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Cellular forums Home > Archive > GPS > May 2007 > Calculate point A from points B & C
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Calculate point A from points B & C
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| Core2Duo 2007-05-19, 7:33 am |
| I need to determine the coordinates of an inaccessible point A using the
coordinates and bearings from 2 other accessible points B & C.
The bearing lines from points B & C point towards point A and therefore
intersect there.
Any help dearly apppreciated.
| |
| Canopus 2007-05-19, 10:33 am |
| Core2Duo scribed:
>I need to determine the coordinates of an inaccessible point A using the
>coordinates and bearings from 2 other accessible points B & C.
>The bearing lines from points B & C point towards point A and therefore
>intersect there.
>
>Any help dearly apppreciated.
There's not much info to go on here, but, if A, B and C are on a straight
line upon which you were travelling then you could use average speed to
calculate aprox. location of A. If, however, A, B and C form a triangle
you could either use trigonometry to calculate A or position C and D on a
map, construct lines from C and D using the bearings from them to A and
where they intersect is point A. This is simple practical geometry.
--
Rob
http://www.flickr.com/photos/canopus_archives/
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| Core2Duo 2007-05-19, 10:33 am |
| Yes, "A, B and C" do form a triangle.
thanks
"Canopus" < JLNKOOECOCGY@spammot
el.com> wrote in message
news:5b8aa8F2qulm5U1
@mid.individual.net...
> Core2Duo scribed:
>
>
> There's not much info to go on here, but, if A, B and C are on a straight
> line upon which you were travelling then you could use average speed to
> calculate aprox. location of A. If, however, A, B and C form a triangle
> you could either use trigonometry to calculate A or position C and D on a
> map, construct lines from C and D using the bearings from them to A and
> where they intersect is point A. This is simple practical geometry.
>
> --
> Rob
>
> http://www.flickr.com/photos/canopus_archives/
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| On May 19, 6:50 am, "Core2Duo" <Core2...@theinternet.com> wrote:
> I need to determine the coordinates of an inaccessible point A using the
> coordinates and bearings from 2 other accessible points B & C.
> The bearing lines from points B & C point towards point A and therefore
> intersect there.
This is a pretty easy one if you remember your agebra. The equation
for a straight line is y = mx + b where m is the slope (bearing) and b
is the y-intercept (value of y when x is 0).
There are two lines we need m and b for. One is the line AB, the
other is the line AC. Where these two lines intercect is point A. So
A fits the equations for both lines.
First we need m and b for each of these two lines.
You have a bearing, plug it into the equation as a slope. That means
taking the tangent of the angle first. Then use the basic equation to
get the y-intercept, b.
m = tan(bearing)
y = mx + b
b = y - mx
Repeat for the other equation. Now you should have m and b for line
AB and m and b for line AC. Again you use the line equation to find
the point that lies on a common point of the two lines. Since the y
in each case has the same value, you can set the two equations
equal.
m(AB)x(A) + b(AB) = m(AC)x(A) + b(AC)
Solving for x gives you
x(A) = (b(AC)-b(AB)) / (m(AB)-m(AC))
Once you have the value of x at point A, you can easily find y using
the same equation...
y(A) = m(AB)x(A) + b(AB)
It actually does not matter which m and b you use here since A is on
both lines.
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| Bob L 2007-05-19, 12:33 pm |
|
"Core2Duo" < Core2Duo@theinternet
.com> wrote in message
news:zDA3i.1580$wH4.971@news-server.bigpond.net.au...
>I need to determine the coordinates of an inaccessible point A using the
>coordinates and bearings from 2 other accessible points B & C.
> The bearing lines from points B & C point towards point A and therefore
> intersect there.
>
> Any help dearly apppreciated.
>
Since lat-lon are spherical coordinates simple cartesian math won't get you
the lat-lon of point A. Try this link
http://williams.best.vwh.net/avform.htm#Intersection
| |
|
| Hello,
As point out by the previous OP, things may looks very different depending
on how you express your position B and C.
In case of cartesian coordinates (such as northing and easting in UTM
coordinates) the position of A (when it exist) can be deduce from
elementary geometric considerations and the associated linear algebra. This
method is not rigorous since it doesn't take account of the shape of the
earth, but can be successfully apply in short distance range with reasonable
accuracy.
