- the segments within a monotone chain never intersect each other
- the envelope of any contiguous subset of the segments in a monotone chain is equal to the envelope of the endpoints of the subset.
Property 2 allows an efficient binary search to be used to find the intersection points of two monotone chains. For many types of real-world data, these properties eliminate a large number of segment comparisons, producing substantial speed gains.
One of the goals of this implementation of MonotoneChains is to be as space and time efficient as possible. One design choice that aids this is that a MonotoneChain is based on a subarray of a list of points. This means that new arrays of points (potentially very large) do not have to be allocated.
MonotoneChains support the following kinds of queries:
- Envelope select: determine all the segments in the chain which intersect a given envelope
- Overlap: determine all the pairs of segments in two chains whose envelopes overlap
The monotone chain search algorithm attempts to optimize performance by not calling the overlap action on chain segments which it can determine do not overlap. However, it *may* call the overlap action on segments which do not actually interact. This saves on the overhead of checking intersection each time, since clients may be able to do this more efficiently.
||MonotoneChain||the search envelope.|
||MonotoneChainOverlapAction||the overlap action to execute on selected segments.|
The monotone chain search algorithm attempts to optimize performance by not calling the select action on chain segments which it can determine are not in the search envelope. However, it *may* call the select action on segments which do not intersect the search envelope. This saves on the overhead of checking envelope intersection each time, since clients may be able to do this more efficiently.
||Envelope||the search envelope.|
||MonotoneChainSelectAction||the select action to execute on selected segments.|