I think I got the formula here so it is a question of translating it to J
and then to get the ring is to do the calculation for i.360 degrees and x
distance
---------------------------------
Formula: α = d/R (angular distance)
lat2 = lat1 + α.cos(θ)
Δφ = ln(tan(lat2/2+π/4)/tan(lat1/2+π/4))
if E:W line q = cos(lat1)
otherwise q = Δlat/Δφ
Δlon = α.sin(θ)/q
lon2 = (lon1+Δlon+π) % 2.π − π
where ln is natural log and % is modulo, Δlon is taking shortest route
(<180°), and R is the earth’s radius
JavaScript:
lat2 = lat1 + d*Math.cos(brng);
var dPhi = Math.log(Math.tan(lat2/2+Math.PI/4)/Math.tan(lat1/2+Math.PI/4));
var q = (Math.abs(lat2-lat1) > 1e-10) ? (lat2-lat1)/dPhi : Math.cos(lat1);
var dLon = d*Math.sin(brng)/q;
// check for some daft bugger going past the pole, normalise latitude if so
if (Math.abs(lat2) > Math.PI/2) lat2 = lat2>0 ? Math.PI-lat2 :
-(Math.PI-lat2);
lon2 = (lon1+dLon+Math.PI)%(2*Math.PI) - Math.PI;
--------------------
Formula: lat2 = asin(sin(lat1)*cos(d/R) + cos(lat1)*sin(d/R)*cos(θ))
lon2 = lon1 + atan2(sin(θ)*sin(d/R)*cos(lat1),
cos(d/R)−sin(lat1)*sin(lat2))
d/R is the angular distance (in radians), where d is the distance
travelled and R is the earth’s radius
JavaScript:
var lat2 = Math.asin( Math.sin(lat1)*Math.cos(d/R) +
Math.cos(lat1)*Math.sin(d/R)*Math.cos(brng) );
var lon2 = lon1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(lat1),
Math.cos(d/R)-Math.sin(lat1)*Math.sin(lat2));
Excel: lat2: =ASIN(SIN(lat1)*COS(d/ER) + COS(lat1)*SIN(d/ER)*COS(brng))
lon2: =lon1 + ATAN2(COS(d/ER)-SIN(lat1)*SIN(lat2),
SIN(brng)*SIN(d/ER)*COS(lat1))
---------------------------
Trig functions take arguments in radians, so latitude, longitude, and
bearings in degrees
(either decimal or degrees/minutes/seconds) need to be converted to
radians, rad = π.deg/180.
When converting radians back to degrees (deg = 180.rad/π), West is negative
if using signed
decimal degrees. For bearings, values in the range -π to +π [-180° to +180°]
need to be converted
to 0 to +2π [0°–360°]; this can be done by (brng+2.π)%2.π [brng+360)%360]
where % is the modulo
operator.
2009/3/29 Björn Helgason <[email protected]>
> Thx
> I took a quick look at the links and it looks like there are good formulas
> available.
> I hope to get some time soon to translate them into J as I want.
>
> 2009/3/28 Brian Schott <[email protected]>
>
> Bjorn,
>>
>> This search provides some good leads, I believe.
>>
>>
>> http://www.google.com/search?hl=en&client=safari&rls=en&q=distance%2Cbearing+sphere&btnG=Search
>>
>>
>>
>> --
>> (B=) <-----my sig
>> Brian Schott
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
>>
>
>
>
> --
> Björn Helgason, Verkfræðingur
> Fugl&Fiskur ehf,
> Þerneyjarsundi 23, Hraunborgum
> Po Box 127,801 Selfoss ,
> t-póst: [email protected]
> gsm: +3546985532
> Landslags og skrúðgarðagerð, gröfuþjónusta
> http://groups.google.com/group/J-Programming
>
>
> Tæknikunnátta höndlar hið flókna, sköpunargáfa er meistari einfaldleikans
>
> góður kennari getur stigið á tær án þess að glansinn fari af skónum
> /|_ .-----------------------------------.
> ,' .\ / | Með léttri lund verður |
> ,--' _,' | Dagurinn í dag |
> / / | Enn betri en gærdagurinn |
> ( -. | `-----------------------------------'
> | ) | (\_ _/)
> (`-. '--.) (='.'=) ♖♘♗♕♔♙
> `. )----' (")_(") ☃☠
>
--
Björn Helgason, Verkfræðingur
Fugl&Fiskur ehf,
Þerneyjarsundi 23, Hraunborgum
Po Box 127,801 Selfoss ,
t-póst: [email protected]
gsm: +3546985532
Landslags og skrúðgarðagerð, gröfuþjónusta
http://groups.google.com/group/J-Programming
Tæknikunnátta höndlar hið flókna, sköpunargáfa er meistari einfaldleikans
góður kennari getur stigið á tær án þess að glansinn fari af skónum
/|_ .-----------------------------------.
,' .\ / | Með léttri lund verður |
,--' _,' | Dagurinn í dag |
/ / | Enn betri en gærdagurinn |
( -. | `-----------------------------------'
| ) | (\_ _/)
(`-. '--.) (='.'=) ♖♘♗♕♔♙
`. )----' (")_(") ☃☠
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
