#include <cmath>   //for sqrt, abs
#include "point.h"
using namespace std;

const point point_origin;

//Return the distance between this point and the origin.

double point::dist() const
{
	const double dx = point_origin.x - x;
	const double dy = point_origin.y - y;

	return sqrt(dx * dx + dy * dy);               //Pythagorean theorem
}

//Return the distance between points A and B.

double dist(const point& A, const point& B)
{
	const double dx = A.x - B.x;
	const double dy = A.y - B.y;

	return sqrt(dx * dx + dy * dy);
}

//Return the area of triangle ABC.

double area(const point& A, const point& B, const point& C)
{
        return abs(A.x * B.y + B.x * C.y + C.x * A.y
                 - A.y * B.x - B.y * C.x - C.y * A.x) / 2;
}

/*
Return true if the triangle ABC contains the point D, or if D is on the
perimeter.  Ideally area(A, B, C) would equal sum exactly, but floating point
arithmetic is never exact.  We return true if area(A, B, C) is within
point_error of sum.
*/

bool contains(const point& A, const point& B, const point& C, const point& D)
{
	const double sum = area(A, B, D) + area(B, C, D) + area(C, A, D);
	return abs(area(A, B, C) - sum) < point_error;
}