  We present a robust and fast algorithm for performing astrometry and source
cross-identification on two dimensional point lists, such as between a
catalogue and an astronomical image, or between two images. The method is based
on minimal assumptions: the lists can be rotated, magnified and inverted with
respect to each other in an arbitrary way. The algorithm is tailored to work
efficiently on wide fields with large number of sources and significant
non-linear distortions, as long as the distortions can be approximated with
linear transformations locally, over the scale-length of the average distance
between the points. The procedure is based on symmetric point matching in a
newly defined continuous triangle space that consists of triangles generated by
an extended Delaunay triangulation. Our software implementation performed at
the 99.995% success rate on ~260,000 frames taken by the HATNet project.