In case of lat/lon coordinates are expressed in degree, method of
intersecting radials have to be use. This method is far more rigorous and is
accurate for long distance projection (such used in avionic and marine
navigation). Beware to convert lat/lon coordinate from degre to radian to
run the computation.
In both case, your bearing have ot be 'true bearing'. The zero degree
bearing has to point to 'true north' (or 'geographic north'). If magnetic
bearing have to be used, magnetic declination has to be consider and the
corrections apply.
An another way to determine the positon of A is to use a map. You can report
position of point B and C and deduce the position of A by drawing bearing
'line' from B and C in direction of the intercept point A.
But remember that bearing may not necessery correspond to a straight line on
your map. Depending of the map projection, a bearing may have to be draw as
a curve. The bearing may only correspond to a straight line on transverse
mercator projection maps (navigation maps) for a reasonable short distance.
C.Ret
Up to now no carriage returns
"Core2Duo" < Core2Duo@theinternet
.com> wrote in
news:zDA3i.1580$wH4.971@news-server.bigpond.net.au...
> I need to determine the coordinates of an inaccessible point A using the
> coordinates and bearings from 2 other accessible points B & C.
> The bearing lines from points B & C point towards point A and therefore
> intersect there.
>
> Any help dearly apppreciated.
>
>
| |
| Bob L 2007-05-19, 10:33 pm |
|
"CRet" <c.ret@wanadoo.fr> wrote in message
news:464f7a81$0$5103
$ba4acef3@news.orange.fr...
> Hello,
>
> As point out by the previous OP, things may looks very different depending
> on how you express your position B and C.
>
> In case of cartesian coordinates (such as northing and easting in UTM
> coordinates) the position of A (when it exist) can be deduce from
> elementary geometric considerations and the associated linear algebra.
> This
> method is not rigorous since it doesn't take account of the shape of the
> earth, but can be successfully apply in short distance range with
> reasonable
> accuracy.
>
> In case of lat/lon coordinates are expressed in degree, method of
> intersecting radials have to be use. This method is far more rigorous and
> is
> accurate for long distance projection (such used in avionic and marine
> navigation). Beware to convert lat/lon coordinate from degre to radian to
> run the computation.
>
> In both case, your bearing have ot be 'true bearing'. The zero degree
> bearing has to point to 'true north' (or 'geographic north'). If magnetic
> bearing have to be used, magnetic declination has to be consider and the
> corrections apply.
For UTM you would use grid north rather than true north. They can be a few
degrees different at the edges of the UTM zones.
| |
| Core2Duo 2007-05-20, 4:33 am |
|
"Bob L" <bob_lloyd@hotmail.com> wrote in message
news:- uadnWn0f_QZt9LbnZ2dn
UVZ_rOqnZ2d@comcast.com...
>
> "Core2Duo" < Core2Duo@theinternet
.com> wrote in message
> news:zDA3i.1580$wH4.971@news-server.bigpond.net.au...
>
> Since lat-lon are spherical coordinates simple cartesian math won't get
> you the lat-lon of point A. Try this link
> http://williams.best.vwh.net/avform.htm#Intersection
>
>
>
>
Thanks Bob.
I think I'll try the calculations you provided and compare them to nemo's
tips when I get a chance.
It'll be *interesting* to compare the results.
Just a thought: I'd require a computer to calculate point A using Ed
Williams's Aviation Formulary.
| |
|
| Just somthing a little different.
If you have a Garmin GPS, and their MapSource program, you may be able to
select each point on the map, and use the Route tool.
Drag the line out on the bearing. The bearing shows at the bottom of the
map.
(Set Routh Calculation to manual).
Don't know the finer details on the accuracy at large distances though.
--
Dana
"Core2Duo" < Core2Duo@theinternet
.com> wrote in message
news:zDA3i.1580$wH4.971@news-server.bigpond.net.au...
>I need to determine the coordinates of an inaccessible point A using the
>coordinates and bearings from 2 other accessible points B & C.
> The bearing lines from points B & C point towards point A and therefore
> intersect there.
>
> Any help dearly apppreciated.
>
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