[GRASS-user] g.transform: forward and reverse rmse

[Maciej Sieczka]

Thanks Glynn. One question more below.

Glynn Clements pisze:

> Note that, unless order=1, the two transformations will typically not
> be exact inverses as the inverse of a polynomial containing quadratic
> or higher terms is not itself a polynomial.

Even for order=1 I get rather huge differences between forward and 
reverse. Normal? Order 1-3 examples for a single GCP set, g.transform -s 
group=tmp format=idx,fd,rd:

# Order=1:

index forward reverse
  0 140.159347 30.366192
  1 75.549553 16.157024
  2 20.384295 4.152418
  3 88.853688 19.265900
  4 88.257880 19.471545
  5 28.997927 6.360764
  6 96.951029 21.909275
  7 98.251481 21.344657
  8 75.633328 17.289931
  9 55.503010 12.158829
  10 52.191730 11.329603
  11 121.973315 27.215642
  12 69.859427 15.239316
  13 137.981202 29.362434
Number of active points: 14
Forward:
x[13] = 127.41
y[11] = 119.24
g[0] = 140.16
RMS = 89.31
Reverse:
x[13] = 28.74
y[11] = 25.14
g[0] = 30.37
RMS = 19.52


# Order=2:

index forward reverse
  0 93.801673 19.746141
  1 56.120534 11.776122
  2 44.347503 9.766772
  3 87.236869 19.091564
  4 57.147439 12.625245
  5 41.602974 9.331447
  6 67.226825 14.996778
  7 117.409320 26.196235
  8 23.107091 5.814319
  9 68.110687 14.954173
  10 68.366499 15.039828
  11 96.381244 20.478652
  12 38.714956 8.008384
  13 91.457126 18.595213
Number of active points: 14
Forward:
x[13] = 90.45
y[7] = 96.79
g[7] = 117.41
RMS = 72.62
Reverse:
x[13] = 18.58
y[7] = 24.29
g[7] = 26.20
RMS = 15.72


# Order=3:

index forward reverse
  0 30.058621 5.273581
  1 9.214810 2.597311
  2 23.887028 5.573190
  3 43.321031 10.109480
  4 58.855332 13.138564
  5 52.926125 10.500470
  6 43.858184 11.035265
  7 81.241239 19.131565
  8 14.513041 3.562930
  9 39.791625 7.880774
  10 51.354498 12.139448
  11 44.211574 10.147233
  12 8.597234 1.926148
  13 37.500769 7.736833
Number of active points: 14
Forward:
x[7] = 35.53
y[7] = 73.06
g[7] = 81.24
RMS = 43.17
Reverse:
x[7] = 9.76
y[7] = 16.46
g[7] = 19.13
RMS = 9.74

Maciek

-- 
Maciej Sieczka
www.sieczka.org