Sporadic Collision Detection

Question

I've been working on detecting collision between to object in my game. Right now everything tavels vertically, but would like to keep the option for other movement open. It's classic 2d vertical space shooter.

Right now I loop through every object, checking for collisions:

for(std::list<Object*>::iterator iter = mObjectList.begin(); iter != mObjectList.end();) {
    Object *m = (*iter);
    for(std::list<Object*>::iterator innerIter = ++iter; innerIter != mObjectList.end(); innerIter++ ) {
            Object *s = (*innerIter);

            if(m->getType() == s->getType()) {
                break;
            }

            if(m->checkCollision(s)) {
                m->onCollision(s);
                s->onCollision(m);
            }
        }
    }

Here is how I check for a collision:

bool checkCollision(Object *other) {
        float radius = mDiameter / 2.f;
        float theirRadius = other->getDiameter() / 2.f;
        Vector<float> ourMidPoint = getAbsoluteMidPoint();
        Vector<float> theirMidPoint = other->getAbsoluteMidPoint();

        // If the other object is in between our path on the y axis
        if(std::min(getAbsoluteMidPoint().y - radius, getPreviousAbsoluteMidPoint().y - radius) <= theirMidPoint.y &&
            theirMidPoint.y <= std::max(getAbsoluteMidPoint().y + radius, getPreviousAbsoluteMidPoint().y + radius)) {

                // Get the distance between the midpoints on the x axis
                float xd = abs(ourMidPoint.x - theirMidPoint.x);

                // If the distance between the two midpoints
                // is greater than both of their radii together
                // then they are too far away to collide
                if(xd > radius+theirRadius) {
                    return false;
                } else {
                    return true;
                }

        }
        return false;
}

The problem is it will randomly detect collisions correctly, but other times does not detect it at all. It's not the if statement breaking away from the object loop because the objects do have different types. The closer the object is to the top of the screen, the better chance it has of collision getting detected correctly. Closer to the bottom of the screen, the less chance it has of getting detected correctly or even at all. However, these situations don't always occur. The diameter for the objects are massive (10 and 20) to see if that was the problem, but it doesn't help much at all.

EDIT - Updated Code

bool checkCollision(Object *other) {
    float radius = mDiameter / 2.f;
    float theirRadius = other->getDiameter() / 2.f;
    Vector<float> ourMidPoint = getAbsoluteMidPoint();
    Vector<float> theirMidPoint = other->getAbsoluteMidPoint();

    // Find the distance between the two points from the center of the object
    float a = theirMidPoint.x - ourMidPoint.x;
    float b = theirMidPoint.y - ourMidPoint.y;

    // Find the hypotenues
    double c = (a*a)+(b*b);
    double radii = pow(radius+theirRadius, 2.f);

    // If the distance between the points is less than or equal to the radius
    // then the circles intersect
    if(c <= radii*radii) {
        return true;
    } else { 
        return false;
    }
}

Answer 1

Two circular objects collide when the distance between their centers is small enough. You can use the following code to check this:

double distanceSquared =
    pow(ourMidPoint.x - theirMidPoint.x, 2.0) +
    pow(ourMidPoint.x - theirMidPoint.x, 2.0);
bool haveCollided = (distanceSquared <= pow(radius + theirRadius, 2.0));

In order to check whether there was a collision between two points in time, you can check for collision at the start of the time interval and at the end of it; however, if the objects move very fast, the collision detection can fail (i guess you have encountered this problem for falling objects that have the fastest speed at the bottom of the screen).

The following might make the collision detection more reliable (though still not perfect). Suppose the objects move with constant speed; then, their position is a linear function of time:

our_x(t) = our_x0 + our_vx * t;
our_y(t) = our_y0 + our_vy * t;
their_x(t) = their_x0 + their_vx * t;
their_y(t) = their_y0 + their_vy * t;

Now you can define the (squared) distance between them as a quadratic function of time. Find at which time it assumes its minimum value (i.e. its derivative is 0); if this time belongs to current time interval, calculate the minimum value and check it for collision.

This must be enough to detect collisions almost perfectly; if your application works heavily with free-falling objects, you might want to refine the movement functions to be quadratic:

our_x(t) = our_x0 + our_v0x * t;
our_y(t) = our_y0 + our_v0y * t + g/2 * t^2;

Answer 2

This logic is wrong:

if(std::min(getAbsoluteMidPoint().y - radius, getPreviousAbsoluteMidPoint().y - radius) <= theirMidPoint.y &&
        theirMidPoint.y <= std::max(getAbsoluteMidPoint().y + radius, getPreviousAbsoluteMidPoint().y + radius))
{
  // then a collision is possible, check x
}

(The logic inside the braces is wrong too, but that should produce false positives, not false negatives.) Checking whether a collision has occurred during a time interval can be tricky; I'd suggest checking for a collision at the present time, and getting that to work first. When you check for a collision (now) you can't check x and y independently, you must look at the distance between the object centers.

EDIT:

The edited code is still not quite right.

// Find the hypotenues
double c = (a*a)+(b*b); // actual hypotenuse squared
double radii = pow(radius+theirRadius, 2.f); // critical hypotenuse squared

if(c <= radii*radii) { // now you compare a distance^2 to a distance^4
    return true; // collision
}

It should be either this:

double c2 = (a*a)+(b*b); // actual hypotenuse squared
double r2 = pow(radius+theirRadius, 2.f); // critical hypotenuse squared

if(c2 <= r2) {
    return true; // collision

}

or this:

double c2 = (a*a)+(b*b); // actual hypotenuse squared
double c = pow(c2, 0.5); // actual hypotenuse
double r = radius + theirRadius; // critical hypotenuse

if(c <= r) {
    return true; // collision

}

Answer 3

Your inner loop needs to start at mObjectList.begin() instead of iter.

The inner loop needs to iterate over the entire list otherwise you miss collision candidates the further you progress in the outer loop.