signed triangle area / rotation direction

signed_area.cxx

#include <iostream>
#include <iomanip>

struct point_t
{
    using coord_t = int;
    coord_t x;
    coord_t y;
};

constexpr auto null_coord = point_t::coord_t{};

auto operator-(const point_t& a, const point_t& b)
{
    return point_t{a.x - b.x, a.y - b.y};
}

/*
 *         B(b.x, b.y)
 *        /
 *  (0, 0)--A(a.x, a.y)
 *
 * |a c|
 * |   | = a*d - b*c
 * |b d|
 *
 *         |a.x a.y|
 * a ^ b = |       | = a.x * b.y - b.x * a.y
 *         |b.x b.y|
 */
auto signed_area(const point_t& a, const point_t& b)
{
    return a.x * b.y - b.x * a.y;
}

/*
 *             B(b.x, b.y)
 *            /
 * (c.x, c.y)C--A(a.x, a.y)
 */
auto signed_area(const point_t& a, const point_t& b, const point_t& c)
{
    return signed_area(a - c, b - c);
}

/* clockwise:
 *
 *  A --> B
 *   \   /
 *    \ /
 *     C
 */
auto is_cw_rotation(const point_t& a, const point_t& b, const point_t& c)
{
    return signed_area(a, b, c) < null_coord;
}

/* counter clockwise:
 *
 *  B <-- A
 *   \   /
 *    \ /
 *     C
 */
auto is_ccw_rotation(const point_t& a, const point_t& b, const point_t& c)
{
    return signed_area(a, b, c) > null_coord;
}

int main() {
    point_t a = {1, 2};
    point_t b = {2, 1};
    point_t c = {3, 3};

    std::cout << std::setw(5);
    std::cout << "-   :" << std::setw(5)
              << signed_area(a, b) << std::endl;
    std::cout << "+   :" << std::setw(5)
              << signed_area(b, a) << std::endl;
    std::cout << "ccw :" << std::setw(5) << std::boolalpha
              << is_ccw_rotation(a, b, c) << std::endl;
    std::cout << "ccw :" << std::setw(5) << std::boolalpha
              << is_ccw_rotation(b, a, c) << std::endl;
    return 0;
}