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, value interface{}) bool {
println(value.(string)) // 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

Same as 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.

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.

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.

License

rtree source code is available under the MIT License.