Parameter +range in polynomial transformation +horner

[Jochem-L]

I found two problems with the range parameter in the polynomial transformation +horner. I assume the range parameter was added because a polynomial transformation gives terrible results outside its area of validity.

Problem 1

The +range parameter (default value 500 000) applies on the input coordinates in the forward and inverse transformation. I think it should apply on the input coordinates in the forward transformation, but it should apply on the output coordinates in the inverse transformation. That would mean one can use the same range for the forward and inverse transformation. This is currently not the case, which is confusing.

Forward example

(echo 30000.00 100000.00 & echo 30000.00 120000.00) | cct -d 2 -z 0 +proj=horner +deg=3 +fwd_origin=0,0 
+fwd_u=+120025.8705,+0.999986846,-0.0250515e-8,+0.1471965e-14,+0.006918172,-0.0860518e-8,-0.0398590e-14,+0.0011249e-8,+0.4556545e-14,+0.1991105e-14 
+fwd_v=+390181.7849,+0.999993024,-0.0338879e-8,+0.1184845e-14,-0.006907254,-0.0492600e-8,-0.1945916e-14,+0.0222878e-8,+0.9244571e-14,-0.1091684e-14 
+inv_tolerance=0.001
    150717.96      489970.61          0.00           inf
    150857.90      509969.45          0.00           inf

Inverse example

(echo 150717.96 489970.61 & echo 150857.90 509969.45) | cct -d 2 -z 0 +proj=horner +deg=3 +fwd_origin=0,0 
+fwd_u=+120025.8705,+0.999986846,-0.0250515e-8,+0.1471965e-14,+0.006918172,-0.0860518e-8,-0.0398590e-14,+0.0011249e-8,+0.4556545e-14,+0.1991105e-14 
+fwd_v=+390181.7849,+0.999993024,-0.0338879e-8,+0.1184845e-14,-0.006907254,-0.0492600e-8,-0.1945916e-14,+0.0222878e-8,+0.9244571e-14,-0.1091684e-14 
+inv_tolerance=0.001 +inv
     30000.00      100000.00          0.00           inf
#Record 1 TRANSFORMATION ERROR: 150857.90 509969.45
 (Point outside of projection domain)

To solve the error, a different range parameter needs to be specified.

(echo 150717.96 489970.61 & echo 150857.90 509969.45) | cct -d 2 -z 0 +proj=horner +deg=3 +fwd_origin=0,0 
+fwd_u=+120025.8705,+0.999986846,-0.0250515e-8,+0.1471965e-14,+0.006918172,-0.0860518e-8,-0.0398590e-14,+0.0011249e-8,+0.4556545e-14,+0.1991105e-14 
+fwd_v=+390181.7849,+0.999993024,-0.0338879e-8,+0.1184845e-14,-0.006907254,-0.0492600e-8,-0.1945916e-14,+0.0222878e-8,+0.9244571e-14,-0.1091684e-14 
+inv_tolerance=0.001 +range=600000 +inv
     30000.00      100000.00          0.00           inf
     30000.00      120000.00          0.00           inf  

Problem 2

It makes no sense to use a range parameter if the origin is not in the centre of the area of use (e.g. in case of false easting and northing). A bounding box would be more appropriate.

In the example given above the input coordinates for the forward transformation are approximately:
-100 000 < x < +200 000
-100 000 < y < +200 000

But the input coordinates in the inverse transformation are:
0 < x < +300 000
+300 000 < y < +600 000