is_inside_triangle.cc

#include <iostream>

struct Point { // 2-D
    double x, y;
    Point(double x, double y) : x(x), y(y) {}
};

// Barycentric method - https://stackoverflow.com/a/9755252
bool isInsideTriangle(const Point& a, const Point& b, const Point& c, const Point& s)
{
    // collinearity, (a, b, c) is not a triangle
    if (a.x == b.x == c.x || a.y == b.y == c.y)
        return false;

    double as_x = s.x - a.x;
    double as_y = s.y - a.y;
    bool s_ab = (b.x - a.x) * as_y - (b.y - a.y) * as_x > 0;

    if ((c.x - a.x) * as_y - (c.y - a.y) * as_x > 0 == s_ab) return false;

    if ((c.x - b.x) * (s.y - b.y) - (c.y - b.y) * (s.x - b.x) > 0 != s_ab) return false;

    return true;
}

int main()
{
    Point origin{0, 0};

    Point p1{-340, 495};
    Point p2{-153, -910};
    Point p3{835, -947};

    std::cout << std::boolalpha << isInsideTriangle(p1, p2, p3, origin) << std::endl;

    return 0;
}