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From "Curtis Jensen (JIRA)" <j...@apache.org>
Subject [jira] [Updated] (MATH-880) Polygon difference produces erronious results in some cases
Date Fri, 12 Oct 2012 17:35:03 GMT

     [ https://issues.apache.org/jira/browse/MATH-880?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]

Curtis Jensen updated MATH-880:
-------------------------------

    Description: 
The 2D polygon difference method is returning incorrect
results.  Below is a test case of subtracting two polygons (Sorry,
this is the simplest case that I could find that duplicates the
problem).  

There are three problems with the result. The first is that the first
point of the first set of vertices is null (and the first point of the
second set is also null).  The second is that, even if the first null
points are ignored,  the returned polygon is not the correct result.
The first and last points are way off, and the remaining points do not
match the original polygon boundaries.  Additionally, there are two
holes that are returned in the results.  This subtraction case should
not have holes.

{code:title="Complex Polygon Difference Test"}
public void testComplexDifference() {
        Vector2D[][] vertices1 = new Vector2D[][] {
            new Vector2D[] {
                    new Vector2D( 90.08714908223715,  38.370299337260235),
                    new Vector2D( 90.08709517675004,  38.3702895991413),
                    new Vector2D( 90.08401538704919,  38.368849330127944),
                    new Vector2D( 90.08258210430711,  38.367634558585564),
                    new Vector2D( 90.08251455106665,  38.36763409247078),
                    new Vector2D( 90.08106599752608,  38.36761621664249),
                    new Vector2D( 90.08249585300035,  38.36753627557965),
                    new Vector2D( 90.09075743352184,  38.35914647644972),
                    new Vector2D( 90.09099945896571,  38.35896264724079),
                    new Vector2D( 90.09269383800086,  38.34595756121246),
                    new Vector2D( 90.09638631543191,  38.3457988093121),
                    new Vector2D( 90.09666417351019,  38.34523360999418),
                    new Vector2D( 90.1297082145872,  38.337670454923625),
                    new Vector2D( 90.12971687748956,  38.337669827794684),
                    new Vector2D( 90.1240820219179,  38.34328502001131),
                    new Vector2D( 90.13084259656404,  38.34017811765017),
                    new Vector2D( 90.13378567942857,  38.33860579180606),
                    new Vector2D( 90.13519557833206,  38.33621054663689),
                    new Vector2D( 90.13545616732307,  38.33614965452864),
                    new Vector2D( 90.13553111202748,  38.33613962818305),
                    new Vector2D( 90.1356903436448,  38.33610227127048),
                    new Vector2D( 90.13576283227428,  38.33609255422783),
                    new Vector2D( 90.13595870833188,  38.33604606376991),
                    new Vector2D( 90.1361556630693,  38.3360024198866),
                    new Vector2D( 90.13622408795709,  38.335987048115726),
                    new Vector2D( 90.13696189099994,  38.33581914328681),
                    new Vector2D( 90.13746655304897,  38.33616706665265),
