Even when no spatial index is available, this comes at additional cost in managing the heap.

This usually involves using database techniques such as spatial indices.

These sets are indexed via a Spatial index which allow for group searching.

Spatial indexes are used to allow searching on both two and three dimensional coordinates spaces.

In the case of Euclidean space this approach is known as spatial index or spatial access methods.

Instead, spatial databases use a spatial index to speed up database operations.

This is a binary spatial index file, which is used only by Esri software.

When a spatial index is available, it does however play a practical role when it comes to complexity.

Spatial indices are well suited for handling the complexity of Grid resource queries.

Common spatial index methods include:

Given a spatial index that grants a neighborhood query in runtime, an overall runtime of is obtained.

Grid (spatial index)

Spatial index structures:

Ingres (no valid spatial index)

Shapefile spatial index format ()

Following Marinos, he assigned coordinates to all the places and geographic features he knew, in a Grid (spatial index) that spanned the globe.

Spatial indices are used by spatial databases (databases which store information related to objects in space) to optimize spatial queries.

R-tree-over-GiST (Generalised Search Tree) spatial indexes for high speed spatial querying.

MAP file is saved by MapInfo Professional its objects are sorted into a storage sequence based on an R-tree spatial index.

The spatial indices are raised and lowered using the spatial metric and its inverse : and , , where is the Kronecker delta.

PolygonLib, C++ and COM libraries for 2D polygons (optimized for large polygon sets, built-in spatial indices).

Prior versions of the format required a spatial index file (SIF), with an optional key index file (KIF) to speed access to the file.

In practice, construction of grid-based spatial indices entails allocation of relevant objects to their position or positions in the grid, then creating an index of object identifiers vs. grid cell identifiers for rapid access.

Most references adopt notation in which four dimensional tensors are written in abstract index notation, and that Greek indices are spacetime indices taking values (0, 1, 2, 3) and Latin indices are spatial indices taking values (1, 2, 3).

A grid-based spatial index has the advantage that the structure of the index can be created first, and data added on an ongoing basis without requiring any change to the index structure; indeed, if a common grid is used by disparate data collecting and indexing activities, such indices can easily be merged from a variety of sources.