class QuadTreeRTPartitioning extends QuadtreePartitioning
The class is used to build an R-tree over a random sample of another dataset and uses distance bounds to ensure efficient local kNN joins.
By calculating distance bounds and using circle range queries, it ensures that the subsets Si, containing all necessary points for accurate kNN results. The final union of local join results provides the complete kNN join result for the datasets R and S.
It generates List<List<Integer>> expandedPartitionedBoundaries based on the quad tree.
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        buildSTRTree(samples: List[Envelope], k: Int): STRtree
      
      
      This function is used to build the STR tree from the quad-tree built from the samples. This function is used to build the STR tree from the quad-tree built from the samples. It is used to expand the partitioned boundaries. - samples
- the samples 
- k
- the number of neighbor samples 
 
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-  def getMbrSpatialIndex(): STRtree
-  def getMbrs(): HashMap[Integer, List[Envelope]]
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        getMinimalEnvelopeWidth(partitionMBRs: List[QuadRectangle]): Double
      
      
      This function is used to calculate the minimal envelope width of the partitioned MBRs. 
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        getPartitionTree(): StandardQuadTree[_]
      
      
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-  def processPartitions(partitionMBRs: List[QuadRectangle], mbrs: Map[Integer, List[Envelope]], k: Int, sampleTree: STRtree, geometryFactory: GeometryFactory): Unit
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