How would I generalize multiple adjacent polygons?

Question

When you have a table with a Geometry type field (or Geography), you can call the Reduce() function to have the shapes reduced in number of vertices. Works very nicely. However, when sevral of the polygons are adjacent (they share parts of their borders), the reduced polygons do not necessarily do so.

Example

The SQL batch:

CREATE TABLE #Shapes (
shape geometry,
naam varchar(50)
 )

-- exact:
insert into #Shapes (naam, shape) VALUES ('Area A',Geometry::STGeomFromText('POLYGON ((52.084744368912652 5.1304192959796637, 52.085234231548384 5.1304194002877921, 52.085474282948049 5.1304486630822, 52.0857341082301 5.1304792705923319, 52.086134375073016 5.1306082883384079, 52.086594087770209 5.13079824927263, 52.087194303050637 5.1311187236569822, 52.089074697112665 5.1323992793913931, 52.089834430487826 5.1333390253130347, 52.090353938518092 5.1341692635323852, 52.090254480473 5.1342997345712416, 52.090824429301414 5.13520842681262, 52.09141399711384 5.1360295349486274, 52.091884278226644 5.1365492835175246, 52.092085719574243 5.1367767199408263, 52.092194211203605 5.1368992186617106, 52.092494247804545 5.1372492032188495, 52.092884057915427 5.13754907634854, 52.093083867570385 5.137679290259257, 52.093254011290028 5.1378082139755827, 52.093554640188813 5.1380093733314425, 52.094204571098089 5.1384683684445918, 52.094214495038614 5.1384888619650155, 52.093702809136488 5.1390791568504124, 52.0939114689827 5.1395669728517532, 52.0938675517682 5.1396009074524045, 52.093849835848111 5.1396084928439114, 52.093797143315896 5.1396473892964423, 52.093789743114428 5.1396500989447063, 52.093731224210721 5.13969055645838, 52.093728204024956 5.1396938753314316, 52.093717452138662 5.1397007238119841, 52.09355255169794 5.139717671321705, 52.093311328208074 5.1395945930853486, 52.093306955655407 5.1395602072316251, 52.093115365831181 5.1400826557073742, 52.093052050564438 5.1401469679549336, 52.092979203676805 5.1401289247442037, 52.092756105586886 5.1398569964803755, 52.092737412561 5.1397823067194368, 52.09235419591127 5.1398883965623128, 52.092214386788811 5.1400686172528616, 52.092164272349919 5.1401695687556135, 52.09208471653983 5.1403786691371351, 52.0920239102561 5.1405293103307486, 52.091924546519294 5.1407297900877893, 52.091534494888037 5.1407990844454616, 52.091654436912947 5.1401591910829172, 52.091713753540262 5.1397284107361845, 52.091763769509271 5.1391488309018314, 52.091774359305148 5.1390583129178058, 52.09170373348757 5.1383788494901648, 52.0907391263172 5.1386201300192624, 52.090711282333359 5.1385075189173222, 52.090718721970916 5.1384486802853644, 52.090745792724192 5.1383893731981516, 52.090758387919244 5.1383728119598793, 52.090776969445869 5.1383237342815846, 52.090780415022657 5.1383173598065737, 52.090745287947357 5.1382717578671873, 52.090742629869759 5.1382662602414895, 52.090704807080328 5.1382211977615952, 52.0906867091544 5.1381677808240056, 52.090701617482885 5.1380081428639635, 52.090564404382455 5.138029116065514, 52.09062412660569 5.1386488282587379, 52.090704361908138 5.1396187201607972, 52.09069472597912 5.1397384563460946, 52.090674098813906 5.1398086878471076, 52.090624484543433 5.1397491229489587, 52.090589968811038 5.1397359627815975, 52.090441891923547 5.140045978827402, 52.090305342804641 5.1400443047750741, 52.0902322656475 5.139729289803654, 52.090199632104486 5.1394877941347659, 52.090188750764355 5.1393666968215257, 52.0902532400633 5.1393868076773792, 52.09003754449077 5.1387802169192582, 52.090024582457204 5.1386965749382565, 52.090020758565515 5.1386840578634292, 52.0900124781623 5.1386172670806785, 52.090003480669111 5.1385827830526978, 52.08999918546494 5.1385372205978728, 52.089985796017572 5.1384773049503565, 52.089996868744493 5.1384535257238895, 52.090046249330044 5.138385351980105, 52.090212456043091 5.1382693609882955, 52.090183896290647 5.1379786310671935, 52.090166853580648 