Hi !
I'm searching for a robust way to cut a lat/lon segment (a segment over
earth's surface between 2 LatLonPoints) in multiple sub-segments (ie, find
N equally distributed points between two points).
I thought that the Geo class was the best choice, but I quickly ran into
problems.
That's why I created a little test program for the "Geo" class, which shows
potential bugs...
Before continuing with the test results, could you tell me if the "Geo"
class really was the best choice ? Should I have used GreatCircle instead ?
Maybe something else ?... Thanks in advance !
So, let's continue with the test program itself. It performs two tests on
two "Geo" points : g1 and g2 :
- Test 1 :
Computes the distance and azimuth from g1 to g2.
Moves g1 by this distance, and following this azimuth.
The result should be g2. We show the deviation between g2 and the observed
result.
- Test 2 :
[The first step is the same as test1's.]
Divides the distance by 10.
Moves 10 times g1 by this distance (still following the same azimuth).
Again the result should be g2. We show the deviation between g2 and the
observed result.
This program has been run on both openMap 4.6.3 and openMap 4.6.4b.
It shows that 4.6.4b implementation seems broken...
For both implementations, the second test shows high deviations !
In my case, little deviations are not a problem since distances are below 1
decimal degree. But 4.6.4b's deviations are far too high !!
And here is the output :
-----------------------------------------------------------
USING OPENMAP 4.6.3
-----------------------------------------------------------
g1 : Geo[20.0,20.0]
g2 : Geo[29.999999999999996,29.999999999999993]
distance (radians) : 0.23487253299926453
azimuth (radians) : 0.7040153367957178
g1 after offset (distance, azimuth) :
Geo[29.999999999999996,29.999999999999993]
Deviation from g2 (lat, lon) : (0.0, 0.0)
1/10 distance (radians) : 0.02348725329992645
Moving g1 (offset) 10 times, without changing azimuth, by this distance :
after offset 1 : Geo[21.02853320245362,20.932366413556945]
after offset 2 : Geo[22.056764030886367,21.871285544459013]
after offset 3 : Geo[23.084684148889718,22.817152986960153]
after offset 4 : Geo[24.112285318805373,23.770377508240788]
after offset 5 : Geo[25.139559402852676,24.731382071201555]
after offset 6 : Geo[26.16649836331953,25.70060492940822]
after offset 7 : Geo[27.19309426175399,26.678500801632477]
after offset 8 : Geo[28.219339257088087,27.665542134254125]
after offset 9 : Geo[29.24522560261881,28.662220460722107]
after offset 10 : Geo[30.270745641763757,29.66904786833158]
Deviation from g2 (lat, lon) : (-0.27074564176376015, 0.3309521316684112)
-----------------------------------------------------------
g1 : Geo[20.0,20.0]
g2 : Geo[40.00000000000001,80.0]
distance (radians) : 0.9534362072036422
azimuth (radians) : 0.9541945202085064
g1 after offset (distance, azimuth) : Geo[39.99999999999998,80.00000000000001]
Deviation from g2 (lat, lon) : (2.8421709430404007E-14,
-1.4210854715202004E-14)
1/10 distance (radians) : 0.09534362072036422
Moving g1 (offset) 10 times, without changing azimuth, by this distance :
after offset 1 : Geo[23.106955527243272,24.838982767838413]
after offset 2 : Geo[26.20095215725036,29.79837364605876]
after offset 3 : Geo[29.281283903720595,34.898892931740185]
after offset 4 : Geo[32.34715497252656,40.16367725585349]
after offset 5 : Geo[35.39766054765095,45.6188574286973]
after offset 6 : Geo[38.43176139254251,51.29427962161371]
after offset 7 : Geo[41.44825038924716,57.22441888539887]
after offset 8 : Geo[44.44570837586461,63.44955327525972]
after offset 9 : Geo[47.42244551735262,70.01729526907744]
after offset 10 : Geo[50.37642275309575,76.98461972142428]
Deviation from g2 (lat, lon) : (-10.376422753095746, 3.0153802785757193)
-----------------------------------------------------------
USING OPENMAP 4.6.4b
-----------------------------------------------------------
g1 : Geo[20.0,20.0]
g2 : Geo[29.999999999999996,29.999999999999993]
distance (radians) : 0.23487253299926453
azimuth (radians) : 0.6738791803760931
g1 after offset (distance, azimuth) : Geo[30.27824184184844,29.664327499230744]
Deviation from g2 (lat, lon) : (-0.2782418418484447, 0.3356725007692489)
1/10 distance (radians) : 0.02348725329992645
Moving g1 (offset) 10 times, without changing azimuth, by this distance :
after offset 1 : Geo[21.054615479862942,20.899012387668222]
after offset 2 : Geo[22.108926299466045,21.80451692628775]
after offset 3 : Geo[23.1629236643685,22.716915339478042]
after offset 4 : Geo[24.21659890231631,23.636623125331568]
after offset 5 : Geo[25.269943465157084,24.564070653699424]
after offset 6 : Geo[26.32294892972509,25.49970434324379]
after offset 7 : Geo[27.37560699762677,26.443987926717686]
after offset 8 : Geo[28.4279094938509,27.397403813894215]
after offset 9 : Geo[29.4798483641196,28.360454562663193]
after offset 10 : Geo[30.531415670888602,29.3336644700637]
Deviation from g2 (lat, lon) : (-0.531415670888606, 0.6663355299362941)
-----------------------------------------------------------
g1 : Geo[20.0,20.0]
g2 : Geo[40.00000000000001,80.0]
distance (radians) : 0.9534362072036422
azimuth (radians) : 0.9249371695398085
g1 after offset (distance, azimuth) : Geo[41.36598261305894,79.89583328336424]
Deviation from g2 (lat, lon) : (-1.3659826130589323, 0.10416671663575983)
1/10 distance (radians) : 0.09534362072036422
Moving g1 (offset) 10 times, without changing azimuth, by this distance :
after offset 1 : Geo[23.23921888006311,24.740982014513776]
after offset 2 : Geo[26.465307390769393,29.6061708120319]
after offset 3 : Geo[29.677503706192955,34.61787909360868]
after offset 4 : Geo[32.87494738293999,39.80119573293444]
after offset 5 : Geo[36.05665646556723,45.18468526615926]
after offset 6 : Geo[39.221496757280626,50.80127375015558]
after offset 7 : Geo[42.36814069287761,56.68938912280942]
after offset 8 : Geo[45.49501213015433,62.89445321022558]
after offset 9 : Geo[48.60021167293886,69.47086650377678]
after offset 10 : Geo[51.681414498457734,76.48469474221949]
Deviation from g2 (lat, lon) : (-11.681414498457727, 3.5153052577805113)
Regards,
Stephane
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Received on Wed Mar 21 2007 - 09:55:25 EDT