, c = (aa * dd * dd) / (cc * cc) + bb, d = dd;
	double x = dd, y = bb;  // x0, y0

    double delta = (b + 1 - a * (d + 1) * (d + 1) - b * (d + 1) - c);   // first error
    double plus_one = 1;
    int where = optY - 10;

    if (a < 0)
    {
       where = 10;
       delta = b - 1 - a * (d + 1) * (d + 1) - b * (d + 1) - c;   // first error
       plus_one = -1;
    }

    cout<<"first delta = "<<delta<<endl;
   // cout<<y<<" "<<x<<endl;

        double to_focus = (x + 1 - d) * (x + 1 - d) + (y + plus_one  - (b + (plus_one) * 1/(4*a))) * (y + plus_one  - (b + (plus_one) * 1/(4*a)));
        double to_direc = (y + plus_one  - (b + (-plus_one) * 1/(4*a))) * (y + plus_one  - (b + (-plus_one) * 1/(4*a)));
    delta =  -to_direc + to_focus;

	while ((where - (int)(y * dp) > 0) && (halfX - x * dp > 0))
	{
         //cout<< where - y * dp<<" "<<   halfX - x * dp << endl;

                 draw_pixel(x, y, where);
        draw_pixel(dd - x, y, where);

        if (delta < 0)              // horizontal or diagonal point
        {
            double horiz_to_focus = (x + 1 - d) * (x + 1 - d) + (y - (b +(plus_one) * 1/(4*a))) * (y - (b +(plus_one) * 1/(4*a)));
            double horiz_to_direc = (y - (b +(-plus_one) * 1/(4*a))) * (y - (b +(-plus_one) * 1/(4*a)));
            double epsH = fabs(horiz_to_direc - horiz_to_focus);

            double diagon_to_focus = (x + 1 - d) * (x + 1 - d) + (y + plus_one - (b +(plus_one) * 1/(4*a))) * (y + plus_one - (b +(plus_one) * 1/(4*a)));
            double diagon_to_direc = (y + plus_one - (b +(-plus_one) * 1/(4*a))) * (y + plus_one - (b +(-plus_one) * 1/(4*a)));
            double epsD = fabs(diagon_to_direc - diagon_to_focus);

            double epsilon = epsH - epsD;
            if (epsilon < 0)                     // до h ближе -> его и берем
            {
               x++;
            }
            else                      // до d ближе
            {
               x++;
               y += plus_one;
            }
        }
        else if (delta > 0)              // v or d
        {
            double vertical_to_focus = (x - d) * (x - d) + (y + plus_one - (b +(plus_one) * 1/(4*a))) * (y + plus_one - (b +(plus_one) * 1/(4*a)));
            double verical_to_direc = (y + plus_one - (b +(-plus_one) * 1/(4*a))) * (y + plus_one - (b +(-plus_one) * 1/(4*a)));
            double epsV = fabs(verical_to_direc - vertical_to_focus);

            double diagon_to_focus = (x + 1 - d) * (x + 1 - d) + (y + plus_one - (b +(plus_one) * 1/(4*a))) * (y + plus_one - (b +(plus_one) * 1/(4*a)));
            double diagon_to_direc = (y + plus_one - (b +(-plus_one) * 1/(4*a))) * (y + plus_one - (b +(-plus_one) * 1/(4*a)));
            double epsD = fabs(diagon_to_direc - diagon_to_focus);

            double epsilon = epsD - epsV;
            if (epsilon <= 0)                  // take d
            {
               x++;
               y += plus_one;
            }
            else     // take V
            {
                y += plus_one;
            }
        }
        else if (delta == 0)
        {
             x++;
             y += plus_one;
        }
        double to_focus = (x + 1 - d) * (x + 1 - d) + (y + plus_one  - (b + (plus_one) * 1/(4*a))) * (y + plus_one  - (b + (plus_one) * 1/(4*a)));
        double to_direc = (y + plus_one  - (b + (-plus_one) * 1/(4*a))) * (y + plus_one  - (b + (-plus_one) * 1/(4*a)));
        delta =  -to_direc + to_focus;
    }
}