5.1378115779987894, 52.0899735938292 5.137785307597369, 52.089885840192437 5.1377143466379493, 52.08985487697646 5.137671007309109, 52.089845903217793 5.1376524229999632, 52.089844238944352 5.1376464897766709, 52.089850628050044 5.1375868958421052, 52.089852778393364 5.137576853302618, 52.089863699774533 5.1374888862706634, 52.089867451693863 5.1373642447870225, 52.089883847394958 5.1373361134901643, 52.089941705111414 5.1372730266302824, 52.090002277167514 5.1372403032146394, 52.090108146462811 5.1372361269295483, 52.09006458793673 5.1368091938053615, 52.089683820260689 5.1369396857917309, 52.089193989204269 5.1364887236994123, 52.088854428613558 5.1373995044268668, 52.088474480202422 5.1383894786704332, 52.088474343996495 5.1383894337341189, 52.088464433038652 5.1383690948872287, 52.088414154422111 5.13834898790222, 52.088394471909851 5.1383694768883288, 52.0883943233639 5.1383694719988853, 52.08832395415709 5.1382487505018526, 52.087933741509914 5.1377592226490378, 52.087544413445592 5.1372594955892383, 52.087484167695806 5.1372292107739481, 52.087364645209163 5.1372284211684018, 52.0869538753575 5.1372190437554366, 52.085683952551335 5.1372596949804574, 52.085304662585258 5.137269108556211, 52.085084051657141 5.1370588609653955, 52.084904317976907 5.137469710316509, 52.084444417446747 5.1384497439414369, 52.084454428168293 5.1385195698547266, 52.084484005579725 5.1385092278942466, 52.084537888644263 5.1385357407853007, 52.084511198022149 5.1389506391238067, 52.084534639492631 5.1391157133039087, 52.084215438459069 5.139372929232195, 52.084103818604156 5.1389697602953825, 52.083964082412422 5.1391396226827055, 52.083963935496286 5.139139630831778, 52.083883681101725 5.1390291205607355, 52.083994359437455 5.1386593720505784, 52.084013982437057 5.1385892418004318, 52.084053878448593 5.1383293403318735, 52.084054407430678 5.1377297231794907, 52.084053982747719 5.1375283871311694, 52.084063940448686 5.1371387927792966, 52.084070490673184 5.13703247718513, 52.084070608951151 5.1370323959272355, 52.084217049471441 5.1370617711960529, 52.0842700656977 5.1370595147110754, 52.084318579515468 5.1370449147663777, 52.084365648221834 5.137017846536426, 52.084410294202549 5.1369791406907863, 52.084451525192954 5.1369308069453, 52.084497402298688 5.1368615722581685, 52.084511263761669 5.1368357082828879, 52.084539652187722 5.1367929205345337, 52.084559679031372 5.1367565956898034, 52.084580525973493 5.1367251129565776, 52.0845936126653 5.1367018828692963, 52.084593039704487 5.1366802926640958, 52.084593520236 5.1366613829106731, 52.084592797560617 5.136602794053033, 52.0845930285151 5.1365417347624449, 52.084591784281656 5.1365062294062227, 52.084592622431977 5.1364672367903337, 52.084591892315075 5.1364289335906506, 52.084595442516729 5.13633631542325, 52.084596794845957 5.1363224481129421, 52.084599652094766 5.13625919749029, 52.084600140111739 5.1362545876124468, 52.084603969780289 5.1361925578721053, 52.084604394622147 5.1361672168131918, 52.084607248043845 5.1361305358165161, 52.084609296828042 5.13606852098146, 52.084609103156254 5.1360535530839115, 52.084611643842678 5.1360064989442122, 52.08461217648793 5.1359452261162533, 52.084612038685009 5.1359415214974433, 52.084614087827504 5.1358594063203782, 52.084640604443848 5.1355516116600484, 52.084642857778817 5.135543460957706, 52.084982043160878 5.1354961035347806, 52.085083917947486 5.1345288194715977, 52.085104202153161 5.1343492493033409, 52.08524441709433 5.1330996853375064, 52.085165794240311 5.1330994283780456, 52.085158604676472 5.1330777355575146, 52.084887840552256 5.1328501671087, 52.084870130718066 5.1327825202649118, 52.084810143569484 5.132734818616882, 52.084766256157309 5.1326845148578286, 52.084753367166229 5.1326649976350005, 52.084720281418413 5.1326657184399664, 52.084673544857651 5.1326567681971937, 52.084627489326522 5.13263783371076, 52.084616634761915 5.1326309095602483, 52.084607382304966 