I have a need to take a 2D graph of n points and reduce it the r points (where r is a specific number less than n). For example, I may have two datasets with slightly different number of total points, say 1021 and 1001 and I'd like to force both datasets to have 1000 points. I am aware of a couple of simplification algorithms: Lang Simplification and Douglas-Peucker. I have used Lang in a previous project with slightly different requirements.
The specific properties of the algorithm I am looking for is:
1) must preserve the shape of the line
2) must allow me reduce dataset to a specific number of points
3) is relatively fast
This post is a discussion of the merits of the different algorithms. I will post a second message for advice on implementations in Java or Groovy (why reinvent the wheel).
I am concerned about requirement 2 above. I am not an expert enough in these algorithms to know whether I can dictate the exact number of output points. The implementation of Lang that I've used took lookAhead, tolerance and the array of Points as input, so I don't see how to dictate the number of points in the output. This is a critical requirement of my current needs. Perhaps this is due to the specific implementation of Lang we had used, but I have not seen a lot of information on Lang on the web. Alternatively we could use Douglas-Peucker but again I am not sure if the number of points in the output can be specified.
I should add I am not an expert on these types of algorithms or any kind of math wiz, so I am looking for mere mortal type advice :) How do I satisfy requirements 1 and 2 above? I would sacrifice performance for the right solution.
You can find my C++ implementation and article on Douglas-Peucker simplification here and here. I also provide a modified version of the Douglas-Peucker simplification that allows you to specify the number of points of the resulting simplified line. It uses a priority queue as mentioned by 'Peter Taylor'. Its a lot slower though, so I don't know if it would satisfy the 'is relatively fast' requirement.
I'm planning on providing an implementation for Lang simplification (and several others). Currently I don't see any easy way how to adjust Lang to reduce to a fixed point count. If you could live with a less strict requirement: 'must allow me reduce dataset to an approximate number of points', then you could use an iterative approach. Guess an initial value for lookahead: point count / desired point count. Then slowly increase the lookahead until you approximately hit the desired point count.
I hope this helps.
p.s.: I just remembered something, you could also try the Visvalingam-Whyatt algorithm. In short: -compute the triangle area for each point with its direct neighbors -sort these areas -remove the point with the smallest area -update the area of its neighbors -resort -continue until n points remain