                    new Vector2D( 90.13845973716064,  38.33650776167099),
                    new Vector2D( 90.13950901827667,  38.3368469456463),
                    new Vector2D( 90.14393814424852,  38.337591835857495),
                    new Vector2D( 90.14483839716831,  38.337076122362475),
                    new Vector2D( 90.14565474433601,  38.33769000964429),
                    new Vector2D( 90.14569421179482,  38.3377117256905),
                    new Vector2D( 90.14577067124333,  38.33770883625908),
                    new Vector2D( 90.14600350631684,  38.337714326520995),
                    new Vector2D( 90.14600355139731,  38.33771435193319),
                    new Vector2D( 90.14600369112401,  38.33771443882085),
                    new Vector2D( 90.14600382486884,  38.33771453466096),
                    new Vector2D( 90.14600395205912,  38.33771463904344),
                    new Vector2D( 90.14600407214999,  38.337714751520764),
                    new Vector2D( 90.14600418462749,  38.337714871611695),
                    new Vector2D( 90.14600422249327,  38.337714915811034),
                    new Vector2D( 90.14867838361471,  38.34113888210675),
                    new Vector2D( 90.14923750157374,  38.341582537502575),
                    new Vector2D( 90.14877083250991,  38.34160685841391),
                    new Vector2D( 90.14816667319519,  38.34244232585684),
                    new Vector2D( 90.14797696744586,  38.34248455284745),
                    new Vector2D( 90.14484318014337,  38.34385573215269),
                    new Vector2D( 90.14477919958296,  38.3453797747614),
                    new Vector2D( 90.14202393306448,  38.34464324839456),
                    new Vector2D( 90.14198920640195,  38.344651155237216),
                    new Vector2D( 90.14155207025175,  38.34486424263724),
                    new Vector2D( 90.1415196143314,  38.344871730519),
                    new Vector2D( 90.14128611910814,  38.34500196593859),
                    new Vector2D( 90.14047850603913,  38.34600084496253),
                    new Vector2D( 90.14045907000337,  38.34601860032171),
                    new Vector2D( 90.14039496493928,  38.346223030432384),
                    new Vector2D( 90.14037626063737,  38.346240203360026),
                    new Vector2D( 90.14030005823724,  38.34646920000705),
                    new Vector2D( 90.13799164754806,  38.34903093011013),
                    new Vector2D( 90.11045289492762,  38.36801537312368),
                    new Vector2D( 90.10871471476526,  38.36878044144294),
                    new Vector2D( 90.10424901707671,  38.374300101757),
                    new Vector2D( 90.10263482039932,  38.37310041316073),
                    new Vector2D( 90.09834601753448,  38.373615053823414),
                    new Vector2D( 90.0979455456843,  38.373578376172475),
                    new Vector2D( 90.09086514328669,  38.37527884194668),
                    new Vector2D( 90.09084931407364,  38.37590801712463),
                    new Vector2D( 90.09081227075944,  38.37526295920463),
                    new Vector2D( 90.09081378927135,  38.375193883266434)
            }
        };
        PolygonsSet set1 = buildSet(vertices1);

