C++ :: Structured Data / Nesting Triangles Using Structs And Doing Some Geometric Calculation?

nestedTriangles.cpp description:

The program takes as input a pair of triangles, specified be giving the coordinates of each trangle's vertices. It then determines if either triangle is "nested" within the other, meaning that one triangle lies entirely within the interior of the other.

Pseudocode:

One triangle lies within another if and only if all three vertices of the first triangle lie within the interior of the second triangle.Suppose that we have a triangle with vertices A, B, and C, described by the coordinates (xA, yA), (xB, yB), and (xC, yC), respectively. The sides of the triangle are the line segments AB, BC, and CA.A line passing through two points (x1, y1) and (x2, y2) can be considered to be the set of points (x,y) satisfying the equation

f(x,y) = 0
where f(x,y) is given as
f(x,y) = (x - x1) (y2 - y1) - (y - y1) (x2 - x1)

One of the interesting things about that f(x,y) is that we can use it to determine which "side" of the line an abitrary point (x,y) is on:

If f(x,y) = 0, the point is exactly on the line.

All points for which f(x,y) > 0 are on one side of the line, and All points for which f(x,y) < 0 are on the other side So the problem of determining whether a point (x,y) is on the inside of a trangle can be checking the sign of f(x,y) for each of the three lines making up the triangle.

A complicating factor is that we don't know, for any given triangle, whether those three signs should be all positive, all negative, or some mixture of the two.

The centroid of a triangle can be computed as the "average" of the x and y coordinates of the vertices:

xcen = (xA + xB + xC)/3
ycen = (yA + yB + yC)/3

This point (xcen, ycen) is definitely inside the trangle (unless the triangle is "degenerate" and has no interior points).

The problem of determining whether (x,y) is on the inside of a triangle can therefore be resolved by checking to see if it is on the same side of each of the trangle's line segments as (xcen, ycen).

I want to fill in the missing bodies for the functions eval and areOnSameSideOf, which manipulate line segments. I think calling eval from within areOnSameSideOf will simplify the implementation of the latter.

Code:
#include <iostream>
using namespace std;
/**
* 2D Cartesian coordinates
*/
struct Point {
double x;
double y;

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