RTree

RTree is a high-performance .NET library for 2D spatial indexing of points and rectangles. It's based on an optimized R-tree data structure with bulk insertion support. Compatible with Unity and .Net 3.5

Spatial index is a special data structure for points and rectangles that allows you to perform queries like "all items within this bounding box" very efficiently (e.g. hundreds of times faster than looping over all items). It's most commonly used in maps and data visualizations.

This code has been copied over from the C# RBush library. which in turn was copied over from the Javascript RBush library.

Usage

Creating a Tree

First, define the data item class to implement ISpatialData, which requires that the class expose the Envelope property. Then the class can be used as such:

var tree = new RBush<Point>()

An optional argument (maxEntries: ) to the constructor defines the maximum number of entries in a tree node. 9 (used by default) is a reasonable choice for most applications. Higher value means faster insertion and slower search, and vice versa.

var tree = new RBush<Point>(maxEntries: 16)

Adding Data

Insert an item with an extent:

var item = new Point(double minX, double minY, double maxX, double maxY);
tree.Insert(item);

or

Insert an item with a position:

var item = new Evnelope(float x, float y)
tree.Insert(item);

Removing Data

Remove a previously inserted item:

tree.Delete(item);

By default, RBush uses object.Equals() to select the item. If the item being passed in is not the same reference value, ensure that the class supports object.Equals() equality testing.

Remove all items:

tree.Clear();

Bulk-Inserting Data

Bulk-insert the given data into the tree:

var points = new List<Point>();
tree.BulkLoad(points);

Bulk insertion is usually ~2-3 times faster than inserting items one by one. After bulk loading (bulk insertion into an empty tree), subsequent query performance is also ~20-30% better.

Note that when you do bulk insertion into an existing tree, it bulk-loads the given data into a separate tree and inserts the smaller tree into the larger tree. This means that bulk insertion works very well for clustered data (where items in one update are close to each other), but makes query performance worse if the data is scattered.

Search

var result = tree.Search(
    new Envelope
    {
        MinX: 40,
        MinY: 20,
        MaxX: 80,
        MaxY: 70
    });

Returns an IEnumerable<T> of data items (points or rectangles) that the given bounding box intersects.

var allItems = tree.Search();

Returns all items of the tree.

Credit

This code (and most of this readme) has been adapted from the C# RBush library. Which in turn was adapted from a Javascript library called RBush. The only changes made were to adapt coding styles, preferences and to add compatibility and support for working in Unity game engine.

Algorithms Used

• single insertion: non-recursive R-tree insertion with overlap minimizing split routine from R*-tree (split is very effective in JS, while other R*-tree modifications like reinsertion on overflow and overlap minimizing subtree search are too slow and not worth it)
• single deletion: non-recursive R-tree deletion using depth-first tree traversal with free-at-empty strategy (entries in underflowed nodes are not reinserted, instead underflowed nodes are kept in the tree and deleted only when empty, which is a good compromise of query vs removal performance)
• bulk loading: OMT algorithm (Overlap Minimizing Top-down Bulk Loading) combined with Floyd�Rivest selection algorithm
• bulk insertion: STLT algorithm (Small-Tree-Large-Tree)
• search: standard non-recursive R-tree search

Papers

• R-trees: a Dynamic Index Structure For Spatial Searching
• The R*-tree: An Efficient and Robust Access Method for Points and Rectangles+
• OMT: Overlap Minimizing Top-down Bulk Loading Algorithm for R-tree
• Bulk Insertions into R-Trees Using the Small-Tree-Large-Tree Approach
• R-Trees: Theory and Applications (book)

Compatibility

R_Tree should run on any .NET system that supports .NET Framework 3.5 or later;