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
How to use
Add the library to a dependency list:
libraryDependencies += "com.github.plokhotnyuk.rtree2d" %% "rtree2d-core" % "0.11.12"
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.
How it works
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:
geometryto switch geometry between
spherical(currently available only for the RTree2D library)
nearestMaxa maximum number of entries to return for nearest query
nodeCapacitya maximum number of children nodes (BEWARE: Archery use hard coded 50 for limiting a number of children nodes)
overlapis a size of entries relative to interval between them
partToUpdatea part of RTree to update
rectSizeis a size of rectangle request relative to interval between points
shuffleis a flag to turn on/off shuffling of entries before R-tree building
sizeis a number of entries in the R-tree
apply benchmark tests building of R-tries from a sequence of entires.
nearest benchmark tests search an entry of the R-tree that is nearest to the specified point.
nearestK benchmark tests search up to 10 entries in the R-tree that are nearest to the specified point.
searchByPoint benchmark tests requests that search entries with intersects with the specified point.
searchByRectangle benchmark tests requests that search entries with intersects with the specified rectangle that
can intersect with up to 100 entries.
entries benchmark tests returning of all entries that are indexed in the R-tree.
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.
How to contribute
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/zulu-17 clean 'rtree2d-benchmark/jmh:run -prof gc -rf json -rff rtries.json .*'
It will save benchmark report in
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
sources parameters with an HTTP link to your file(s) in the
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
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
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
(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:
Publish to local Maven repo:
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):
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.