Bin (computational geometry)

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In computational geometry, the bin is a data structure that allows efficient region queries. Each time a data point falls into a bin, the frequency of that bin is increased by one.^[1]

For example, if there are some axis-aligned rectangles on a 2D plane, the structure can answer the question, "Given a query rectangle, what are the rectangles intersecting it?" In the example in the top figure, A, B, C, D, E and F are existing rectangles, so the query with the rectangle Q should return C, D, E and F, if we define all rectangles as closed intervals.

The data structure partitions a region of the 2D plane into uniform-sized bins. The bounding box of the bins encloses all candidate rectangles to be queried. All the bins are arranged in a 2D array. All the candidates are represented also as 2D arrays. The size of a candidate's array is the number of bins it intersects.

For example, in the top figure, candidate B has 6 elements arranged in a 3 row by 2 column array because it intersects 6 bins in such an arrangement. Each bin contains the head of a singly linked list. If a candidate intersects a bin, it is chained to the bin's linked list. Each element in a candidate's array is a link node in the corresponding bin's linked list.