#include <iostream>
#include <vector>
#include <cmath>
using namespace std;

//============== Geometry Stuff ========================================

struct Point{ double x, y, z; };

Point operator + ( Point p , Point q  ) { return { p.x + q.x, p.y + q.y, p.z + q.z }; }
Point operator - ( Point p , Point q  ) { return { p.x - q.x, p.y - q.y, p.z - q.z }; }
Point operator * ( double r, Point p  ) { return {   r * p.x,   r * p.y,   r * p.z }; }
Point operator / ( Point p , double r ) { return {   p.x / r,   p.y / r,   p.z / r }; }
double       dot ( Point p , Point q  ) { return p.x * q.x + p.y * q.y + p.z * q.z  ; }
Point      cross ( Point p , Point q  ) { return { p.y * q.z - p.z * q.y, p.z * q.x - p.x * q.z, p.x * q.y - p.y * q.x }; }
double    normsq ( Point p            ) { return dot( p, p ); }
double       abs ( Point p            ) { return sqrt( normsq( p ) ); }

ostream &operator << ( ostream &out, const Point &p ) { return out << p.x << '\t' << p.y << '\t' << p.z; }
istream &operator >> ( istream &in ,       Point &p ) { return in  >> p.x         >> p.y         >> p.z; }

//======================================================================

void forceSystem( const vector<Point> &f, const vector<Point> &x, Point &F, Point &M, Point &X )
{
   const double SMALL = 1.0e-30;

   Point centroid;
   F = M = centroid = Point{ 0, 0, 0 };
   for ( int i = 0; i < f.size(); i++ )
   {
      F = F + f[i];
      M = M + cross( x[i], f[i] );
      centroid = centroid + x[i];
   }
   centroid = centroid / f.size();

   // Find point on resultant line of action that is closest to centroid (arbitrary choice)
   if ( abs( F ) < SMALL )
   {
      cout << "Net force is zero\n";
      X = Point{ 0, 0, 0 };
   }
   else
   {
      X = ( cross( F, M ) - dot( F, centroid ) * F ) / normsq( F );
   }
}

//======================================================================

int main()
{
   // Data is that of your example; note the x, y, z directions and origin
   vector<Point> f = { {  0, 0, -90 }, {   0,  0, -105 }, {    0,  0, -160 }, {    0,    0, -50 } };
   vector<Point> x = { { 12, 1,   0 }, { 5.5, -5,    0 }, { 14.5, -3,    0 }, { 22.5, -5.5,   0 } };

   Point F, M, X;
   forceSystem( f, x, F, M, X );
   cout << "Net force  = " << F << '\n'
        << "Net moment = " << M << '\n'
        << "\nEquivalent force system is\n"
        << "force " << F << '\n'
        << "acting at " << X << '\n'
        << "(or any point on a line parallel to F passing through that point)";
}

#include<iostream>

int main()
{
    double P{0}, x{0}, y{0};
    
    double sigma_P{0}, sigma_Mx{0}, sigma_My{0};
    
    while(1)
    {
        std::cout << "P x y: ";
        std::cin >> P >> x >> y;
        
        sigma_P += P;
        sigma_Mx += P * y;
        sigma_My += P * x;
        
        std::cout
        << "Single equivalent force: " << sigma_P << '\n'
        << "   Sigma M about X axis: " << sigma_Mx << '\n'
        << "   Sigma M about Y axis: " << sigma_My << '\n'
        << "             X location: " << sigma_My/sigma_P << '\n'
        << "             Y location: " << sigma_Mx/sigma_P << '\n';
    }
    return 0;
}

#include<iostream>

int main()
{
//Code works for the info provided from Part A (2D Plane)
double P{0}, x{0}, y{0};
double sigma_P{0}, sigma_Mx{0}, sigma_My{0};
  
while(1)
    {
//Requires the user to input a vertical force and its x-y distance in order to calculate the resultant (single equivalent force), and its location on the plane
std:: cout << "\nPlease input a force (P), x-distance (x), and y-distance (y)";

std::cout << "\n\nIn this format, P, x, y: ";
std::cin >> P >> x >> y;

//Calculates the single force equivalent (resultant)
sigma_P += P;
//Calculates the 
sigma_Mx += P * y;
sigma_My += P * x;
        
std::cout
<< "\nSingle equivalent force: " << sigma_P << " lb" << '\n'
<< "\nSigma M about X axis: " << sigma_Mx << " lb*ft" << '\n'
<< "Sigma M about Y axis: " << sigma_My << " lb*ft" << '\n'
<< "\nX location: " << sigma_My/sigma_P << " ft" << '\n'
<< "Y location: " << sigma_Mx/sigma_P << " ft" << '\n';
  }
  
  return 0;
}