Geometry Boost List: Re: [geometry] Support for geographic coordinate system

Subject: Re: [geometry] Support for geographic coordinate system
From: Adam Wulkiewicz (adam.wulkiewicz_at_[hidden])
Date: 2014-11-06 18:00:32

Hi Barend,

Barend Gehrels wrote:
> Adam Wulkiewicz wrote On 6-11-2014 17:06:
>> I'm planning to begin the implementation of the support for 
>> geographical CS and would like to hear your opinion. Esspecially from 
>> people already using the geographical extensions.
>> Basically, to support this CS we need a distance strategy and side 
>> strategy. They're already implemented (more or less) though in the 
>> extensions so not officially released yet. To release them we need to 
>> think about the interface first. The geographical strategies should 
>> have an interface similar to the one used in spherical strategies. 
>
> I don't know if that is so important. What is important is that we 
> have one model or concept of the Earth, used in both distance 
> strategies (andoyer, vincenty) and in the geographic projections.
>
> That the interface is a bit different than Haversine, I don't know if 
> that is a problem (maybe, but we can examine that). Or maybe they both 
> can be implemented with a default constructor.
>

Yes, this is what I'd like to know, gather some feedback, etc.
The interface may be different but it should be consistent, i.e. 
familiar for someone already knowing the spherical strategies, the 
default parameters should be intuitive in both cases, etc.

<snip>

>
>>
>> GEOGRAPHICAL:
>>
>> - a spherical side strategy is just used by default which I guess 
>> should be changed. I think the most precise would be a strategy 
>> finding the side using the geographic courses found using the inverse 
>> Vincenty's formula but this requires some testing
>
> As far as I know, the spherical side strategy works for the geographic 
> Earth too, please indicate if that is not the case.
>
> See also
> http://barendgehrels.blogspot.nl/2011/06/spherical-side-formula.html
>
> But I might be wrong, it is good to research this.

I feel that Vincenty's formula should give different results in some 
edge cases because the shape of geodesic on ellipsoid is different than 
on a sphere but I must perform some tests to be sure.

>
>> - for distance there are 2 strategies, both taking 
>> detail::ellipsoid<RadiusType>, andoyer also has a ctor taking a 
>> flattening of type RadiusType (like detail::ellipsoid<>). If 1 
>> parameter is passed (flattening) then the radius is set to 1.0 but if 
>> 2 parameters are passed then A and B radiuses are set. Furthermore by 
>> default Earth's radiuses are used. So the situation looks like this:
>>
>> vincenty<RadiusType> s(detail::ellipsoid<RadiusType>()); // A = 
>> 6378137.0, B = 6356752.314245
>> vincenty<RadiusType> s(detail::ellipsoid<RadiusType>(f)); // A = 1.0, 
>> B = [some fraction for oblate spheroid]
>> vincenty<RadiusType> s(detail::ellipsoid<RadiusType>(a, b)); // A = 
>> a, B = b
>> andoyer<RadiusType> s; // A = 6378137.0, B = 6356752.314245
>> andoyer<RadiusType> s(f); // A = 1.0, B = [some fraction for oblate 
>> spheroid]
>>
>> It's confusing (this 1 and 2 paramers difference) and inconsistent 
>> with spherical strategies.
>
>
> Yes this should be harmonized with one "libary-universal" concept of 
> the Earth model.

I'm not sure if one "universal" model would be sufficient. Or do you 
think about the model for geographic CS? E.g. Earth approximated as a 
sphere could have some radius "not compatible" with the ellipsoid model. 
E.g. mean radius may be calculated in various ways. So I'm guessing that 
we shouldn't use ellipsoidal model for spherical CS.

>
>> Furthermore flattening should be stored using some Floating Point 
>> type and currently it's just RadiusType. E.g. for integral RadiusType 
>> the default ctor would initialize flattening with 0.
>>
>> PROPOSAL:
>>
>> 1. I propose to keep it simple for now, don't release 
>> detail::ellipsoid and change the default parameters to make the 
>> strategies close to the spherical ones:
>>
>> vincenty<RadiusType> s(); // A = 1.0, B = [fraction], F= 
>> [fraction,default] - unit WGS84 spheroid
>> vincenty<RadiusType> s(a); // A = a, B = [calculated from a using 
>> default flattening], F= [fraction,default]
>> vincenty<RadiusType> s(a, b); // A = a, B = b, F= [calculated from a 
>> and b]
>>
>> This way the calls:
>>
>> distance(p1, p2, vincenty<RadiusType>(a));
>> distance(p1, p2) * a;
>
> I don't know - will anybody call Vincenty with the unit sphere?
> I would prefer specifying the ellipsoid.
>

I suggested it to be consistent with the spherical CS.
We could do other way around. Make the spherical CS consistent with the 
geographical CS taking care about the backward compatibility.

However I don't have an idea how to do it in a "good" way. If we just 
allowed passing a Sphere model besides a raw radius it could have some 
different default value (spherical Earth radius). But then depending on 
the type the default would be different so this would be unintuitive and 
error-prone:

haversine<double> s; // radius = 1
haversine<sphere<double>> s // radius = ... e.g. 6367446.98883 or one of 
the other mean radius values

Though this would be similar in the case of geographical CS, where 
defaults are Earth's semi- major and minor axes.

