FA-70339 / Map projection transforms / Member archive

Seven-parameter Helmert datum shift: translation scaling · case 04

Z coordinates are off by the scale times the translation.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Input [X, Y, Z, tx, ty, tz, rx, ry, rz, s, convention] with metres, rotations in arc-seconds and scale in ppm. Rotations are converted to radians; for "coordinate_frame" they are negated, for "position_vector" used as is. m = 1 + s*1e-6. X' = tx + m(X - rz Y + ry Z); Y' = ty + m(rz X + Y - rx Z); Z' = tz + m(-ry X + rx Y + Z). Return [X', Y', Z'] rounded to 3 decimals.

Why this case matters

Datum transformations between national and global frames use these seven parameters; convention and unit slips cause metre-level offsets that pass casual inspection.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
control #3	`[-189556.8, 3352227.961, -2404422.459]`	`[-189556.8, 3352227.961, -2404422.458]`	Failed

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