RTree2D is a 2D immutable R-tree with STR (Sort-Tile-Recursive) packing for ultra-fast nearest and intersection queries.

Main our requirements was:

• efficiency - we wanted the R-Tree to be able to search through millions of entries efficiently even in case of highly overlapped entries, also, we needed to be able to quickly rebuild R-tries with a per minute rate producing minimum pressure on GC
• immutability - different threads needed to be able to work with the same R-tree without problems, at the same time some thread can build a new version of the R-tree reusing immutable entries from the previous version

To archive these goals we have used:

• STR packing that is a one of the most efficient packing method which produces balanced R-tree
• a memory representation and access patterns to it which are aware of a cache hierarchy of contemporary CPUs
• an efficient TimSort version of merge sorting from Java which minimize access to memory during packing
• efficient implementations of nearest and range search functions with minimum of virtual calls and allocations

Add the library to a dependency list:

libraryDependencies += "com.github.plokhotnyuk.rtree2d" %% "rtree2d-core" % "0.11.13"

Entries of R-tree are represented by RTreeEntry instances which contains payload and 4 coordinates of the minimum bounding rectangle (MBR) for it.

Add import, create entries, build an R-tree from them, and use it for search a nearest entry or search intersections by point or rectangle requests:

import com.github.plokhotnyuk.rtree2d.core._                                                         
import EuclideanPlane._                                                                  
                                                                                         
val box1 = entry(1.0f, 1.0f, 2.0f, 2.0f, "Box 1")                                        
val box2 = entry(2.0f, 2.0f, 3.0f, 3.0f, "Box 2")                                        
val entries = Seq(box1, box2)                                                            
                                                                                         
val rtree = RTree(entries)                                                               
                                                                                         
assert(rtree.entries == entries)                                                         
assert(rtree.nearestOption(0.0f, 0.0f) == Some(box1))                      
assert(rtree.nearestOption(0.0f, 0.0f, maxDist = 1.0f) == None)                          
assert(rtree.nearestK(0.0f, 0.0f, k = 1) == Seq(box1))                     
assert(rtree.nearestK(0.0f, 0.0f, k = 2, maxDist = 10f) == Seq(box2, box1))  
assert(rtree.searchAll(0.0f, 0.0f) == Nil)                                               
assert(rtree.searchAll(1.5f, 1.5f) == Seq(box1))                                         
assert(rtree.searchAll(2.5f, 2.5f) == Seq(box2))                                         
assert(rtree.searchAll(2.0f, 2.0f) == Seq(box1, box2))                                   
assert(rtree.searchAll(2.5f, 2.5f, 3.5f, 3.5f) == Seq(box2))                             
assert(rtree.searchAll(1.5f, 1.5f, 2.5f, 2.5f).forall(entries.contains))                 

RTree2D can be used for indexing spherical coordinates, where X-axis is used for latitudes, and Y-axis for longitudes in degrees. Result distances are in kilometers:

import com.github.plokhotnyuk.rtree2d.core._
import SphericalEarth._

val city1 = entry(50.0614f, 19.9383f, "Kraków")
val city2 = entry(50.4500f, 30.5233f, "Kyiv")
val entries = Seq(city1, city2)

val rtree = RTree(entries, nodeCapacity = 4/* the best capacity for nearest queries for spherical geometry */)

assert(rtree.entries == entries)
assert(rtree.nearestOption(0.0f, 0.0f) == Some(city1))
assert(rtree.nearestOption(50f, 20f, maxDist = 1.0f) == None)
assert(rtree.nearestK(50f, 20f, k = 1) == Seq(city1))
assert(rtree.nearestK(50f, 20f, k = 2, maxDist = 1000f) == Seq(city2, city1))
assert(rtree.searchAll(50f, 30f, 51f, 31f) == Seq(city2))
assert(rtree.searchAll(0f, -180f, 90f, 180f).forall(entries.contains))

Precision of 32-bit float number allows to locate points with a maximum error ±1 meter at anti-meridian.

Used spherical model of the Earth with the Mean radius and Haversine formula allow to get ±0.3% accuracy in calculation of distances comparing with Vincenty’s formulae on an oblate spheroid model.

Please, check out Scala docs in sources and tests for other functions which allows filtering or accumulating found entries without allocations.

Charts below are latest results of benchmarks which compare RTree2D with Archery, David Monten's rtree, and JTS libraries on the following environment: Intel® Core™ i9-11900H CPU @ 2.5GHz (max 4.9GHz), RAM 32Gb DDR4-3200, Ubuntu 22.04, Oracle JDK 17.