        Vector2D[][] vertices2 = new Vector2D[][] {
            new Vector2D[] {
                    new Vector2D( 90.13067558880044,  38.36977255037573),
                    new Vector2D( 90.12907570488,  38.36817308242706),
                    new Vector2D( 90.1342774136516,  38.356886880294724),
                    new Vector2D( 90.13090330629757,  38.34664392676211),
                    new Vector2D( 90.13078571364593,  38.344904617518466),
                    new Vector2D( 90.1315602208914,  38.3447185040846),
                    new Vector2D( 90.1316336226821,  38.34470643148342),
                    new Vector2D( 90.134020944832,  38.340936644972885),
                    new Vector2D( 90.13912536387306,  38.335497255122334),
                    new Vector2D( 90.1396178806582,  38.334878075552126),
                    new Vector2D( 90.14083049696671,  38.33316530644106),
                    new Vector2D( 90.14145252901329,  38.33152722916191),
                    new Vector2D( 90.1404779335565,  38.32863516047786),
                    new Vector2D( 90.14282712131586,  38.327504432532066),
                    new Vector2D( 90.14616669875488,  38.3237354115015),
                    new Vector2D( 90.14860976050608,  38.315714862457924),
                    new Vector2D( 90.14999277782437,  38.3164932507504),
                    new Vector2D( 90.15005207194997,  38.316534677663356),
                    new Vector2D( 90.15508513859612,  38.31878731691609),
                    new Vector2D( 90.15919938519221,  38.31852743183782),
                    new Vector2D( 90.16093758658837,  38.31880662005153),
                    new Vector2D( 90.16099420184912,  38.318825953291594),
                    new Vector2D( 90.1665411125756,  38.31859497874757),
                    new Vector2D( 90.16999653861313,  38.32505772048029),
                    new Vector2D( 90.17475243391698,  38.32594398441148),
                    new Vector2D( 90.17940844844992,  38.327427213761325),
                    new Vector2D( 90.20951909541378,  38.330616833491774),
                    new Vector2D( 90.2155400467941,  38.331746223670336),
                    new Vector2D( 90.21559881391778,  38.33175551425302),
                    new Vector2D( 90.21916646426041,  38.332584299620805),
                    new Vector2D( 90.23863749852285,  38.34778978875795),
                    new Vector2D( 90.25459855175802,  38.357790570608984),
                    new Vector2D( 90.25964298227257,  38.356918010203174),
                    new Vector2D( 90.26024593994703,  38.361692743151366),
                    new Vector2D( 90.26146187570015,  38.36311080550837),
                    new Vector2D( 90.26614159359622,  38.36510808579902),
                    new Vector2D( 90.26621342936448,  38.36507942500333),
                    new Vector2D( 90.26652190211962,  38.36494042196722),
                    new Vector2D( 90.26621240678867,  38.365113172030874),
                    new Vector2D( 90.26614057102057,  38.365141832826794),
                    new Vector2D( 90.26380080055299,  38.3660381760273),
                    new Vector2D( 90.26315345241,  38.36670658276421),
                    new Vector2D( 90.26251574942881,  38.367490323488084),
                    new Vector2D( 90.26247873448426,  38.36755266444749),
                    new Vector2D( 90.26234628016698,  38.36787989125406),
                    new Vector2D( 90.26214559424784,  38.36945909356126),
                    new Vector2D( 90.25861728442555,  38.37200753430875),
                    new Vector2D( 90.23905557537864,  38.375405314295904),
                    new Vector2D( 90.22517251874075,  38.38984691662256),
                    new Vector2D( 90.22549955153215,  38.3911564273979),
                    new Vector2D( 90.22434386063355,  38.391476432092134),
                    new Vector2D( 90.22147729457276,  38.39134652252034),
                    new Vector2D( 90.22142070120117,  38.391349167741964),
                    new Vector2D( 90.20665060751588,  38.39475580900313),
                    new Vector2D( 90.20042268367109,  38.39842558622888),
                    new Vector2D( 90.17423771242085,  38.402727751805344),
                    new Vector2D( 90.16756796257476,  38.40913898597597),
                    new Vector2D( 90.16728283954308,  38.411255399912875),
                    new Vector2D( 90.16703538220418,  38.41136059866693),
                    new Vector2D( 90.16725865657685,  38.41013618805954),
                    new Vector2D( 90.16746107640665,  38.40902614307544),
                    new Vector2D( 90.16122795307462,  38.39773101873203)
            }
        };
        PolygonsSet set2 = buildSet(vertices2);
        PolygonsSet set  = (PolygonsSet) new
RegionFactory<Euclidean2D>().difference(set1.copySelf(),

