Module pattern 

The geometry shared by the index builder and the index solver: the 4-star pattern descriptor, its quantised hash key, the canonical vertex order that gives a star correspondence, and the tangent-plane projection.

The descriptor is the six pairwise distances of a quad, sorted, divided by the largest — the five ratios ASTAP’s quads use too (quads/). It is invariant to translation, rotation, scale and reflection, so one index entry serves both image parities. Unlike astrometry.net’s code space it does not say which star is which, so the vertices are put in a canonical order (ascending total distance to the other three), which both sides compute the same way; near-ties in that order are the one ambiguity, and orderings enumerates the alternatives on the image side. A wrong correspondence fails the affine shape check, so trying an extra ordering costs a few multiplications, never a false match.

Any change to BINS, descriptor, key or canonical changes which entries an index holds or how they hash, and must bump the format version in format.rs.

Structs

Tangent

A gnomonic tangent plane: its centre and local east and north unit vectors. Standard coordinates are radians, east and north positive.

Constants

BINS

Quantisation bins per descriptor dimension. A bin is 1/128 = 0.0078 wide, about the hinted solver’s default quad tolerance (0.007).

PROBE_EPS

Probe the neighbouring bin when a ratio lies within this distance of a bin edge. Measurement noise can only move a ratio across an edge it is already close to, so only those dimensions need a second probe: typically one to four keys per quad instead of 3⁵.

Functions

canonical

The canonical vertex order of a quad and its longest edge.

descriptor

The five sorted distance ratios of a quad, each in (0, 1].

fit_affine

Least-squares affine map q = A·p + t from points p to points q, returned as [a, b, c, d, e, f] with qx = a·px + b·py + c, qy = d·px + e·py + f. None when the points are collinear or fewer than three.

invert_affine

Invert an affine map; None if singular.

key

The descriptor’s home bucket: each ratio floored into one of BINS bins, packed eight bits per dimension, first ratio most significant.

orderings

The canonical order plus the alternatives that a near-tie makes possible: each adjacent pair whose totals differ by less than TIE_EPS (1.5 %) may be swapped. At most eight orders (three independent adjacent swaps).

probe_keys

Every key a measured descriptor could have had in the index: the home bucket, plus the neighbouring bin in any dimension within PROBE_EPS of an edge. Written into out, which is cleared first.

shape_error

How far an affine map is from a similarity (rotation + uniform scale, either parity): the larger of the column-length mismatch and the columns’ cosine. Zero for a perfect similarity.

unit

Unit vector of (ra, dec), radians.