But if those models had a word 'Earth' in the name explicitly then it'd 
be obvious what default values there may be:

// it's obvious that by default those'd have some "real" radius values
haversine<spherical_earth<double>>
vincenty<ellipsoidal_earth<double>>

>
>>
>> would be equivalent (assuming that RadiusType is not integral type?).
>>
>> By default FlatteningType would be:
>> - for floating point RadiusType <=> RadiusType
>> - for integral RadiusType <=> promoted to FP of the same size (int-> 
>> float, long long-> double)
>> - for user defined types <=> UDT
>> The FlatteningType could be optionally passed as a second template 
>> parameter of a strategy however I'm not sure about it since it 
>> wouldn't play nice with possible future improvement 3 (see below).
>>
>> ALTERNATIVES (FUTURE ADDITIONS)
>>
>> 2. To decrease the probability of a mistake the strategy could take 
>> wrapped parameters (only?). This way it'd also be possible to create 
>> an ellipsoid from A,B A,F or B,F pair:
>>
>> // below are functions returning wrapped values
>> vincenty<RadiusType> s(major_radius(a), minor_radius(b));
>> vincenty<RadiusType> s(major_radius(a), flattening(f));
>> vincenty<RadiusType> s(minor_radius(b), inverse_flattening(if));
>>
>> 3. Desing concepts for models parameters. And then always pass a type 
>> adapted to model's parameters concept to the strategy, instead of 
>> RadiusType. Actually a single number could be adapted to e.g. sphere 
>> parameters concept (radius) but why reserve it specifically for sphere?
>>
>> haversine< parameters::sphere<RadiusType> > 
>> s(parameters::sphere<RadiusType>(radius));
>> vincenty< parameters::ellipsoid<RadiusType> > 
>> s(parameters::ellipsoid<RadiusType>(a, b));
>> vincenty< parameters::ellipsoid_af<RadiusType> > 
>> s(parameters::ellipsoid_af<RadiusType>(a, f));
>> vincenty< parameters::ellipsoid_unit_flattening<RadiusType> > 
>> s(parameters::ellipsoid_unit_flattening<RadiusType>(f));
>> vincenty< parameters::ellipsoid_wgs84_1996<RadiusType> > 
>> s(parameters::ellipsoid_wgs84_1996<RadiusType>());
>> vincenty< parameters::ellipsoid_wgs84_2004<RadiusType> > 
>> s(parameters::ellipsoid_wgs84_2004<RadiusType>());
>> vincenty< parameters::ellipsoid_latest<RadiusType> > 
>> s(parameters::ellipsoid_latest<RadiusType>());
>>
>> FYI, all names of namespaces, structs and functions are examples.
>>
>> For sphere we'd already have a small problem with this. However this 
>> could be implemented in a backward compatible way. But then it could 
>> be done this way in the future, for both coordinate systems.
>>
>> 4. 2 and 3 together:
>>
>> vincenty< parameters::ellipsoid<RadiusType> > 
>> s(parameters::ellipsoid<RadiusType>(major_radius(a), minor_radius(b)));
>>
>> Do you have any thoughts or requests regarding the above?
>>
>
> Yes, I opt for a more simple model, one constructor and not many 
> overloads, with the model of the Earth. As discussed earlier. So 
> something like this, as you suggest:
>
> vincenty<RadiusType> s(detail::ellipsoid<RadiusType>()); // A = 
> 6378137.0, B = 6356752.314245
> andoyer<RadiusType> s(detail::ellipsoid<RadiusType>()); // A = 
> 6378137.0, B = 6356752.314245
>

Are you saying that if a user wanted to use some different A or B he 
should define his own model instead of passing some parameters?

What do you think about passing a model as a Strategy tempalte parameter 
instead of a RadiusType?
It'd be less error-prone, since the radius type would be defined in one 
place (the model).
It'd also simplify things in the case is we needed more than 1 type in 
some future model.

So:

vincenty<EllipsoidModel> s(EllipsoidModel())
andoyer<EllipsoidModel> s(EllipsoidModel())
haversine<SphereModel> s(SphereModel())
// or rather
haversine<SphereModelOrRadius> s(SphereModel())
// for backward compatibility

, e.g.:

typedef strategy::ellipsoid<double> ellipsoid;
strategy::vincenty<ellipsoid> s(ellipsoid(a, b));

vs

typedef strategy::ellipsoid<double> ellipsoid;
strategy::vincenty<double> s(ellipsoid(a, b));

We could then pass a Sphere model to the haversine<> and handle it 
differently than raw radius (as mentioned above).

Btw, I think Vincenty's formula could also be used in side calculation 
so it could also be a name for a side strategy. But let's leave the 
names for later.

> (but the ellipsoid should not reside in detail)
>
> This harmonization is the main reason why it is not moved earlier from 
> extensions to the main library. As soon as this is fixed we can 
> probably release them together. The main work will probably be in the 
> projection part. 

Should we also provide similar model for spherical CS with some default 
mean Earth radius?
Another possibility would be to somehow extract this radius from an 
ellipsoid<>:
- just take semi-major axis
- use one of those mean values: 
http://en.wikipedia.org/wiki/Earth_radius#Mean_radii
- or one of those: 
http://math.wikia.com/wiki/Ellipsoidal_quadratic_mean_radius
So I'd rather leave it to the user.

Or do you think otherwise?

Btw, some time ago we talked about convenient strategies specification 
for Variant geometries and this would be "in line" with it, e.g.:

boost::variant<SphPoint, SphLinestring, SphPolygon> var1, var2;
// ...
distance(var1, var2, strategy::default & 
strategy::sphere<RadiusType>(radius))

And this object of type strategy::sphere<> could go directly into the 
Strategy. But this is another story...

Regards,
Adam