Detect when a 2D moving object crosses its own path? - math

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
}