5.1326056816615164, 52.084589018020779 5.1325388213153929, 52.084566780831665 5.1324195361230522, 52.08455663616769 5.1322953840717673, 52.084555578185245 5.1322289216332138, 52.084558193339035 5.1321669477038085, 52.084565328201279 5.1320932512171566, 52.084573237691075 5.1320388016756624, 52.084590001497418 5.1319514436181635, 52.084614846622571 5.1318454830907285, 52.084674907008818 5.1317076328407039, 52.084733415627852 5.1315451303962618, 52.084768428234277 5.1314570531469457, 52.084772500442341 5.131445026723668, 52.084790059469135 5.1313976899708305, 52.084790684864267 5.1313653332182225, 52.084789962507784 5.1313581170979887, 52.084786229995423 5.1313093374080232, 52.084781658835709 5.1312665985897183, 52.084776584757492 5.131205978570506, 52.084776126593319 5.1311985920700378, 52.084773858077824 5.1311737054493278, 52.084770929767942 5.1311195062007151, 52.084764682454988 5.1310441740788519, 52.084762406875207 5.1310067452953634, 52.084759807214141 5.1309909871779382, 52.084745739819482 5.1308908765204251, 52.084737451048568 5.1308199469931424, 52.084731393493712 5.1307550501078367, 52.084726219235463 5.130682019587562, 52.084717591805187 5.130595849588774, 52.084696356672794 5.1304316397290677, 52.084744368912652 5.1304192959796637))', 1) );
insert into #Shapes (naam,  shape) VALUES ('Area B', Geometry::STGeomFromText('POLYGON ((52.089193944586441 5.1364884474314749, 52.089683880347387 5.1369394774090678, 52.090064640389755 5.1368089618626982, 52.090064767515287 5.13680902402848, 52.090108351781964 5.1372362461406738, 52.0900023451254 5.137240494616317, 52.089941830607358 5.1372731845887953, 52.089884013120034 5.1373362265352416, 52.089867649300196 5.13736428650584, 52.089863897534087 5.1374888976570219, 52.089852973818779 5.1375768855214119, 52.089850827719964 5.1375869208953633, 52.08984444080243 5.1376464707614575, 52.089846089016071 5.1376523461555816, 52.089855048116348 5.13767090524721, 52.089885986401136 5.1377142074887443, 52.089973680692943 5.137785122508185, 52.090167043032125 5.1378114717081189, 52.090184094849974 5.1379786091856658, 52.090212659211829 5.138269433286041, 52.090046387117965 5.1383854977954284, 52.089997038751484 5.1384536319841185, 52.089986001565585 5.1384773087642488, 52.0899993844796 5.138537187827751, 52.090003677353721 5.1385827515141784, 52.0900126749184 5.1386172289494425, 52.090020956756526 5.1386840232833055, 52.0900247762911 5.1386965326964855, 52.090037737332914 5.1387801609122805, 52.090253500966355 5.1393869426101446, 52.090253373142332 5.1393870580941439, 52.09018895904866 5.1393668668649326, 52.09019982968524 5.1394877681651483, 52.090232462748588 5.1397292593531256, 52.090305473417473 5.1400441225035083, 52.090441768325739 5.1400458008552627, 52.0905898406636 5.1397357748355716, 52.090624607168138 5.1397489595692605, 52.090674059544682 5.1398083794509937, 52.090694529374325 5.1397384163970843, 52.090704163346672 5.1396187301667995, 52.0906239267189 5.1386488468750029, 52.090564216952771 5.1380289690569043, 52.090701825218275 5.138007998932153, 52.090686907175666 5.1381677433547006, 52.090704979235063 5.1382210930865915, 52.090742795495316 5.13826614478603, 52.090745454392028 5.1382716438933382, 52.090780634433031 5.138317345874384, 52.090777151606311 5.1383238151729582, 52.090758565347642 5.1383729032240808, 52.090745967798135 5.1383894728374937, 52.090718918413778 5.1384487237036574, 52.09071148235433 5.1385074989634694, 52.090739235906476 5.1386199161658359, 52.091703911079094 5.1383786785881966, 52.091774561209604 5.1390583219472319, 52.091763966455993 5.1391488551129392, 52.091713952366263 5.1397284283302724, 52.091654634801671 5.1401592225302011, 52.091534660555041 5.1407988700928273, 52.091924405223438 5.1407296329252166, 52.092023730557614 5.1405292234111544, 52.092084533682055 5.1403785903667165, 52.092164086876437 5.1401694919914007, 52.092214212752879 5.1400685210246593, 52.092354092746973 5.1398882211651653, 