Best way to calculate distance between geographicalpoints

Dear Karl,

I think that the relative errors are more relevant than absolute errors.
The relative error on the equatorial circumference for "geo.dist" is
0.33%, which is not that accurate. The relative error on the meridional
distance is only about 0.085%, which should accurant enough for most
applications.

From the code of rdist.earth(), it is using a sphere with a 6378388m 

Just my 2 eurocents.

Thierry


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ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
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Research Institute for Nature and Forest
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tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be
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-----Oorspronkelijk bericht-----
Van: r-sig-geo-bounces at stat.math.ethz.ch
[mailto:r-sig-geo-bounces at stat.math.ethz.ch] Namens Karl Ove Hufthammer
Verzonden: donderdag 14 januari 2010 10:57
Aan: r-sig-geo at stat.math.ethz.ch
Onderwerp: Re: [R-sig-Geo] Best way to calculate distance between
geographicalpoints

On Thu, 14 Jan 2010 10:27:17 +0100 Karl Ove Hufthammer <karl at huftis.org>
wrote:

I have found three functions for calculating the distance between
geographical points, 'geo.dist' in the 'oce' package, 'rdist.earth' in

the 'fields' package, and 'spDistsN1' in the 'sp' package. They all
give slightly difference answers, so my question is: which of them is
best, i.e., gives the most accurate answer?

One simple test would be to calculate the circumference of the earth at
the equator and the meridian. But this test gives conflicting answers.

According to Wikipedia, "http://en.wikipedia.org/wiki/Earth" the
equatorial circumference is 40075.02 km and the meridional circumference
is 40007.86 km.

When calculating half the equatorial circumference, 'spDistsN1' is best,
and gives the *exact* answer, while 'rdist.earth' is close (less than
one km difference), and 'geo.dist' is far from the correct answer
(133.92 km difference). So it would initially seem that 'spDistsN1' is
the one to use, and one should avoid 'geo.dist'.

But when calculating the meridional distance, 'geo.dist' gives the exact
answer, while both 'rdist.earth' and 'spDistsN1' are both off by about
34 km (but in difference directions).

So which to use is still an open question ...

Here is the code I used:

library(oce)
library(fields)
library(sp)

# Equatorial
lt1=0
lt2=0
lg1=0
lg2=180

a=matrix(c(lg1,lt1),nrow=1)
b=matrix(c(lg2,lt2),nrow=1)

# Calculated distance
geod.dist(lt1,lg1,lt2,lg2)
rdist.earth(a,b, miles=FALSE)
spDistsN1(a,b, longlat=TRUE)

# Correct distance (according to Wikipedia)
40075.02/2


# Meridional
lt1=-90
lt2=90
lg1=0
lg2=0

a=matrix(c(lg1,lt1),nrow=1)
b=matrix(c(lg2,lt2),nrow=1)

# Calculated distance
geod.dist(lt1,lg1,lt2,lg2)
rdist.earth(a,b, miles=FALSE)
spDistsN1(a,b, longlat=TRUE)

# Correct distance (according to Wikipedia)
40007.86/2

--
Karl Ove Hufthammer