              set2.copySelf());

        Vector2D[][] verticies = set.getVertices();
        Assert.assertTrue(verticies[0][0] != null);
        Assert.assertEquals(1, verticies.length);
    }
{code}

  was:
The 2D polygon difference method is returning incorrect
results.  Below is a test case of subtracting two polygons (Sorry,
this is the simplest case that I could find that duplicates the
problem).  

There are three problems with the result. The first is that the first
point of the first set of vertices is null (and the first point of the
second set is also null).  The second is that, even if the first null
points are ignored,  the returned polygon is not the correct result.
The first and last points are way off, and the remaining points do not
match the original polygon boundaries.  Additionally, there are two
holes that are returned in the results.  This subtraction case should
not have holes.

public void testComplexDifference() {
        Vector2D[][] vertices1 = new Vector2D[][] {
            new Vector2D[] {
                    new Vector2D( 90.08714908223715,  38.370299337260235),
                    new Vector2D( 90.08709517675004,  38.3702895991413),
                    new Vector2D( 90.08401538704919,  38.368849330127944),
                    new Vector2D( 90.08258210430711,  38.367634558585564),
                    new Vector2D( 90.08251455106665,  38.36763409247078),
                    new Vector2D( 90.08106599752608,  38.36761621664249),
                    new Vector2D( 90.08249585300035,  38.36753627557965),
                    new Vector2D( 90.09075743352184,  38.35914647644972),
                    new Vector2D( 90.09099945896571,  38.35896264724079),
                    new Vector2D( 90.09269383800086,  38.34595756121246),
                    new Vector2D( 90.09638631543191,  38.3457988093121),
                    new Vector2D( 90.09666417351019,  38.34523360999418),
                    new Vector2D( 90.1297082145872,  38.337670454923625),
                    new Vector2D( 90.12971687748956,  38.337669827794684),
                    new Vector2D( 90.1240820219179,  38.34328502001131),
                    new Vector2D( 90.13084259656404,  38.34017811765017),
                    new Vector2D( 90.13378567942857,  38.33860579180606),
                    new Vector2D( 90.13519557833206,  38.33621054663689),
                    new Vector2D( 90.13545616732307,  38.33614965452864),
                    new Vector2D( 90.13553111202748,  38.33613962818305),
                    new Vector2D( 90.1356903436448,  38.33610227127048),
                    new Vector2D( 90.13576283227428,  38.33609255422783),
                    new Vector2D( 90.13595870833188,  38.33604606376991),
                    new Vector2D( 90.1361556630693,  38.3360024198866),
                    new Vector2D( 90.13622408795709,  38.335987048115726),
                    new Vector2D( 90.13696189099994,  38.33581914328681),
                    new Vector2D( 90.13746655304897,  38.33616706665265),
                    new Vector2D( 90.13845973716064,  38.33650776167099),
                    new Vector2D( 90.13950901827667,  38.3368469456463),
                    new Vector2D( 90.14393814424852,  38.337591835857495),
                    new Vector2D( 90.14483839716831,  38.337076122362475),
                    new Vector2D( 90.14565474433601,  38.33769000964429),
                    new Vector2D( 90.14569421179482,  38.3377117256905),
                    new Vector2D( 90.14577067124333,  38.33770883625908),
                    new Vector2D( 90.14600350631684,  38.337714326520995),
                    new Vector2D( 90.14600355139731,  38.33771435193319),
                    new Vector2D( 90.14600369112401,  38.33771443882085),
                    new Vector2D( 90.14600382486884,  38.33771453466096),
                    new Vector2D( 90.14600395205912,  38.33771463904344),
                    new Vector2D( 90.14600407214999,  38.337714751520764),
                    new Vector2D( 90.14600418462749,  38.337714871611695),
                    new Vector2D( 90.14600422249327,  38.337714915811034),
                    new Vector2D( 90.14867838361471,  38.34113888210675),
                    new Vector2D( 90.14923750157374,  38.341582537502575),
                    new Vector2D( 90.14877083250991,  38.34160685841391),
                    new Vector2D( 90.14816667319519,  38.34244232585684),
                    new Vector2D( 90.14797696744586,  38.34248455284745),
                    new Vector2D( 90.14484318014337,  38.34385573215269),
                    new Vector2D( 90.14477919958296,  38.3453797747614),
                    new Vector2D( 90.14202393306448,  38.34464324839456),
                    new Vector2D( 90.14198920640195,  38.344651155237216),
                    new Vector2D( 90.14155207025175,  38.34486424263724),
                    new Vector2D( 90.1415196143314,  38.344871730519),
                    new Vector2D( 90.14128611910814,  38.34500196593859),
                    new Vector2D( 90.14047850603913,  38.34600084496253),
                    new Vector2D( 90.14045907000337,  38.34601860032171),
                    new Vector2D( 90.14039496493928,  38.346223030432384),
                    new Vector2D( 90.14037626063737,  38.346240203360026),
                    new Vector2D( 90.14030005823724,  38.34646920000705),
                    new Vector2D( 90.13799164754806,  38.34903093011013),
                    new Vector2D( 90.11045289492762,  38.36801537312368),
                    new Vector2D( 90.10871471476526,  38.36878044144294),
                    new Vector2D( 90.10424901707671,  38.374300101757),
                    new Vector2D( 90.10263482039932,  38.37310041316073),
                    new Vector2D( 90.09834601753448,  38.373615053823414),
                    new Vector2D( 90.0979455456843,  38.373578376172475),
                    new Vector2D( 90.09086514328669,  38.37527884194668),
                    new Vector2D( 90.09084931407364,  38.37590801712463),
                    new Vector2D( 90.09081227075944,  38.37526295920463),
                    new Vector2D( 90.09081378927135,  38.375193883266434)
            }
        };
        PolygonsSet set1 = buildSet(vertices1);