52.092737518250942 5.1397820895072073, 52.092756280866688 5.1398568955139261, 52.092979332917338 5.1401287692562034, 52.093051998862443 5.14014675848039, 52.093115186976668 5.1400825616937738, 52.093306944705546 5.1395597066730261, 52.093307103263214 5.139559774659574, 52.093311476645688 5.1395944439214718, 52.093552575019729 5.1397174675798443, 52.093717376162488 5.1397005364784905, 52.093728081547653 5.1396937158987059, 52.093731097411364 5.1396904007997364, 52.093789641978219 5.1396499255206436, 52.09379703433958 5.139647218074332, 52.093849730910733 5.139608321711421, 52.0938674450952 5.1396007388582916, 52.093911277158938 5.13956686834194, 52.093702596845105 5.1390791060402989, 52.094214342534542 5.1384887341409922, 52.094234085874632 5.1384696427267045, 52.094364419566851 5.1384893088412067, 52.094364145770669 5.1383595434017479, 52.094394268468022 5.1381287302356213, 52.09443390479516 5.138148912037261, 52.094484106955747 5.1381194878988437, 52.094514668919146 5.1380682252347469, 52.094674076435417 5.1382088991813486, 52.095094393635229 5.1384881954232995, 52.0952940530714 5.1385585838544232, 52.095604252303019 5.1385889891535044, 52.095554116032766 5.1386696371579523, 52.095534724403237 5.1388492132525849, 52.095524277190037 5.1390082753444624, 52.095594465266913 5.1390487975440919, 52.095594199141487 5.1393494226504117, 52.09559461963309 5.1399783839006, 52.095604153974683 5.1410990775805754, 52.095644179129778 5.1413294123732438, 52.09575448022224 5.1416396433487535, 52.095824270925078 5.1419194503811445, 52.096084321906162 5.1429293346052836, 52.096143952025322 5.1430793148784755, 52.096264120657 5.1433793206233531, 52.096193926805284 5.1433798011214318, 52.096113997035054 5.14339920294765, 52.096024247104872 5.1434492955148228, 52.095944452364236 5.1435387324349744, 52.095874538511147 5.14362958598761, 52.095844099589421 5.143679338650661, 52.095844470186279 5.1438587997111922, 52.095854729064243 5.1440396906996444, 52.095894579105732 5.1441883100385768, 52.095964113250375 5.144369007088244, 52.09580374216273 5.144229786732418, 52.095674295010134 5.1441983953353239, 52.095563816432822 5.14421941922198, 52.095403983902024 5.1442888717546564, 52.095254029380158 5.1443597327452153, 52.094414402963594 5.1447291097138077, 52.094194360597214 5.1448091029165, 52.093554132385179 5.1451087987516075, 52.09298392268829 5.14536870829761, 52.092384074527615 5.1456389861371825, 52.091314621968991 5.1461291963244005, 52.091214230906282 5.1462493549551356, 52.091174073517323 5.1464188823010772, 52.0911739426665 5.146418813848868, 52.09113409327086 5.1462687528401041, 52.091084660668564 5.146199182483377, 52.091033940669149 5.1464488115161657, 52.090953806928624 5.1464084108564867, 52.090854425442245 5.1464496781230418, 52.089684411417693 5.1471287335734814, 52.0895846124041 5.1471190678897267, 52.088994233263378 5.1476095448153067, 52.088864096673205 5.1477386702317744, 52.088784483494237 5.1475289191585034, 52.088713807872537 5.1472491544173726, 52.088664193741309 5.1471487923554067, 52.088594123489734 5.1471287621828763, 52.088524112701435 5.1471597642893574, 52.088323859963566 5.1472586041782051, 52.088194384938106 5.1472490853630006, 52.088083737995476 5.147229231428355, 52.087984558660537 5.1470896604005247, 52.0871439545881 5.144788873847574, 52.086584153570342 5.1431184258301306, 52.086113808001116 5.1425490758657, 52.085764196002856 5.142129332292825, 52.085273851326242 5.1414594290601263, 52.084604130359367 5.1405483337584883, 52.08448414108716 5.1403388837352395, 52.084363697096705 5.1399091542698443, 52.084215331124142 5.1393728284165263, 52.084534444796994 5.1391156225659822, 52.084510998101905 5.1389506384730339, 52.084537685041475 5.1385358115798789, 52.084483979582181 5.1385094355204064, 52.084454281721264 5.138519779080525, 52.084444217151031 5.1384497005492449, 52.084904137838336 5.1374696237373572, 52.08508396637626 5.1370586035773158, 52.085304709049147 5.1372689084542849, 52.085683944402767 5.1372594968589222, 52.08695387118496 5.1372188439127058, 52.087364651495307 5.1372282228088277, 52.087484228890389 5.137229019543156, 52.087544555542991 5.1372593543492258, 52.087933897256818 5.1377590987963755, 52.088324117939919 5.1382486345246434, 52.088394418613781 5.138369242607296, 52.088414155179635 5.1383487726561725, 52.0884645585902 5.1383689332287759, 52.0884744236222 5.1383891381781037, 52.088854240353591 5.1373994332191018, 52.089193944586441 5.1364884474314749))', 1) );
