grid-tree

Pixel quadtrees and voxel octrees.

Store any type in an OctreeI32, OctreeU32, QuadtreeI32, or QuadtreeU32, all of which are specific instances of the generic Tree. A Tree represents a map from (Level, Integer Coordinates) to T. Thus it is useful for storing pixel or voxel data with level-of-detail. The tree also requires that if a node slot is occupied (has data), then all ancestor slots are also filled.

Design Advantages

• Since a Tree has its own internal allocators, any pointers are completely local to the data structure. In principle, this makes it easy to clone the tree for e.g. uploading to a GPU (although we haven't tried it for ourselves).
• The level 0 allocator does not store pointers, only values. Pointer overhead at higher levels can be amortized using chunked data, i.e. [T; CHUNK_SIZE]. The alternative "pointerless" octrees take up less memory, but are also more complex to edit and traverse.
• By using a hash map of root nodes, the addressable space is not limited by the height of the tree, and it is not necessary to "translate" the octree as it follows a focal point.
• By having a very simple data layout, access using a NodePtr is simply an array lookup.
• The NodeEntry and Tree::child_entry APIs allow for very simple code that fills entire trees with a single visitor closure.
• By implementing VectorKey for a custom key type, the addressable range can be extended to coordinates of arbitrary precision.

Performance

This structure is optimized for iteration speed and spatial queries that benefit from a bounding volume hierarchy (like raycasting). Finding a single node by NodeKey starting from the root should be minimized as much as possible, so you might find it useful to cache NodePtrs or amortize the search with a full tree traversal. Memory usage is decent given the simplicity of the implementation, and the pointer overhead is easily amortized by using dense chunk values.

• random access with NodeKey: O(depth)
• random access with NodePtr: O(1)
• iteration: O(nodes)
• memory usage per node:
  • level 0: size_of::<T>() bytes
  • level N > 0: size_of::<T>() + CHILDREN * 4 bytes
  • where CHILDREN=4 for a quadtree and CHILDREN=8 for an octree

License: MIT OR Apache-2.0