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class MonotoneChain extends AnyRef

Monotone Chains are a way of partitioning the segments of a linestring to allow for fast searching of intersections. They have the following properties:

  • 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 1 means that there is no need to test pairs of segments from within the same monotone chain for intersection.

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

This implementation of MonotoneChains uses the concept of internal iterators ({link MonotoneChainSelectAction} and {link MonotoneChainOverlapAction}) to return the results for queries. This has time and space advantages, since it is not necessary to build lists of instantiated objects to represent the segments returned by the query. Queries made in this manner are thread-safe.

MonotoneChains support being assigned an integer id value to provide a total ordering for a set of chains. This can be used during some kinds of processing to avoid redundant comparisons (i.e. by comparing only chains where the first id is less than the second).

Version

1.7

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Instance Constructors

  1. new MonotoneChain(pts: Array[Coordinate], start: Int, end: Int, context: Any)

Value Members

  1. final def !=(arg0: Any): Boolean
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  6. def computeOverlaps(mc: MonotoneChain, mco: MonotoneChainOverlapAction): Unit

    Determine all the line segments in two chains which may overlap, and process them.

    Determine all the line segments in two chains which may overlap, and process them.

    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.

    mco

    the overlap action to execute on selected segments

  7. val context: Any
  8. val end: Int
  9. final def eq(arg0: AnyRef): Boolean
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  11. def finalize(): Unit
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  12. final def getClass(): Class[_ <: AnyRef]
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  13. def getContext: Any

    Gets the user-defined context data value.

    Gets the user-defined context data value.

    return a data value

  14. def getCoordinates: Array[Coordinate]

    Return the subsequence of coordinates forming this chain.

    Return the subsequence of coordinates forming this chain. Allocates a new array to hold the Coordinates

  15. def getEndIndex: Int

    Gets the index of the end of the monotone chain in the underlying array of points.

    Gets the index of the end of the monotone chain in the underlying array of points.

    return the end index of the chain

  16. def getEnvelope: Envelope

    Gets the envelope of the chain.

    Gets the envelope of the chain.

    return the envelope of the chain

  17. def getId: Int

    Gets the id of this chain.

    Gets the id of this chain.

    return the id value

  18. def getLineSegment(index: Int, ls: LineSegment): Unit

    Gets the line segment starting at index

    Gets the line segment starting at index

    index

    index of segment

    ls

    line segment to extract into

  19. def getStartIndex: Int

    Gets the index of the start of the monotone chain in the underlying array of points.

    Gets the index of the start of the monotone chain in the underlying array of points.

    return the start index of the chain

  20. def hashCode(): Int
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  24. final def notifyAll(): Unit
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  25. var pts: Array[Coordinate]
  26. def select(searchEnv: Envelope, mcs: MonotoneChainSelectAction): Unit

    Determine all the line segments in the chain whose envelopes overlap the searchEnvelope, and process them.

    Determine all the line segments in the chain whose envelopes overlap the searchEnvelope, and process them.

    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.

    searchEnv

    the search envelope

    mcs

    the select action to execute on selected segments

  27. def setId(id: Int): Unit

    Sets the id of this chain.

    Sets the id of this chain. Useful for assigning an ordering to a set of chains, which can be used to avoid redundant processing.

    id

    an id value

  28. val start: Int
  29. final def synchronized[T0](arg0: => T0): T0
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