Seven-parameter scale not divided by 1e6 shifts 20 km points by 24 km

• Points within 1 km of the local origin agree with known control to under 1 m.
• A check point 20 km out lands 24 km from its known position, always along the radius away from the origin.
• Changing the scale parameter from -1.2 to -1.2e-6 restores every point at once.

1. Take check points at three distances (1 km, 10 km, 20 km) and compute the residual at each.
2. If the residual is proportional to distance, suspect a unit error in the scale or rotation parameters.
3. Recompute with m as ppm and as a dimensionless number and compare residual magnitudes.
4. Check the rotations too: arc-seconds must be divided by 206265 to become radians.
5. Confirm the unit of each of the seven parameters before trusting any result.

Normalise units at the entry point: metres for delta-X/Y/Z, radians for omega-x/y/z, and m*1e-6 for the scale; then use only SI units inside the transform.

X' = ΔX + (1 + m) · (X + ωz·Y - ωy·Z)
Y' = ΔY + (1 + m) · (Y - ωz·X + ωx·Z)
Z' = ΔZ + (1 + m) · (Z + ωy·X - ωx·Y)
其中 m 需代入 m_ppm × 1e-6

const pts = [
  { d: 1000,  err: 1180 },
  { d: 10000, err: 12010 },
  { d: 20000, err: 24050 }
];
console.log(pts.map(p => (p.err / p.d).toFixed(4)));
// [1.1800, 1.2010, 1.2025]  -> 比例约 1.2，等于 m 的值

• Putting the ppm scale into the seventh slot of +towgs84 as a dimensionless factor; towgs84 takes only three translations and three rotations in arc-seconds.
• Tuning the translations to hide a scale error, which fixes the origin region and makes the edges worse.