/**
*
* Solution to homework task
* Introduction to programming course
* Faculty of Mathematics and Informatics of Sofia University
* Winter semester 2017/2018
*
* @author NATALIJA STOJANOVA
* @idnumber 855301
* @task 7
* @compiler GCC
*
*/
#include<iostream>
#include<cmath>
using namespace std;

int orientation(int ax, int ay, int bx, int by, int cx, int cy)
{
    int dx1=bx-ax;
    int dy1=by-ay;
    int dx2=cx-ax;
    int dy2=cy-ay;
    return (dx1*dy2-dy1*dx2);
}
// intersect function finds if the side of first and second triangle intersect
bool intersect(int ax, int ay, int bx, int by, int cx, int cy, int dx, int dy)
{
    return ((orientation(ax, ay, cx, cy, dx, dy)*orientation(bx, by, cx, cy, dx, dy)<0) && (orientation(cx, cy, ax, ay, bx, by)*orientation(dx, dy, ax, ay, bx, by)<0));
}

int main ()
{
    cout<<"THIS PROGRAM DEFINES THE KIND OF TRIANGLES AND MEASURE THE AREA OF CROSS SECTION OF THE TRIANGLES "<<endl;
    float a1x, a1y, b1x, b1y, c1x, c1y, a2x, a2y, b2x, b2y, c2x, c2y;
    //a1x and a1y defines the first vertex in first triangle
    //b1x and b1y defines the second vertex in first triangle
    //c1x and c1y defines the third vertex in first triangle
    //a2x and a2y defines the first vertex in second triangle
    //b2x and b2y defines the second vertex in second triangle
    //c2x and c2y defines the third vertex in second triangle

    cout<<"Enter the vertex of first triangle. Vertex A1"<<endl;
    cin>>a1x>>a1y;
    cout<<"Enter the vertex of first triangle Vertex B1"<<endl;
    cin>>b1x>>b1y;
    cout<<"Enter the vertex of first triangle Vertex C1"<<endl;
    cin>>c1x>>c1y;
    cout<<"Enter the vertex of second triangle. Vertex A2"<<endl;
    cin>>a2x>>a2y;
    cout<<"Enter the vertex of second triangle. Vertex B2"<<endl;
    cin>>b2x>>b2y;
    cout<<"Enter the vertex of second triangle. Vertex C2"<<endl;
    cin>>c2x>>c2y;
    bool flag11=0, flag12=0, flag21=0, flag22=0;
    // calculates the size of sides (a,b and c) with formula for distance between two points (first triangle)
   float a=sqrt((b1x-c1x)*(b1x-c1x)+(b1y-c1y)*(b1y-c1y)), b=sqrt((a1x-c1x)*(a1x-c1x)+(a1y-c1y)*(a1y-c1y)), c=sqrt((b1x-a1x)*(b1x-a1x)+(b1y-a1y)*(b1y-a1y));
   if (a==b && b==c)flag11=1; //Checks whether the triangle is equilateral
   // calculates the size of sides (a,b and c) with formula for distance between two points (second triangle)
    a=sqrt((b2x-c2x)*(b2x-c2x)+(b2y-c2y)*(b2y-c2y)), b=sqrt((a2x-c2x)*(a2x-c2x)+(a2y-c2y)*(a2y-c2y)), c=sqrt((b2x-a2x)*(b2x-a2x)+(b2y-a2y)*(b2y-a2y));
   if (a==b && b==c)flag12=1; //Checks whether the triangle is equilateral
    if(a1y==b1y){
        if(c1y>a1y)flag21=1; //Checks whether the triangle is upright
        if(a1x>b1x)swap(a1x, b1x); //sorts the vertexes
    }
    else if(a1y==c1y){
        if(b1y>a1y)flag21=1; //Checks whether the triangle is upright
        if(a1x>c1x)swap(a1x, c1x); //sorts the vertexes
    }
    else if(c1y==b1y){
        if(a1y>b1y)flag21=1; //Checks whether the triangle is upright
        if(b1x>c1x)swap(b1x, c1x); //sorts the vertexes
    }
    if(a2y==b2y){
        if(c2y>a2y)flag22=1; //Checks whether the triangle is upright
        if(a2x>b2x)swap(a2x, b2x);  //sorts the  vertexes
    }
    else if(a2y==c2y){
        if(b2y>a2y)flag22=1; //Checks whether the triangle is upright
        if(a2x>c2x)swap(a2x, c2x);  //sorts the  vertexes
    }
    else if(c2y==b2y){
        if(a2y>b2y)flag22=1; //Checks whether the triangle is upright
        if(b2x>c2x)swap(b2x, c2x); //sorts the  vertexes
    }
    if (flag11&&flag21)
        cout<<"First triangle is upright and equilateral"<<endl;
    else cout<<"First triangle is not upright or equilateral"<<endl;
    if (flag12 && flag22)
        cout<<"Second triangle is upright and equilateral"<<endl;
    else cout<<"Second triangle is not upright or equilateral"<<endl;
    float x1, y1, x2, y2; //x1 and y1 defines the first vertex of new triangle. x2 and y2 defines the second vertex of new triangle
    //The cross section of the triangles is also a equilateral triangle
    float a1, b1, c1;
    float a2, a3, b2, b3, c2, c3;
    if(flag11 && flag12 && flag21 && flag22)
    {
        float dx1, dx2, dy2;
        if(a1y==b1y)
        {
            if(a2y==b2y && intersect(a1x, a1y, c1x, c1y, a2x, a2y, b2x, b2y))
            {
                a1=a1y-c1y, b1=c1x-a1x, c1=a1x*c1y-c1x*a1y, a2=a2y-b2y, b2=b2x-a2x, c2=a2x*b2y-b2x*a2y;
                x1=(-c1*b2+c2*b1)/(a1*b2-a2*b1);
                y1=(-a1*c2+a2*c1)/(a1*b2-a2*b1);
                if(intersect(b1x, b1y, c1x, c1y, a2x, a2y, b2x, b2y))
                {
                    a3=a2y-b2y, b3=b2x-a2x, c3=a2x*b2y-b2x*a2y;
                    x2=(-c1*b3+c3*b1)/(a1*b3-a3*b1);
                    y2=(-a1*c3+a3*c1)/(a1*b3-a3*b1);
                }
                else if(intersect(b1x, b1y, c1x, c1y, a2x, a2y, c2x, c2y))
                {
                    a3=b2y-c2y, b3=c2x-b2x, c3=b2x*c2y-c2x*b2y;
                    x2=(-c1*b3+c3*b1)/(a1*b3-a3*b1);
                    y2=(-a1*c3+a3*c1)/(a1*b3-a3*b1);
                }
                else if(intersect(a1x, a1y, c1x, c1y, b2x, b2y, c2x, c2y))
                {
                    a3=b2y-c2y, b3=c2x-b2x, c3=b2x*c2y-c2x*b2y;
                    x2=(-c1*b3+c3*b1)/(a1*b3-a3*b1);
                    y2=(-a1*c3+a3*c1)/(a1*b3-a3*b1);
                }
            }
        }
        float Area;
        float Side_newTriagle = sqrt((x2-x1)*(x2-x1)-(y2-y1)*(y2-y1));
        Area = (sqrt(3)*Side_newTriagle*Side_newTriagle)/4;
        cout<<"The area of cross section of the triangles is: "<<Area;

    }
    else
            cout<<"The cross section of the triangles can not be measured because they are not uprighted and equilateral";

    return 0;
}