        Vector2D[][] vertices2 = new Vector2D[][] {
            new Vector2D[] {
                    new Vector2D( 90.13067558880044,  38.36977255037573),
                    new Vector2D( 90.12907570488,  38.36817308242706),
                    new Vector2D( 90.1342774136516,  38.356886880294724),
                    new Vector2D( 90.13090330629757,  38.34664392676211),
                    new Vector2D( 90.13078571364593,  38.344904617518466),
                    new Vector2D( 90.1315602208914,  38.3447185040846),
                    new Vector2D( 90.1316336226821,  38.34470643148342),
                    new Vector2D( 90.134020944832,  38.340936644972885),
                    new Vector2D( 90.13912536387306,  38.335497255122334),
                    new Vector2D( 90.1396178806582,  38.334878075552126),
                    new Vector2D( 90.14083049696671,  38.33316530644106),
                    new Vector2D( 90.14145252901329,  38.33152722916191),
                    new Vector2D( 90.1404779335565,  38.32863516047786),
                    new Vector2D( 90.14282712131586,  38.327504432532066),
                    new Vector2D( 90.14616669875488,  38.3237354115015),
                    new Vector2D( 90.14860976050608,  38.315714862457924),
                    new Vector2D( 90.14999277782437,  38.3164932507504),
                    new Vector2D( 90.15005207194997,  38.316534677663356),
                    new Vector2D( 90.15508513859612,  38.31878731691609),
                    new Vector2D( 90.15919938519221,  38.31852743183782),
                    new Vector2D( 90.16093758658837,  38.31880662005153),
                    new Vector2D( 90.16099420184912,  38.318825953291594),
                    new Vector2D( 90.1665411125756,  38.31859497874757),
                    new Vector2D( 90.16999653861313,  38.32505772048029),
                    new Vector2D( 90.17475243391698,  38.32594398441148),
                    new Vector2D( 90.17940844844992,  38.327427213761325),
                    new Vector2D( 90.20951909541378,  38.330616833491774),
                    new Vector2D( 90.2155400467941,  38.331746223670336),
                    new Vector2D( 90.21559881391778,  38.33175551425302),
                    new Vector2D( 90.21916646426041,  38.332584299620805),
                    new Vector2D( 90.23863749852285,  38.34778978875795),
                    new Vector2D( 90.25459855175802,  38.357790570608984),
                    new Vector2D( 90.25964298227257,  38.356918010203174),
                    new Vector2D( 90.26024593994703,  38.361692743151366),
                    new Vector2D( 90.26146187570015,  38.36311080550837),
                    new Vector2D( 90.26614159359622,  38.36510808579902),
                    new Vector2D( 90.26621342936448,  38.36507942500333),
                    new Vector2D( 90.26652190211962,  38.36494042196722),
                    new Vector2D( 90.26621240678867,  38.365113172030874),
                    new Vector2D( 90.26614057102057,  38.365141832826794),
                    new Vector2D( 90.26380080055299,  38.3660381760273),
                    new Vector2D( 90.26315345241,  38.36670658276421),
                    new Vector2D( 90.26251574942881,  38.367490323488084),
                    new Vector2D( 90.26247873448426,  38.36755266444749),
                    new Vector2D( 90.26234628016698,  38.36787989125406),
                    new Vector2D( 90.26214559424784,  38.36945909356126),
                    new Vector2D( 90.25861728442555,  38.37200753430875),
                    new Vector2D( 90.23905557537864,  38.375405314295904),
                    new Vector2D( 90.22517251874075,  38.38984691662256),
                    new Vector2D( 90.22549955153215,  38.3911564273979),
                    new Vector2D( 90.22434386063355,  38.391476432092134),
                    new Vector2D( 90.22147729457276,  38.39134652252034),
                    new Vector2D( 90.22142070120117,  38.391349167741964),
                    new Vector2D( 90.20665060751588,  38.39475580900313),
                    new Vector2D( 90.20042268367109,  38.39842558622888),
                    new Vector2D( 90.17423771242085,  38.402727751805344),
                    new Vector2D( 90.16756796257476,  38.40913898597597),
                    new Vector2D( 90.16728283954308,  38.411255399912875),
                    new Vector2D( 90.16703538220418,  38.41136059866693),
                    new Vector2D( 90.16725865657685,  38.41013618805954),
                    new Vector2D( 90.16746107640665,  38.40902614307544),
                    new Vector2D( 90.16122795307462,  38.39773101873203)
            }
        };
        PolygonsSet set2 = buildSet(vertices2);
        PolygonsSet set  = (PolygonsSet) new
RegionFactory<Euclidean2D>().difference(set1.copySelf(),

