I have two set of points. One set defines the left lane and other set the right lane. And I also have another set of points(black and purple below) and I need to find points in third set which are outside these two lanes. From the below figure I need to extract all purple points.
If they are two straight lines I can just find the points on right side of right line and on left side of left line to filter these points. Since lanes are not straight I cannot use this approach. Is there a way I can filter the points outsides these lanes efficiently?
It looks like a computational geometry problem.
Make a triangle with the closest points in Left set. check the points x coordinates. If they are < that given point p. then p is on the right side of "those two points", otherwise p is on the left of the left.
Do the same with Right set.
However this may "sometimes" work if $Max[L_{x}] < Min[R_{x}]$. If there is a knot then the problem has to be redefined.
Sometimes it will give wrong results if $\exists t\in L \;: q_{x}<t_{x}<p_{x} \;and\; t_{y}>p_{y} \;and\; q_{y}>r_{y} $ and q,r are the closest points to p to make a triangle