How to reduce set of points?

How to reduce set of points?

I have a ordered list of points(lat,long) on a route. I have a ordered
list of stops (lat,long). Let's say I have 1000 points and 20 stops. I
would like to reduce the 1000 points to something like 100 depending upon
which points are more relevant for the route. Like points which induce
turns for example.
One way I think I can do this is to cluster around stops and choose points
maybe at random. But it still does not seem effective to me. Any ideas?