YAY FOR MATH

#include <algorithm>
#include <iostream>
#include <sstream>
#include <fstream>
#include <math.h>
#include <vector>
#include <bitset>
#include <string>
#include <stack>
#include <queue>
#include <map>
#include <set>
#define _CRT_SECURE_NO_DEPRECATE

using namespace std;

string filename( "palsquare" );
ifstream in( filename+".in" );
ofstream out( filename+".out" );

double crossproduct( double x1, double y1, double x2, double y2 )
{
    return x1*y2 - y1*x2;
}

bool capturedpt( double x1, double y1, double minx, double maxx, double miny, double maxy )
{
    if( minx < x1 && maxx >= x1 &&
        miny < y1 && maxy >= y1 )
        return true;
    else
        return false;
}

double MAX( double a, double b, double c, double d )
{
    return max( a, max( b, max( c, d ) ) );
}

int main()
{
    double x1 = 2;
    double y1 = 6;
    double x2 = 5;
    double y2 = 5;
    double x3 = 6;
    double y3 = 2;
    double x4 = 4;
    double y4 = 10;

    double MAXY = MAX( y1, y2, y3, y4 ) + 1;
    double MAXX = MAX( x1, x2, x3, x4 )+1;
    double SCALE = 20.0;

    for( double y = 0; y <= MAXY; y += MAXY/SCALE )
    {
        for( double x = 0; x <= MAXX; x += MAXX/SCALE )
        {
            if( capturedpt( x1, y1, x, x+ MAXX/SCALE, y, y+ MAXY/SCALE ) )
                cout << "A";
            else if( capturedpt( x2, y2, x, x+ MAXX/SCALE, y, y+ MAXY/SCALE ) )
                cout << "a";
            else if( capturedpt( x3, y3, x, x+ MAXX/SCALE, y, y+ MAXY/SCALE ) )
                cout << "B";
            else if( capturedpt( x4, y4, x, x+ MAXX/SCALE, y, y+ MAXY/SCALE ) )
                cout << "b";
            else
                cout << ".";
        }
        cout << endl;
    }
    if( crossproduct( x3-x1, y3-y1, x3-x2, y3-y2 ) * crossproduct( x4-x1, y4-y1, x4-x2, y4-y2 ) < 0
        && crossproduct( x1-x3, y1-y3, x1-x4, y1-y4 ) * crossproduct( x2-x3, y2-y3, x2-x4, y2-y4 ) < 0 )
        cout << "THEY INTERSECT!";
    else
        cout << "THEY DON'T INTERSECT!";
    cin.get();

    return 0;
}