              set2.copySelf());

        Vector2D[][] verticies = set.getVertices();
        Assert.assertTrue(verticies[0][0] != null);
        Assert.assertEquals(1, verticies.length);
    }

    
> Polygon difference produces erronious results in some cases
> -----------------------------------------------------------
>
>                 Key: MATH-880
>                 URL: https://issues.apache.org/jira/browse/MATH-880
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.0
>            Reporter: Curtis Jensen
>             Fix For: 3.1
>
>
> The 2D polygon difference method is returning incorrect
> results.  Below is a test case of subtracting two polygons (Sorry,
> this is the simplest case that I could find that duplicates the
> problem).  
> There are three problems with the result. The first is that the first
> point of the first set of vertices is null (and the first point of the
> second set is also null).  The second is that, even if the first null
> points are ignored,  the returned polygon is not the correct result.
> The first and last points are way off, and the remaining points do not
> match the original polygon boundaries.  Additionally, there are two
> holes that are returned in the results.  This subtraction case should
> not have holes.
> {code:title="Complex Polygon Difference Test"}
> public void testComplexDifference() {
>         Vector2D[][] vertices1 = new Vector2D[][] {
>             new Vector2D[] {
>                     new Vector2D( 90.08714908223715,  38.370299337260235),
>                     new Vector2D( 90.08709517675004,  38.3702895991413),
>                     new Vector2D( 90.08401538704919,  38.368849330127944),
>                     new Vector2D( 90.08258210430711,  38.367634558585564),
>                     new Vector2D( 90.08251455106665,  38.36763409247078),
>                     new Vector2D( 90.08106599752608,  38.36761621664249),
>                     new Vector2D( 90.08249585300035,  38.36753627557965),
>                     new Vector2D( 90.09075743352184,  38.35914647644972),
>                     new Vector2D( 90.09099945896571,  38.35896264724079),
>                     new Vector2D( 90.09269383800086,  38.34595756121246),
>                     new Vector2D( 90.09638631543191,  38.3457988093121),
>                     new Vector2D( 90.09666417351019,  38.34523360999418),
>                     new Vector2D( 90.1297082145872,  38.337670454923625),
>                     new Vector2D( 90.12971687748956,  38.337669827794684),
>                     new Vector2D( 90.1240820219179,  38.34328502001131),
>                     new Vector2D( 90.13084259656404,  38.34017811765017),
>                     new Vector2D( 90.13378567942857,  38.33860579180606),
>                     new Vector2D( 90.13519557833206,  38.33621054663689),
>                     new Vector2D( 90.13545616732307,  38.33614965452864),
>                     new Vector2D( 90.13553111202748,  38.33613962818305),
>                     new Vector2D( 90.1356903436448,  38.33610227127048),
>                     new Vector2D( 90.13576283227428,  38.33609255422783),
>                     new Vector2D( 90.13595870833188,  38.33604606376991),
>                     new Vector2D( 90.1361556630693,  38.3360024198866),
>                     new Vector2D( 90.13622408795709,  38.335987048115726),
>                     new Vector2D( 90.13696189099994,  38.33581914328681),
>                     new Vector2D( 90.13746655304897,  38.33616706665265),
>                     new Vector2D( 90.13845973716064,  38.33650776167099),
>                     new Vector2D( 90.13950901827667,  38.3368469456463),
>                     new Vector2D( 90.14393814424852,  38.337591835857495),
>                     new Vector2D( 90.14483839716831,  38.337076122362475),
>                     new Vector2D( 90.14565474433601,  38.33769000964429),
>                     new Vector2D( 90.14569421179482,  38.3377117256905),
>                     new Vector2D( 90.14577067124333,  38.33770883625908),
