[Benchmarking] Scale and pixel resolution formulas

Daniel Morissette dmorissette at mapgears.com
Thu Aug 12 10:40:26 EDT 2010

Andrea Aime wrote:
> Hi,
> scale computation this year is going to make a difference
> in tests so I'd like to make sure we're all on the same page,
> otherwise servers will do a different amount of work.
> The SLD spec suggests the following formulas for scale
> denominator computation:
> sd_non_geographic = (bbox_width / image_width) * (DPI / 0.0254)
> sd_geographic = (bbox_width / OGC_DEG_TO_METER) * (DPI / 0.0.254)
> DPI = 25.4 / 0.28  --> 90.714
> OGC_DEG_TO_METER = 6378137.0 * 2.0 * PI / 360
> The above are actually the formulas used by GeoServer.
> As far as I know OpenLayers and MapServer use the same, but with
> DPI=75.
> To get the servers make the same work we all need to have a similar
> scale computation setup. Are we? :-)

For the record, MapServer's default DPI is 72, not 75. However this is a
configurable parameter and can very easily be changed to 90.714 in a

I had a quick look at MapServer's scale calculation code and constants,
and it uses a variant of the formulas above with the constants based on
inches-per-unit. This gives essentially the same results within a small
margin of error.

For instance, in the non-geographic case (projected coordinates in
meters), we use 39.3701 inches per meter which means 0.025399986 meters
per inch, compared to your 0.0254... not a significant difference.

However, in the geographic case, we use 4374754 inches per degree and
using your OGC_DEG_TO_METER I'd get 4382659.48 inches per degree... a
difference of 0.18% ... not very significant either, but I thought I'd
mention it.

Note that this is based on a quick review of the code... I hope I did
not make a mistake that would mislead you.

Another important thing to note when calculating scales is that OGC uses
a pixel edge to pixel edge model when specifying a BBOX ... i.e. the
BBOX correspond to the extents of the outside of the pixels of the
image. However some software, including MapServer's native (non-OGC)
interface, use a pixel-center to pixel-center model. There are logical
reasons for choosing this pixel-center model and other packages may have
chosen to use it too. However this can lead to some scale differences
when serving OGC requests and MapServer has been "fixed" to take this
difference into account and make sure its OGC interfaces do the right thing.

Just mentioning it so that other software packages double-check to make
sure they are using the right model for their BBOX and scale calculations.

Daniel Morissette

More information about the Benchmarking mailing list