rtree

README

rtree

This package provides an in-memory R-Tree implementation for Go. It's designed for Tile38 and is optimized for fast rect inserts and replacements.

Usage

Installing

To start using rtree, install Go and run go get:

$ go get -u github.com/tidwall/rtree

Basic operations

// create a 2D RTree
var tr rtree.RTree

// insert a point
tr.Insert([2]float64{-112.0078, 33.4373}, [2]float64{-112.0078, 33.4373}, "PHX")

// insert a rect
tr.Insert([2]float64{10, 10}, [2]float64{20, 20}, "rect")

// search 
tr.Search([2]float64{-112.1, 33.4}, [2]float64{-112.0, 33.5}, 
 	func(min, max [2]float64, data interface{}) bool {
		println(data.(string)) // prints "PHX"
	},
)

// delete 
tr.Delete([2]float64{-112.0078, 33.4373}, [2]float64{-112.0078, 33.4373}, "PHX")

Support for Generics (Go 1.18+)

// create a 2D RTree
var tr rtree.Generic[string]

// insert a point
tr.Insert([2]float64{-112.0078, 33.4373}, [2]float64{-112.0078, 33.4373}, "PHX")

// insert a rect
tr.Insert([2]float64{10, 10}, [2]float64{20, 20}, "rect")

// search 
tr.Search([2]float64{-112.1, 33.4}, [2]float64{-112.0, 33.5}, 
 	func(min, max [2]float64, data string) bool {
		println(data) // prints "PHX"
	},
)

// delete 
tr.Delete([2]float64{-112.0078, 33.4373}, [2]float64{-112.0078, 33.4373}, "PHX")

Algorithms

This implementation is a variant of the original paper:
R-TREES. A DYNAMIC INDEX STRUCTURE FOR SPATIAL SEARCHING

Inserting

Similar to the original algorithm. From the root to the leaf, the rects which will incur the least enlargment are chosen. Ties go to rects with the smallest area.

Added to this implementation: when a rect does not incur any enlargement at all, it's chosen immediately and without further checks on other rects in the same node. This make point insertion faster.

Deleting

Same as the original algorithm. A target rect is deleted directly. When the number of children in a rect falls below it's minumum entries, it is removed from the tree and it's items are re-inserted.

Searching

Same as the original algorithm.

Splitting

This is a custom algorithm. It attempts to minimize intensive operations such as pre-sorting the children and comparing overlaps & area sizes. The desire is to do simple single axis distance calculations each child only once, with a target 50/50 chance that the child might be moved in-memory.

When a rect has reached it's max number of entries it's largest axis is calculated and the rect is split into two smaller rects, named left and right. Each child rects is then evaluated to determine which smaller rect it should be placed into. Two values, min-dist and max-dist, are calcuated for each child.

• min-dist is the distance from the parent's minumum value of it's largest axis to the child's minumum value of the parent largest axis.
• max-dist is the distance from the parent's maximum value of it's largest axis to the child's maximum value of the parent largest axis.

When the min-dist is less than max-dist then the child is placed into the left rect. When the max-dist is less than min-dist then the child is placed into the right rect. When the min-dist is equal to max-dist then the child is placed into an equal bucket until all of the children are evaluated. Each equal rect is then one-by-one placed in either left or right, whichever has less children.

Finally, sort all the rects in the parent node of the split rect by their minimum x value.

License

rtree source code is available under the MIT License.