>                     new Vector2D( 90.14600350631684,  38.337714326520995),
>                     new Vector2D( 90.14600355139731,  38.33771435193319),
>                     new Vector2D( 90.14600369112401,  38.33771443882085),
>                     new Vector2D( 90.14600382486884,  38.33771453466096),
>                     new Vector2D( 90.14600395205912,  38.33771463904344),
>                     new Vector2D( 90.14600407214999,  38.337714751520764),
>                     new Vector2D( 90.14600418462749,  38.337714871611695),
>                     new Vector2D( 90.14600422249327,  38.337714915811034),
>                     new Vector2D( 90.14867838361471,  38.34113888210675),
>                     new Vector2D( 90.14923750157374,  38.341582537502575),
>                     new Vector2D( 90.14877083250991,  38.34160685841391),
>                     new Vector2D( 90.14816667319519,  38.34244232585684),
>                     new Vector2D( 90.14797696744586,  38.34248455284745),
>                     new Vector2D( 90.14484318014337,  38.34385573215269),
>                     new Vector2D( 90.14477919958296,  38.3453797747614),
>                     new Vector2D( 90.14202393306448,  38.34464324839456),
>                     new Vector2D( 90.14198920640195,  38.344651155237216),
>                     new Vector2D( 90.14155207025175,  38.34486424263724),
>                     new Vector2D( 90.1415196143314,  38.344871730519),
>                     new Vector2D( 90.14128611910814,  38.34500196593859),
>                     new Vector2D( 90.14047850603913,  38.34600084496253),
>                     new Vector2D( 90.14045907000337,  38.34601860032171),
>                     new Vector2D( 90.14039496493928,  38.346223030432384),
>                     new Vector2D( 90.14037626063737,  38.346240203360026),
>                     new Vector2D( 90.14030005823724,  38.34646920000705),
>                     new Vector2D( 90.13799164754806,  38.34903093011013),
>                     new Vector2D( 90.11045289492762,  38.36801537312368),
>                     new Vector2D( 90.10871471476526,  38.36878044144294),
>                     new Vector2D( 90.10424901707671,  38.374300101757),
>                     new Vector2D( 90.10263482039932,  38.37310041316073),
>                     new Vector2D( 90.09834601753448,  38.373615053823414),
>                     new Vector2D( 90.0979455456843,  38.373578376172475),
>                     new Vector2D( 90.09086514328669,  38.37527884194668),
>                     new Vector2D( 90.09084931407364,  38.37590801712463),
>                     new Vector2D( 90.09081227075944,  38.37526295920463),
>                     new Vector2D( 90.09081378927135,  38.375193883266434)
>             }
>         };
>         PolygonsSet set1 = buildSet(vertices1);
>         Vector2D[][] vertices2 = new Vector2D[][] {
>             new Vector2D[] {
>                     new Vector2D( 90.13067558880044,  38.36977255037573),
>                     new Vector2D( 90.12907570488,  38.36817308242706),
>                     new Vector2D( 90.1342774136516,  38.356886880294724),
>                     new Vector2D( 90.13090330629757,  38.34664392676211),
>                     new Vector2D( 90.13078571364593,  38.344904617518466),
>                     new Vector2D( 90.1315602208914,  38.3447185040846),
>                     new Vector2D( 90.1316336226821,  38.34470643148342),
>                     new Vector2D( 90.134020944832,  38.340936644972885),
>                     new Vector2D( 90.13912536387306,  38.335497255122334),
>                     new Vector2D( 90.1396178806582,  38.334878075552126),
>                     new Vector2D( 90.14083049696671,  38.33316530644106),
>                     new Vector2D( 90.14145252901329,  38.33152722916191),
>                     new Vector2D( 90.1404779335565,  38.32863516047786),
>                     new Vector2D( 90.14282712131586,  38.327504432532066),
>                     new Vector2D( 90.14616669875488,  38.3237354115015),
