Question

How can I detect when a 2D moving object has crossed its own path?

I store the path as an array of points based on the plane’s previous positions.

Pseudo-code or any programming language can be used to describe a solution.

Here’s my code I’ve tried already – it detects a full 360 loop. I think I need a different approach.

    CGFloat angleDiff = angleCurr - lastAngleRecorded;
    lastAngleRecorded = angleCurr;

    // Ensure -180 < angleDiff < 180
    angleDiff = angleDiff > M_PI ? angleDiff - (M_PI*2) : angleDiff;
    angleDiff = angleDiff < -M_PI ? angleDiff + (M_PI*2) : angleDiff;

    // Reset tracking of the loop of the plane's angle exceeds (turns too sharply) or falls below the limits

    if(fabsf(angleDiff) < angleDiffMinAllowed || fabsf(angleDiff) > angleDiffMaxAllowed) {
        if(++ringFaultCount >= ringFaultCountMax) {
            [self resetTracking];
            return;
        }
    }

    ringFaultCount = 0;

    // Add plane position to ring polygon
    [ringPoints addObject:[NSValue valueWithCGPoint: ccp(targetPlane.position.x, targetPlane.position.y)]];


    // Add angleDiff to angleTotal
    angleTotal += angleDiff;

    // Completed loop?
    if(fabsf(angleTotal) >= M_PI * 2.f) {

        [self resetTracking];

        if(isRingJoined){
            CCLOG(@"%@ RING COMPLETE", NSStringFromSelector(_cmd));
        }

        return;
    }

Answer 1

I also had the problem, I solved it by making a straight line in a coordinate system:

y = mx+q±­tolerance

Let me explain:
The line is the tangent of the curve at the point you check if there is a collision this is the line the “aircraft” followed in that point.
The tolerance will make the line move a litlle bit up and also one a little bit down.
so you get 2 parralel lines witch can be seen as boundarys.
you also have to make a tolerance on the x-axis

The m is the direction of the line, its: tan(angle), the angle is the angle with the x-axis.

If all that is setup than you have to do this:

if(y_point < mx+q+tolerance && y_point> mx+q-tolerance && x_points > x-tolerance && x_point< x+tolerance
{
// some code
}