Documentation

Index

• type Generic
  • func (tr *Generic[T]) Bounds() (min, max [2]float64)
  • func (tr *Generic[T]) Children(parent interface{}, reuse []child.Child) []child.Child
  • func (tr *Generic[T]) Delete(min, max [2]float64, data T)
  • func (tr *Generic[T]) Insert(min, max [2]float64, value T)
  • func (tr *Generic[T]) Len() int
  • func (tr *Generic[T]) Replace(oldMin, oldMax [2]float64, oldData T, newMin, newMax [2]float64, newData T)
  • func (tr *Generic[T]) Scan(iter func(min, max [2]float64, data T) bool)
  • func (tr *Generic[T]) Search(min, max [2]float64, iter func(min, max [2]float64, value T) bool)
• type RTree
  • func (tr *RTree) Bounds() (min, max [2]float64)
  • func (tr *RTree) Children(parent interface{}, reuse []child.Child) (children []child.Child)
  • func (tr *RTree) Delete(min, max [2]float64, data interface{})
  • func (tr *RTree) Insert(min, max [2]float64, data interface{})
  • func (tr *RTree) Len() int
  • func (tr *RTree) Replace(oldMin, oldMax [2]float64, oldData interface{}, newMin, newMax [2]float64, ...)
  • func (tr *RTree) Scan(iter func(min, max [2]float64, data interface{}) bool)
  • func (tr *RTree) Search(min, max [2]float64, iter func(min, max [2]float64, data interface{}) bool)

Types

type Generic

type Generic[T any] struct {
	// contains filtered or unexported fields
}

func (*Generic[T]) Bounds

func (tr *Generic[T]) Bounds() (min, max [2]float64)

Bounds returns the minimum bounding rect

func (*Generic[T]) Children

func (tr *Generic[T]) Children(
	parent interface{},
	reuse []child.Child,
) []child.Child

Children is a utility function that returns all children for parent node. If parent node is nil then the root nodes should be returned. The min, max, data, and items slices all must have the same lengths. And, each element from all slices must be associated. Returns true for `items` when the the item at the leaf level. The reuse buffers are empty length slices that can optionally be used to avoid extra allocations.

func (*Generic[T]) Delete

func (tr *Generic[T]) Delete(min, max [2]float64, data T)

Delete data from tree

func (*Generic[T]) Insert

func (tr *Generic[T]) Insert(min, max [2]float64, value T)

Insert data into tree

func (*Generic[T]) Len

func (tr *Generic[T]) Len() int

Len returns the number of items in tree

func (*Generic[T]) Replace

func (tr *Generic[T]) Replace(
	oldMin, oldMax [2]float64, oldData T,
	newMin, newMax [2]float64, newData T,
)

Replace an item. If the old item does not exist then the new item is not inserted.

func (*Generic[T]) Scan

func (tr *Generic[T]) Scan(iter func(min, max [2]float64, data T) bool)

Scan iterates through all data in tree.

func (*Generic[T]) Search

func (tr *Generic[T]) Search(
	min, max [2]float64,
	iter func(min, max [2]float64, value T) bool,
)

Search ...

type RTree

type RTree struct {
	// contains filtered or unexported fields
}

func (*RTree) Bounds

func (tr *RTree) Bounds() (min, max [2]float64)

Bounds returns the minimum bounding box

func (*RTree) Children

func (tr *RTree) Children(parent interface{}, reuse []child.Child) (children []child.Child)

Children returns all children for parent node. If parent node is nil then the root nodes should be returned. The reuse buffer is an empty length slice that can optionally be used to avoid extra allocations.

func (*RTree) Delete

func (tr *RTree) Delete(min, max [2]float64, data interface{})

Delete an item from the structure

func (*RTree) Insert

func (tr *RTree) Insert(min, max [2]float64, data interface{})

Insert an item into the structure

func (*RTree) Len

func (tr *RTree) Len() int

Len returns the number of items in tree

func (*RTree) Replace

func (tr *RTree) Replace(
	oldMin, oldMax [2]float64, oldData interface{},
	newMin, newMax [2]float64, newData interface{},
)

Replace an item in the structure. This is effectively just a Delete followed by an Insert. But for some structures it may be possible to optimize the operation to avoid multiple passes

func (*RTree) Scan

func (tr *RTree) Scan(iter func(min, max [2]float64, data interface{}) bool)

Scan iterates through all data in tree in no specified order.

func (*RTree) Search

func (tr *RTree) Search(
	min, max [2]float64,
	iter func(min, max [2]float64, data interface{}) bool,
)

Search the structure for items that intersects the rect param