Check if user is near route checkpoint with GPS - geolocation

Question

Here's the situation:
I have a predetermined GPS route that the user will run. The route has some checkpoints and the user should pass near all of them (think of them as a racing game checkpoint, that prevents the user from taking shortcuts). I need to ensure that the user passes through all the checkpoints.
I want to determine an area that will be considered inside a checkpoint's radius, but I don't want it to be just a radial area, it should be an area taking into consideration the form of the path.
Didn't understand it? Neither did I. Look at this poorly drawn image to understand it better:
The black lines represents the pre-determined path, the blue ball is the checkpoint and the blue polygon is the wanted area. The green line is a more precise user, and the red line is a less accurate user (a drunk guy driving maybe? lol). Both lines should be inside the polygon, but a user who skips totally the route shouldn't.
I already saw somewhere here a function to check is the user is inside a polygon like this, but I need to know how to calculate the polygon.
Any suggestions?
EDIT:
I'm considering using the simple distanceTo() function to just draw an imaginary circle and check if the user is there. That's good because is so much simple to implement and understand, and bad because to make sure the most erronic user passes whithin the checkpoint I would need a big radius, making the correct user enter the checkpoint area sooner than expected.
And just so you guys understand the situation better, this is for an app that is supposed to be used in traffic (car or bus), and the checkpoints should be landmarks or spots that divides your route, for example, somewhere where traffic jam starts or stops.

Answer 1

You could just check the distance between the two, assuming you know the GeoLocation of the checkpoint.
Use the distanceTo function and setup a threshold of however many meters the user needs to be from the checkpoint to continue on.
Edit
Since you want to avoid distanceTo, here is a small function I wrote a while back to check if a point is in a polygon:
public boolean PIP(Point point, List<Point> polygon){
boolean nodepolarity=false;
int sides = polygon.size();
int j = sides -1;
for(int i=0;i<sides;i++){
if((polygon.get(i).y<point.y && polygon.get(j).y>=point.y) ||(polygon.get(j).y<point.y && polygon.get(i).y>=point.y)){
if (polygon.get(i).x+(point.y-polygon.get(i).y)/(polygon.get(j).y-polygon.get(i).y)*(polygon.get(j).x-polygon.get(i).x)<point.x) {
nodepolarity=!nodepolarity;
}
}
j=i;
}
return nodepolarity; //FALSE=OUTSIDE, TRUE=INSIDE
}
List<Point> polygon is a list of the points that make up a polygon.
This uses the Ray casting algorithm to determine how many intersections a ray makes through the polygon.
All you would need to do is create the 'boundary' around the area you need with GeoPoints being translated into pixels using the toPixels method.
Store those points into a List<> of points, and you should be all set.

Answer 2

check a few algos to do this in the link below
http://geospatialpython.com/2011/01/point-in-polygon.html

Answer 3

I know this is an old question, but maybe it would be useful for someone.
This is a simpler method, with much less computation needed. This would not trigger the first time the user comes inside the threshold area, it only gets the closest point where the user has passed near the checkpoint AND (s)he has come close enough.
The idea is to maintain a 3 item list of distances for every checkpoint, with the last three distances in it (so it would be [d(t), d(t-1), d(t-2)]). This list should be rotated on every distance calculation.
If on any distance calculation the previous d(t-1) distance is smaller than the current one d(t) and bigger than the preceding d(t-2), then the moving point has passed the checkpoint. Whether this was a real passing, or it was only a glitch, can be decided by checking the actual distance d(t-1).
private long DISTANCE_THRESHOLD = 2000;
private Checkpoint calculateCheckpoint(Map<Checkpoint, List<Double>> checkpointDistances)
{
Map<Checkpoint, Double> candidates = new LinkedHashMap<Checkpoint, Double>();
for (Checkpoint checkpoint: checkpointDistances.keySet())
{
List<Double> distances = checkpointDistances.get(checkpoint);
if (distances == null || distances.size() < 3)
continue;
if (distances.get(0) > distances.get(1) && distances.get(1) < distances.get(2) && distances.get(1) < (DISTANCE_THRESHOLD)) //TODO: make this depend on current speed
candidates.put(checkpoint, distances.get(1));
}
List<Entry<Checkpoint, Double>> list = new LinkedList<Entry<Checkpoint,Double>>(candidates.entrySet());
Collections.sort(list, comp);
if (list.size() > 0)
return list.get(0).getKey();
else
return null;
}
Comparator<Entry<Checkpoint, Double>> comp = new Comparator<Entry<Checkpoint,Double>>()
{
#Override
public int compare(Entry<Checkpoint, Double> o1, Entry<Checkpoint, Double> o2)
{
return o1.getValue().compareTo(o2.getValue());
}
};
The function gets one parameter - a Map<Checkpoint, List<Double>> with the checkpoints and the list of the last three distances. It outputs the closest Checkpoint passed or null (if there were none).
The DISTANCE_THRESHOLD should be chosen wisely.
The Comparator is just to be able to sort the Checkpoints based on their distance to the user to get the closest one.
Naturally this has some minor flaws, e.g. if the moving point is moving criss-cross, or the error movement from GPS precision is commensurable with the actual speed of the user, than this would give multiple pass marks, but this would hit almost any algorithm.