http://www.ga.gov.au/nmd/geodesy/datums/distance.jsp
has a table showing the difference between different computations.
com.bbn.openmap.geo.Geo converts the geographic latitude into geocentric latitude and then does a spherical calculation using vector math. This shifts the latitude down a bit. The greatest amount is at 45 degress and is 0.19 degrees or about 11 nautical miles.
At 10:48 AM 9/30/2004 -0400, Tony Bigbee wrote:
>>On Sep 30, 2004, at 7:18 AM, Ahmed Al-Obaidy wrote:
>>
>>>Hi
>>>
>>>I am new to GIS..
>>>i'll be glade if someone answer me
>>>which one is better OpenMap or Geotools?
>
>Instead of 'better', I was interested in differences in great circle distance calculation using spheroid versus an ellipsoid as an earth model. Geotools has a very easy way to do this for ellipsoid approach and I compared varying distances at varying latitudes to understand the differences. In short, there is < 1% difference between the distances using either at any distance and any part of the earth--that's small, although it will matter in certain applications. Here is the data I generated (sorry for so many digits of precision). Below these tables are source code fragments showing how Geotools versus OpenMap methods are used.
>
>Delta between longitudes = 0.01 (deg)
>Latitude(deg) Ellipsoid(km) Sphere(km)
>delta(meters)
>0.0 1.113194907792064 1.1131949060017068
>1.790357146091992E-6
>5.0 1.108987062175152 1.1089588637318644
>0.0281984432876925
>10.0 1.0963936405188375 1.096282977962477
>0.11066255636046662
>15.0 1.0755048869765549 1.075263706042469
>0.24118093408583263
>20.0 1.0464708628681796 1.0460610371856813
>0.4098256824984219
>25.0 1.0095009025574666 1.0088972135103194
>0.6036890471472134
>30.0 0.9648628021710947 0.9640550641413635
>0.8077380297310128
>35.0 0.9128816960636721 0.9118758883816486
>1.0058076820234874
>40.0 0.853938569131024 0.852756775472505
>1.1817936585189273
>45.0 0.7884683504373743 0.7871476634477133
>1.3206869896609987
>50.0 0.7169575356263551 0.7155478936740587
>1.4096419522965107
>55.0 0.6399412924332541 0.6385023724414035
>1.4389199918506392
>60.0 0.5580000151941596 0.5565974504424106
>1.4025647517490825
>65.0 0.47175531000231463 0.47045650110206116
>1.298808900253448
>70.0 0.38186541230256915 0.38073509637702
>1.130315925549155
>75.0 0.28902005775281664 0.2881160387584101
>0.904018994406556
>80.0 0.19393485504259525 0.19330429084661938
>0.6305641959758645
>85.0 0.0973452256503901 0.09702127714238581
>0.3239485080042783
>Delta between longitudes = 0.1 (deg)
>Latitude(deg) Ellipsoid(km) Sphere(km)
>delta(meters)
>0.0 11.131949079322641 11.13194907934957
>2.692831913009286E-8
>5.0 11.08987061252135 11.08958864158325
>0.2819709381001303
>10.0 10.96393636486906 10.962829717772614
>1.1066470964451582
>15.0 10.755048780265458 10.752637021035254
>2.4117592302045523
>20.0 10.46470847566653 10.460610249336627
>4.0982263299029
>25.0 10.095008799596467 10.088971906834137
>6.036892762331263
>30.0 9.648627718998803 9.640550389978836
>8.077329019966783
>35.0 9.128816583259336 9.118758464956947
>10.05811830238963
>40.0 8.539385247966706 8.527567286659664
>11.817961307042424
>45.0 7.8846830089999695 7.871476182292002
>13.206826707967593
>50.0 7.169574827599109 7.155478406897489
>14.096420701620445
>55.0 6.39941238476242 6.385023139543167
>14.389245219253098
>60.0 5.579999626076697 5.565974009833259
>14.02561624343707
>65.0 4.717552614140225 4.704564479153118
>12.988134987107514
>70.0 3.818653699556946 3.8073503945816474
>11.303304975298488
>75.0 2.8902002386885184 2.8811600889135227
>9.040149774995825
>80.0 1.9393483140858256 1.933042434481714
>6.305879604111624
>85.0 0.9734521351142168 0.9702131633799607
>3.238971734256097
>Delta between longitudes = 1.0 (deg)
>Latitude(deg) Ellipsoid(km) Sphere(km)
>delta(meters)
>0.0 111.31949079322642 111.31949079326246
>3.604509402066469E-8
>5.0 110.89869553973436 110.8958758303873
>2.8197093470662367
>10.0 109.6393221056147 109.62825563618095
>11.066469433731982
>15.0 107.5503972719354 107.52627970189245
>24.117570042944863
>20.0 104.64693093380886 104.6059487323737
>40.982201435166644
>25.0 100.94986143105032 100.88949263839062
>60.36879265970492
>30.0 96.48597408441964 96.40520105245892
>80.77303196072171
>35.0 91.28778845027853 91.18720767602323
