# [mapguide-dev] area calculation conversion to meters

Paul Spencer pspencer at dmsolutions.ca
Sun Dec 3 22:42:26 EST 2006

over my head, for sure!  I don't think I need that kind of accuracy.
I would like to know if there is a programmatic way to determine a
UTM coordinate system centered on a particular location or, as a
minimum, a way to find the UTM zone that a given coordinate lies in.

Is there some base string I could use and just substitute in some
values?

Cheers

Paul

On 3-Dec-06, at 3:49 PM, Traian Stanev wrote:

>
> Right, I forgot about state planes. Those would have a central
> meridian that's closer to the data.
>
> For distance computations, MapGuide has great circle distance
> functions. Another resource for great circle I've used is here:
>
> http://www.codeguru.com/Cpp/Cpp/algorithms/article.php/c5115
>
>
> The relevant section about a very accurate distance approximation
> on the ellipsoid is at the bottom of the page:
>
> ==================================================
> double ApproxDistance(double lat1, double lon1, double lat2,
>                       double lon2)
> {
>    lat1 = GEO::DE2RA * lat1;
>    lon1 = -GEO::DE2RA * lon1;
>    lat2 = GEO::DE2RA * lat2;
>    lon2 = -GEO::DE2RA * lon2;
>
>    double F = (lat1 + lat2) / 2.0;
>    double G = (lat1 - lat2) / 2.0;
>    double L = (lon1 - lon2) / 2.0;
>
>    double sing = sin(G);
>    double cosl = cos(L);
>    double cosf = cos(F);
>    double sinl = sin(L);
>    double sinf = sin(F);
>    double cosg = cos(G);
>
>    double S = sing*sing*cosl*cosl + cosf*cosf*sinl*sinl;
>    double C = cosg*cosg*cosl*cosl + sinf*sinf*sinl*sinl;
>    double W = atan2(sqrt(S),sqrt(C));
>    double R = sqrt((S*C))/W;
>    double H1 = (3 * R - 1.0) / (2.0 * C);
>    double H2 = (3 * R + 1.0) / (2.0 * S);
>    double D = 2 * W * GEO::ERAD;
>    return (D * (1 + GEO::FLATTENING * H1 * sinf*sinf*cosg*cosg -
>    GEO::FLATTENING*H2*cosf*cosf*sing*sing));
> }
> =======================================
>
>
> Traian
>
> -----Original Message-----
> From:   Orest Halustchak
> Sent:   Sun 12/3/2006 2:33 PM
> To:     dev at mapguide.osgeo.org
> Cc:
> Subject:        RE: [mapguide-dev] area calculation conversion to
> meters
>
> Hi,
>
> Yes, converting to a UTM zone would work. However, if the original
> data is in the US, e.g. Sheboygan, you could project to the
> corresponding State Plane zone. Then you could do length and area
> calculations more accurately.
>
> For UTM, central meridian = zone*6 -183.
>
> For lat/long data, the correct way to compute length is on the
> spheroid. Libraries such as Proj4 or Mentor include distance
> calculation functions based on a particular spheroid. Most
> libraries unfortunately do not include an area calculation on the
> spheroid.
>
> Orest.
>
> -----Original Message-----
> From: Paul Spencer (External)
> Sent: Sun 12/3/2006 2:11 PM
> To: dev at mapguide.osgeo.org
> Cc:
> Subject: Re: [mapguide-dev] area calculation conversion to meters
>
>
>
> Thanks Traian, it hurts my head too!  All calculations will be
> advertised as approximate, but I'd like them to be close to reality.
>
> How can I construct a UTM coordinate system definition centered
> around the meridian that crosses the centroid of the feature?  Or
> find the UTM Zone projection that contains the centroid of a feature
> (I manually found it for the Sheboygan data and it gave decent
> results)?  Would I need to manually build an array of UTM Zone -> LL
> mappings?
>
> Cheers
>
> Paul
>
>
> On 3-Dec-06, at 12:58 PM, Traian Stanev wrote:
>
> > I'm far from an expert either, but here is what makes sense to me...
> >
> > The simplest solution to me seems to transform to the nearest UTM
> > Zone projection in meters and compute the area of the resulting
> > geometry. I think this will be accurate enough for what you are
> > doing, since it is very likely that the original data (for
> > Sheboygan) was measured in that UTM zone and then converted to
> > LatLon after the fact anyway. That's why it seems to me that this
> > approach will give you exact results, even though in theory it is
> > not exact (since the data can be far away from the UTM Zone's
> > central meridian).
> >
> > Another, more generic approach, that would be good for small
> > features, would be to construct a UTM coordinate system definition
> > centered around the meridian that crosses the centroid of the
> > feature. This will give you an LL-UTM transformation with the least
> > distortion for the feature at hand.
> >
> > My hunch is that computing an exact area on the ellipsoid without