Main metric tested by benchmarks is an execution time in nanoseconds. So lesser values are better. Please, check out the Run benchmarks section bellow how to test other metrics like allocations in bytes or number of some CPU events.

Benchmarks have the following parameters:

• geometry to switch geometry between plane and spherical (currently available only for the RTree2D library)
• nearestMax a maximum number of entries to return for nearest query
• nodeCapacity a maximum number of children nodes (BEWARE: Archery use hard coded 50 for limiting a number of children nodes)
• overlap is a size of entries relative to interval between them
• partToUpdate a part of RTree to update
• rectSize is a size of rectangle request relative to interval between points
• shuffle is a flag to turn on/off shuffling of entries before R-tree building
• size is a number of entries in the R-tree

The apply benchmark tests building of R-tries from a sequence of entires.

The nearest benchmark tests search an entry of the R-tree that is nearest to the specified point.

The nearestK benchmark tests search up to 10 entries in the R-tree that are nearest to the specified point.

The searchByPoint benchmark tests requests that search entries with intersects with the specified point.

The searchByRectangle benchmark tests requests that search entries with intersects with the specified rectangle that can intersect with up to 100 entries.

The entries benchmark tests returning of all entries that are indexed in the R-tree.

The update benchmark tests rebuild of R-tree with removing of +10% entries and adding of +10% another entries to it.

Charts with their results are available in subdirectories (each for different value of overlap parameter) of the docs directory.

To compile, run tests, check coverage for different Scala versions use a command:

sbt clean +test
sbt clean coverage test coverageReport mimaReportBinaryIssues

Benchmarks are developed in the separated module using Sbt plugin for JMH tool.

Feel free to modify benchmarks and check how it works with your data, JDK, and Scala versions.

To see throughput with allocation rate run benchmarks with GC profiler using the following command:

sbt -java-home /usr/lib/jvm/jdk-17 clean 'rtree2d-benchmark/jmh:run -prof gc -rf json -rff rtries.json .*'

It will save benchmark report in rtree2d-benchmark/rtries.json file.

Results that are stored in JSON can be easy plotted in JMH Visualizer by drugging & dropping of your file(s) to the drop zone or using the source or sources parameters with an HTTP link to your file(s) in the URLs: http://jmh.morethan.io/?source=<link to json file> or http://jmh.morethan.io/?sources=<link to json file1>,<link to json file2>.

Also, there is an ability to run benchmarks and visualize results with a charts command. It adds -rf and -rff options to all passes options and supply them to jmh:run task, then group results per benchmark and plot main score series to separated images. Here is an example how it can be called for specified version of JVM, value of the overlap parameter, and patterns of benchmark names:

sbt -java-home /usr/lib/jvm/zulu-17 clean 'charts -p overlap=1 -p rectSize=10 -p nearestMax=10 -p nodeCapacity=16 -p partToUpdate=0.1 -p geometry=plane .*'

Results will be places in a cross-build suffixed subdirectory of the benchmark/target directory in *.png files (one file with a chart for each benchmark):

$ ls rtree2d-benchmark/target/scala-2.12/*.png

rtree2d-benchmark/target/scala-2.12/apply[geometry=plane,nearestMax=10,nodeCapacity=16,overlap=1,partToUpdate=0.1,rectSize=10].png
...
rtree2d-benchmark/target/scala-2.12/searchByRectangle[geometry=plane,nearestMax=10,nodeCapacity=16,overlap=1,partToUpdate=0.1,rectSize=10].png

For testing of RTree2D with spherical geometry and different node capacities use the following command (chart files will be placed in the same directory as above):

sbt -java-home /usr/lib/jvm/zulu-17 clean 'charts -p overlap=1 -p rectSize=10 -p nearestMax=10 -p nodeCapacity=4,8,16 -p partToUpdate=0.1 -p geometry=spherical RTree2D.*'

Publish to local Ivy repo:

sbt +publishLocal

Publish to local Maven repo:

sbt +publishM2

For version numbering use Recommended Versioning Scheme that is used in the Scala ecosystem.

Double check binary and source compatibility, including behavior, and release using the following command (credentials are required):

sbt -java-home /usr/lib/jvm/jdk-8 -J-Xmx8g clean release

Do not push changes to github until promoted artifacts for the new version are not available for download on Maven Central Repository to avoid binary compatibility check failures in triggered Travis CI builds.