>100.58077425530064
>40.0 85.39340913015818 85.27523012385468
>118.1790063035005
>45.0 78.84633471022002 78.71426727213426
>132.06743808575266
>50.0 71.6952196063252 71.55425643850035
>140.96316782484064
>55.0 63.9935842734606 63.84969302685498
>143.89124660562084
>60.0 55.79947039335792 55.659215552649066
>140.25484070885432
>65.0 47.175039232263096 47.045159223665266
>129.88000859782915
>70.0 38.1861132933543 38.07308148095403
>113.03181240027334
>75.0 28.901663548081412 28.811263117056082
>90.40043102532945
>80.0 19.393246801387026 19.330188764719583
>63.05803666744032
>85.0 9.734399961888634 9.702010694567285
>32.3892673213486
>Delta between longitudes = 10.0 (deg)
>Latitude(deg) Ellipsoid(km) Sphere(km)
>delta(meters)
>0.0 1113.1949079327344 1113.1949079327371
>2.7939677238464355E-9
>5.0 1108.9763376391795 1108.9481410328883
>28.19660629122518
>10.0 1096.3515545709338 1096.2408948962507
>110.6596746831201
>15.0 1075.4131847022704 1075.172031003202
>241.1536990685854
>20.0 1046.3150761097374 1045.9053169944357
>409.7591153017711
>25.0 1009.2714935842372 1008.6679446577012
>603.5489265359938
>30.0 964.5559669442339 963.7484944716215
>807.4724726123968
>35.0 912.4997712220787 911.4943836106073
>1005.3876114714658
>40.0 853.4900138892174 852.3088415647851
>1181.172324432293
>45.0 787.9673036110453 786.6474626653888
>1319.8409456564113
>50.0 716.42297700166 715.0143877102034
>1408.5892914566211
>55.0 639.3958647022039 637.9581675945327
>1437.697107671178
>60.0 557.4685858573904 556.0673605521295
>1401.225305260974
>65.0 471.2633705226865 469.9659116003878
>1297.4589222986833
>70.0 381.43742227292074 380.3083584609918
>1129.063811928907
>75.0 288.6778476396906 287.7749030439621
>902.9445957284188
>80.0 193.69619412615276 193.06638201745182
>629.8121087009495
>85.0 97.22265341992157 96.89916450578704
>323.48891413453384
>Delta between longitudes = 100.0 (deg)
>Latitude(deg) Ellipsoid(km) Sphere(km)
>delta(meters)
>0.0 11131.949079327342 11131.949079327356
>1.4901161193847656E-8
>5.0 11074.491873849898 11074.254894524236
>236.97932566329837
>10.0 10904.359976941214 10903.418765269173
>941.2116720415652
>15.0 10627.860778648377 10625.775928024572
>2084.850623805076
>20.0 10254.301299970357 10250.697903355796
>3603.3966145608574
>25.0 9794.653276021594 9789.266119389758
>5387.156631836668
>30.0 9260.333396774788 9253.04585258056
>7287.5441942270845
>35.0 8662.315888923762 8653.180752132841
>9135.136790921912
>40.0 8010.615952982325 7999.854606853046
>10761.346129279584
>45.0 7314.0750071550565 7302.057954675393
>12017.052479662932
>50.0 6580.346792131377 6567.561468135687
>12785.32399568893
>55.0 5815.995557198364 5803.007346970454
>12988.210227909498
>60.0 5026.644058681537 5014.055202274522
>12588.856407014653
>65.0 4217.13394292686 4205.543591693387
>11590.351233473979
>70.0 3391.679088879379 3381.6466553441437
>10032.433535235468
>75.0 2554.0038003717677 2546.0169769587187
>7986.823413048871
>80.0 1707.4641604261387 1701.9125003059328
>5551.660120205954
>85.0 855.1541883143486 852.3088415647799
>2845.3467495687073
>
>
>import org.geotools.cs.Ellipsoid;
>import org.geotools.units.Unit;
>import com.bbn.openmap.geo.Geo;
>import com.bbn.openmap.proj.GreatCircle;
>
>//calculating great circle distances using ellipsoid with Geotools
>double km = 1d/1000d; //do the division now and use to convert meters to km when desired.
>//create an ellipsoid earth model based on WGS84
>Ellipsoid ellip = Ellipsoid.WGS84; //only instantiate an Ellipsoid once!
>//get the distance in meters given long1, lat1, long2, lat2. Note the order!
>//call ellip.orthodromicDistance whenever needed to calculate distance
>double distance = ellip.orthodromicDistance(117.5, 34,117.55,34.01);
>System.out.println(distance*km);
>
>//you can also create your own ellipsoid and make it spherical if desired:
>Unit meter = Unit.METRE;
>Ellipsoid sphere = Ellipsoid.createEllipsoid("earth-sphere",6378137.0,6378137.0,meter);
>
>//calculate great circle distance using OpenMap spherical model
>//note: coordinates order is different than Geotools
>Float om_distance = GreatCircle.spherical_distance(lat1,long1,lat2,long2);
>
>Tony
>
>
>--
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Received on Thu Sep 30 2004 - 12:58:46 EDT