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[ascl:2107.022] Kd-match: Correspondences of objects between two catalogs through pattern matching

Kd-match matches stellar catalogs for which the transformation between the coordinate systems of the two catalogs is unknown and might include shearing. The code uses the ratio of sides as the invariant under a coordinate transformation and searches for several triangles with similar transformations by building quadrilaterals from sets of four objects in each catalog and calculating the ratio of areas of the triangles that comprise the quadrilaterals. The k-d tree accelerates this quadrilateral search dramatically and is significantly faster than the customary direct search over triangles.

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