[GRASS-user] BIN raster import
Dylan Beaudette
dylan.beaudette at gmail.com
Thu Sep 4 10:52:03 EDT 2008
Thanks Glynn. I am going to look for a relevant page on the Wiki to
post much of this information, as it may be very helpful to others.
Cheers,
Dylan
On Thu, Sep 4, 2008 at 12:46 AM, Glynn Clements
<glynn at gclements.plus.com> wrote:
>
> Dylan Beaudette wrote:
>
>> > note that GRASS considers the region bound coordinate to be at the
>> > outer edge of the border cells.
>>
>> Now that you mention this, is there an authoritative description of how GRASS
>> (and maybe GDAL) treat cells/pixels:
>
> Inevitably, the authoritative description is the source code. Any
> other documentation describes how modules are supposed to behave,
> while the source code describes how they actually behave.
>
>> 1. region calculations (outer edge of the border cells)
>
> Well, the region isn't limited to raster data; it may also affect some
> vector operations.
>
> The region's bounds describe a rectangle in two-dimensional space. For
> raster operations, this rectangle is subdivided into a grid of
> rectangular cells, so the region's bounds are aligned with the edges
> of the outermost cells.
>
>> 2. cell locations (??? center, edge ???)
>
> Cells are areas, not points, so they don't have locations. Their
> corners have locations, as do their centres.
>
> A cell with array indices (i,j) (easting, northing) corresponds to the
> rectangle:
>
> { (x,y) : west + i * ewres <= x < west + (i+1) * ewres,
> north - (j+1) * nsres <= y < north - j * nsres }
>
> whose centre is at:
>
> (west + (i+1/2) * ewres, north - (j+1/2) * nsres)
>
> [Subject to wrapping of longitude values in lat/lon locations.]
>
>> 3. raster to vector conversions (??? center, edge ???)
>
> IIRC, r.to.vect uses the midpoints of the cell's edges (i.e. one
> coordinate will be on a grid line, the other will be mid-way between
> grid lines).
>
>> 4. resampling (??? center, edge ???)
>
> The built-in nearest-neighbour resampling of raster data calculates
> the centre of each region cell, and takes the value of the raster cell
> in which that point falls.
>
> If the point falls exactly upon a grid line, the exact result will be
> determined by the direction of any rounding error.
>
> [One consequence of this is that downsampling by a factor which is an
> even integer will always sample exactly on the boundary between cells,
> meaning that the result is ill-defined.]
>
> r.resample uses the built-in resampling, so it should produce
> identical results.
>
> r.resamp.interp method=nearest uses the same algorithm, but not the
> same code, so it may not produce identical results in cases which are
> decided by the rounding of floating-point numbers.
>
> For method=bilinear and method=bicubic, the raster values are treated
> as samples at each raster cell's centre, defining a piecewise-
> continuous surface. The resulting raster values are obtained by
> sampling the surface at each region cell's centre.
>
> As the algorithm only interpolates, and doesn't extrapolate, a margin
> of 0.5 (for bilinear) or 1.5 (for bicubic) cells is lost from the
> extent of the original raster. Any samples taken within this margin
> will be null.
>
> AFAIK, r.resamp.rst behaves similarly, i.e. it computes a surface
> assuming that the values are samples at each raster cell's centre, and
> samples the surface at each region cell's centre.
>
> For r.resamp.stats without -w, the value of each region cell is the
> chosen aggregate of the values from all of the raster cells whose
> centres fall within the bounds of the region cell.
>
> With -w, the samples are weighted according to the proportion of the
> raster cell which falls within the bounds of the region cell, so the
> result is normally[1] unaffected by rounding error (a miniscule
> difference in the position of the boundary results in the addition or
> subtraction of a sample weighted by a miniscule factor).
>
> [1] The min and max aggregates can't use weights, so -w has no effect
> for those.
>
>> I have often second-guessed myself on these very topics...
>
> For the most part, the interpretation is the "obvious" one, given:
>
> 1. Cells are areas rather than points.
>
> 2. Operations which need a point (e.g. interpolation) use the cell's
> centre.
>
> From a programming perspective, the functions:
>
> G_row_to_northing()
> G_col_to_easting()
> G_northing_to_row()
> G_easting_to_col()
>
> all transform floating-point values.
>
> Passing integer row or column indices to the first two functions will
> return the coordinates of the cell's top-left corner; for the centre
> coordinates, pass row+0.5 and/or col+0.5.
>
> Similarly, the last two functions will typically return non-integral
> values; use floor() to discard the fractional part and obtain the row
> or column index of the cell within which the point lies.
>
> --
> Glynn Clements <glynn at gclements.plus.com>
>
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