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Python wrappers around Cell-Tree 2D spatial index

Project Description

A module that provides the CellTree data structure as described by Garth and Joy in their 2010 paper

This implementation is 2D specific and includes some additions useful to answering one question:
_"What is the index of the polygon that contains this point?"_

Algorithm Notes

There are two major benefits to this algorithm over other types of BVHs. First is that overlaps in volumes
bounded by nodes do not create duplicates, decreasing the memory footprint. Secondly, the tree is balanced
by splitting a node along the plane that minimizes a cost function that 'weighs' each half. The result is
a tree with no duplicates and that becomes increasingly balanced as the number of buckets used when building
the tree increases (though this linearly increases build time).

This is a 2D version of the algorithm that is oriented towards maximum lookup speed and immediate answer
checking. The basic CellTree does not hold enough information to give conclusive point-in-polygon answers;
the best it can do is provide the (short) list of cells that contain the point. Since a point can be within
the bounds of two different leaves, and it is very possible both children of a parent node will need to be
searched, implementing immediate point-in-polygon checks on each cell as they are encountered is highly
beneficial, as an early success will avoid all further tree traversal.

Usage Notes

The tree needs certain information to be built:
1. 'verts' - A 2xV numpy array containing x/y coordinates of the V vertices
2. 'faces' - A PxN numpy array containing N arrays of P indices of vertices that describe one 'face' or polygon of degree P
3. 'num_buckets' - The # of buckets desired. Must be >= 2 The default is 4. Values higher than 8 begin to provide diminishing returns.
4. 'cells\_per\_leaf' - The # of polygons per leaf node. The default is 2. Using 1 is possible, but doubles memory footprint for only slightly.
faster lookup. If memory is a concern, this value can be increased, but lookup performance will quickly be impacted

IMPORTANT: 'verts' and 'faces' MUST describe a _properly formed_ unstructed grid. Assume that degenerate (0 area) or
overlapping polygons WILL cause a build failure. If the construction of the tree causes a segfault, this is probably
the cause.
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