Intersection tests (AABB and SAT)

#include <cmath>

//AABB intersection test
bool isColliding(const Entity& lhs, const Entity& rhs) {
    SDL_assert(&lhs != &rhs);
    return !(lhs._x + lhs._width < rhs._x ||
        rhs._x + rhs._width < lhs._x ||
        lhs._y + lhs._height < rhs._y ||
        rhs._y + rhs._height < lhs._y);
}

//SAT intersection test. http://www.metanetsoftware.com/technique/tutorialA.html
//Many thanks to Jerry Jonsson and Tommi Lipponen at Uppsala University, GAME,
//for the original implementation of this function: http://pastebin.com/cbJWTfb9
bool getOverlap(const Entity& lhs, const Entity& rhs, int& overlapX, int& overlapY) {
    SDL_assert(&lhs != &rhs);
    overlapX = 0;
    overlapY = 0;
    int centerDeltaX = static_cast<int>(lhs.centerX() - rhs.centerX());
    int halfWidths = (lhs._width + rhs._width) / 2;

    if (std::abs(centerDeltaX) > halfWidths) return false; //no overlap on x == no collision

    int centerDeltaY = static_cast<int>(lhs.centerY() - rhs.centerY());
    int halfHeights = (lhs._height + rhs._height) / 2;

    if (std::abs(centerDeltaY) > halfHeights) return false; //no overlap on y == no collision

    int dx = halfWidths - std::abs(centerDeltaX); //overlap on x
    int dy = halfHeights - std::abs(centerDeltaY); //overlap on y
    if (dy < dx) {
        overlapY = (centerDeltaY < 0) ? -dy : dy;
    } else if (dy > dx) {
        overlapX = (centerDeltaX < 0) ? -dx : dx;
    } else {
        overlapX = (centerDeltaX < 0) ? -dx : dx;
        overlapY = (centerDeltaY < 0) ? -dy : dy;
    }
    return true;
}