> > projection involves elliptical integrals, since even the area of a
> > whole ellipsoid involves those. Elliptic integrals have no closed
> > form solution so you would need a numerical integration approach,
> >
> >
> > Traian
> >
> >
> >
> >
> > -----Original Message-----
> > From: Paul Spencer (External)
> > Sent: Sat 12/2/2006 12:04 PM
> > To: dev at mapguide.osgeo.org
> > Cc:
> > Subject: Re: [mapguide-dev] area calculation conversion to meters
> >
> > Trevor,
> >
> > That would work for GetLength() but I wonder if you need to adjust
> > for latitude as well ... and it doesn't work for area.  I pondered
> > doing this for the square root of the area and then squaring the
> > result ... I think that would work, but again it would have to be
> > adjusted for the latitude ... or am I over-engineering this?
> >
> > Paul
> >
> > On 1-Dec-06, at 4:10 PM, Trevor Wekel wrote:
> >
> > > Hi Paul,
> > >
> > > For the most general case, I think you're on the right track.
> > Most of
> > > the geometry classes support the Transform() operation.  The
> > > MgCoordinateSystemTransform allows transformation from one
> > coordinate
> > > system to another.  I'm not a coordinate system expert but from
> > what I
> > > understand most coordinate systems projections have an accurate
> > sweet
> > > spot in the center and become more inaccurate around the edges.  I
> > > wonder if there is a programmatic way to determine the
> > appropriateness
> > > of the target system?  Possibly based on center point of the
> > > projection?
> > >
> > > But if your target system is in decimal degrees, doesn't that
> > imply a
> > > direct mapping to the world space?  Isn't a decimal degree some
> > number
> > > of meters?  Could you just use
> > > MgCoordinateSystem::ConvertCoordinateSystemUnitsToMeters(double
> > units)
> > > as the conversion factor?  I suspect this may also work in the
> sweet
> > > spot of projected systems as well.
> > >
> > > Thanks,
> > > Trevor
> > >
> > > -----Original Message-----
> > > From: Paul Spencer (External)
> > > Sent: Thursday, November 30, 2006 3:03 PM
> > > To: dev at mapguide.osgeo.org
> > > Subject: [mapguide-dev] area calculation conversion to meters
> > >
> > > Hi all,
> > >
> > > I'm measuring the area and length of features using
> > > MgGeometricEntity::GetArea() and GetLength() in the Sheboygan
> data.
> > > This returns values in the units of the projection, which happens
> > > to be
> > > decimal degrees.  Not so useful.  I'd like the result to be in
> > meters.
> > >
> > > Since this code needs to be generic, I've implemented some
> stuff to
> > > transform the geometry into a coordinate system that supports
> > meters.
> > > This is not too accurate since I arbitrarily picked a World LCC
> > > projection wkt :)
> > >
> > > What is the recommended way of doing this calculation?
> > >
> > > Cheers
> > >
> > > Paul
> > >
> > >
> +-----------------------------------------------------------------+
> > > |Paul Spencer
> pspencer at dmsolutions.ca    |
> > >
> +-----------------------------------------------------------------+
> > > |Chief Technology
> Officer                                         |
> > > |DM Solutions Group Inc                http://
> www.dmsolutions.ca/ |
> > >
> +-----------------------------------------------------------------+
> > >
> > >
> > >
> > >
> > >
> > >
> >
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> > +-----------------------------------------------------------------+
> > |Paul Spencer                          pspencer at dmsolutions.ca    |
> > +-----------------------------------------------------------------+
> > |Chief Technology Officer                                         |
> > |DM Solutions Group Inc                http://www.dmsolutions.ca/ |
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> +-----------------------------------------------------------------+
> |Paul Spencer                          pspencer at dmsolutions.ca    |
> +-----------------------------------------------------------------+
> |Chief Technology Officer                                         |
> |DM Solutions Group Inc                http://www.dmsolutions.ca/ |
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+-----------------------------------------------------------------+
|Paul Spencer                          pspencer at dmsolutions.ca    |
+-----------------------------------------------------------------+
|Chief Technology Officer                                         |
|DM Solutions Group Inc                http://www.dmsolutions.ca/ |
+-----------------------------------------------------------------+