>                     new Vector2D( 90.14860976050608,  38.315714862457924),
>                     new Vector2D( 90.14999277782437,  38.3164932507504),
>                     new Vector2D( 90.15005207194997,  38.316534677663356),
>                     new Vector2D( 90.15508513859612,  38.31878731691609),
>                     new Vector2D( 90.15919938519221,  38.31852743183782),
>                     new Vector2D( 90.16093758658837,  38.31880662005153),
>                     new Vector2D( 90.16099420184912,  38.318825953291594),
>                     new Vector2D( 90.1665411125756,  38.31859497874757),
>                     new Vector2D( 90.16999653861313,  38.32505772048029),
>                     new Vector2D( 90.17475243391698,  38.32594398441148),
>                     new Vector2D( 90.17940844844992,  38.327427213761325),
>                     new Vector2D( 90.20951909541378,  38.330616833491774),
>                     new Vector2D( 90.2155400467941,  38.331746223670336),
>                     new Vector2D( 90.21559881391778,  38.33175551425302),
>                     new Vector2D( 90.21916646426041,  38.332584299620805),
>                     new Vector2D( 90.23863749852285,  38.34778978875795),
>                     new Vector2D( 90.25459855175802,  38.357790570608984),
>                     new Vector2D( 90.25964298227257,  38.356918010203174),
>                     new Vector2D( 90.26024593994703,  38.361692743151366),
>                     new Vector2D( 90.26146187570015,  38.36311080550837),
>                     new Vector2D( 90.26614159359622,  38.36510808579902),
>                     new Vector2D( 90.26621342936448,  38.36507942500333),
>                     new Vector2D( 90.26652190211962,  38.36494042196722),
>                     new Vector2D( 90.26621240678867,  38.365113172030874),
>                     new Vector2D( 90.26614057102057,  38.365141832826794),
>                     new Vector2D( 90.26380080055299,  38.3660381760273),
>                     new Vector2D( 90.26315345241,  38.36670658276421),
>                     new Vector2D( 90.26251574942881,  38.367490323488084),
>                     new Vector2D( 90.26247873448426,  38.36755266444749),
>                     new Vector2D( 90.26234628016698,  38.36787989125406),
>                     new Vector2D( 90.26214559424784,  38.36945909356126),
>                     new Vector2D( 90.25861728442555,  38.37200753430875),
>                     new Vector2D( 90.23905557537864,  38.375405314295904),
>                     new Vector2D( 90.22517251874075,  38.38984691662256),
>                     new Vector2D( 90.22549955153215,  38.3911564273979),
>                     new Vector2D( 90.22434386063355,  38.391476432092134),
>                     new Vector2D( 90.22147729457276,  38.39134652252034),
>                     new Vector2D( 90.22142070120117,  38.391349167741964),
>                     new Vector2D( 90.20665060751588,  38.39475580900313),
>                     new Vector2D( 90.20042268367109,  38.39842558622888),
>                     new Vector2D( 90.17423771242085,  38.402727751805344),
>                     new Vector2D( 90.16756796257476,  38.40913898597597),
>                     new Vector2D( 90.16728283954308,  38.411255399912875),
>                     new Vector2D( 90.16703538220418,  38.41136059866693),
>                     new Vector2D( 90.16725865657685,  38.41013618805954),
>                     new Vector2D( 90.16746107640665,  38.40902614307544),
>                     new Vector2D( 90.16122795307462,  38.39773101873203)
>             }
>         };
>         PolygonsSet set2 = buildSet(vertices2);
>         PolygonsSet set  = (PolygonsSet) new
> RegionFactory<Euclidean2D>().difference(set1.copySelf(),
>               set2.copySelf());
>         Vector2D[][] verticies = set.getVertices();
>         Assert.assertTrue(verticies[0][0] != null);
>         Assert.assertEquals(1, verticies.length);
>     }
> {code}

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