Dear @AndersMS and colleagues

Thanks again for the new version. I find it very clear and comprehensive. I 
have a few comments.

## Chapter 8

"Tie point mapping attribute" mentions "target dimension", which is not a 
phrase used elsewhere. Should this be "interpolated dimension"?

You say, "For the purpose of bounds interpolation, a single bounds tie point is 
created for each coordinate tie point, and is selected as the vertex of the tie 
point cell that is the closest to the boundary of the interpolation subarea 
with respect to each interpolated dimension." I don't understand why there is a 
choice of bounds tie points, because there's no index variable for them. 
Doesn't the tie point index variable dictate the choice of tie points for 
bounds?

## Appendix J

The title says Appendix A. Presumably that's something to do with automatic 
numbering.

All of the subsections listed at the start (Common Definitions and Notation, 
Common conversions and formulas, Interpolation Methods, Coordinate Compression 
Steps, Coordinate Uncompression Steps) should have subsection headings, I 
think. They will be Sections J.1 etc. At the moment the last two are labelled 
as Tables J.1 and J.2 rather than subsections, but they're never referenced as 
tables.

Fig 1ff. `s` is explained beneath the fig, but it would be useful it explain it 
at the side of the fig as well, as you do for `tp` `i` and `u`. Also, it would 
be useful to put the paragraph explaining notation _before_ Fig 1, because Fig 
1 uses the notation.

You say, "When an interpolation method is referred to as linear or quadratic, 
it means that the method is linear or quadratic in the indices of the 
interpolated dimensions." Linear also means that the coordinates of the 
interpolated points are evenly spaced, doesn't it; if so, that would be helpful 
to state.

You say, "In the case of two dimensional interpolation, the two variables are 
equivalently computed as ...". I would say "similarly", not "equivalently", 
which I would understand to mean that `s1` and `s2` are equivalent.

`quadratic`. It would be better not to use `c` for the coefficient, because it 
can be confused with the point **c**.

Please put the "Common conversion and formulae" table before the interpolation 
methods, or at least refer to it. Otherwise the reader encounters `fdot` 
`fcross` `fplus` `fminus` `fmultiply` etc. without having seen their 
definitions. Actually you list it before the interpolation methods in the 
preamble.

[`bi_`]`quadratic_remote_sensing`. Why not call it 
[`bi_`]`quadratic_latitude_longitude`, which describes the method, rather than 
its typical application? What does it mean to treat them as Cartesian or not? I 
would describe bilinear interpolation in lat,lon as treating them as Cartesian 
coordinates, but you must mean something different. Is there a projection plane 
involved?

Where is `latitude_limit` defined?

A couple of times, you write, "For each of the interpolated dimension". There 
should be an -s.

## Conformance

For "Each **`tie_point_variable`** token specifies a tie point variable that 
must exist in the file, and each **`interpolation_variable`** token specifies 
an interpolation variable that must exist in the file," I think all you can say 
is that there are variables of these names in the file, since a checker can't 
tell they are definitely the "kind" of variable you intend.

Regarding, "The legal values for the **`interpolation_name`** attribute are 
contained in Appendix J," it would be helpful for the author of the checker to 
say _where_ they can be found in the appendix.

Best wishes

Jonathan


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