insert into #Shapes (naam,  shape) VALUES ('Area C', Geometry::STGeomFromText('POLYGON ((52.081104027922265 5.1258389879949391, 52.081314665614627 5.1259588550310582, 52.082414517994039 5.1266395719721913, 52.082954646321014 5.1270186660112813, 52.083513987367041 5.127549389610067, 52.083794155623764 5.1278395495610312, 52.084174386574887 5.1282589976908639, 52.084274505455781 5.1284189013796713, 52.08453426125925 5.1288288246141747, 52.085124507819643 5.1299386160409242, 52.08521465482071 5.1300693768952019, 52.0853342462746 5.1301182725468744, 52.0854241597699 5.1300988405710086, 52.0854743384989 5.1304488354362547, 52.085234220619661 5.130419600171515, 52.084744388967557 5.1304194940048324, 52.08439406089019 5.1305090384557843, 52.083914360133932 5.1306285039224422, 52.083414051565342 5.1307787221157923, 52.082813916262239 5.13094844610896, 52.082724283281529 5.1306586048111562, 52.082483787322417 5.1300093204481527, 52.08225411306649 5.1293789464909949, 52.082194455789093 5.1292188489812043, 52.082134172902443 5.1291885531973094, 52.082084508962 5.1290896165883169, 52.082023798371665 5.1288696515839547, 52.081883911043406 5.1281993770971894, 52.081856097793207 5.12798699515406, 52.081856237724423 5.1279869175050408, 52.082000762340613 5.1280515332473442, 52.082027135184035 5.1280940270517021, 52.0820355968099 5.1281161647869, 52.08205282002023 5.1281410993754166, 52.08213594150827 5.1278323108932256, 52.0820438895719 5.1277594091965328, 52.081953932996839 5.1277496579568833, 52.081884289887846 5.1271693162703134, 52.081813924670755 5.1270196131258938, 52.081552422139794 5.1268787173321471, 52.08152364961375 5.1267665265884057, 52.081485387952739 5.1266524291002371, 52.081442847483068 5.1265567842247837, 52.081396028901857 5.1264795880384764, 52.081344932177927 5.1264208389159505, 52.081293396464417 5.1263833287749234, 52.081279310281388 5.1263776289997622, 52.081249886541627 5.1263603481929749, 52.081222431567454 5.12633884719625, 52.081221418222412 5.1263384295161813, 52.081197269726545 5.126324187265709, 52.081195053295232 5.1263138890499249, 52.081184833077714 5.1262332251062617, 52.0811841667945 5.1261982778874859, 52.081168951815926 5.1261331316782162, 52.081164751928249 5.1260440781433525, 52.081066497950815 5.1259329431923106, 52.081104027922265 5.1258389879949391))', 1) );
insert into #Shapes (naam,  shape) VALUES ('Area D', Geometry::STGeomFromText('POLYGON ((52.084103860426694 5.1389694481622428, 52.084363892148971 5.1399091025981294, 52.084484331319835 5.1403388143996294, 52.084604299141489 5.1405482272725367, 52.08527401345782 5.1414593127556145, 52.085764355740025 5.1421292096101565, 52.086113962111995 5.1425489480607212, 52.086584335425869 5.1431183374952525, 52.087144145466013 5.1447888108543749, 52.087984736636635 5.1470895681108679, 52.088083857744529 5.1472290623707631, 52.088194406595086 5.14724888795369, 52.088323822820605 5.1472584035787792, 52.088524032849818 5.14715958177112, 52.088594117900357 5.1471285563893616, 52.08866433496587 5.1471486398950219, 52.088713997742161 5.1472490890882909, 52.088784678140655 5.1475289016962051, 52.088534413350153 5.1477695436890123, 52.088604030199349 5.1479895326774567, 52.08846407078854 5.1481186849763318, 52.088304384844378 5.1482683648355305, 52.087993860917578 5.1484991029959017, 52.087834112113342 5.1486196045298129, 52.0874739959836 5.1487791088875383, 52.087183827068657 5.1488594498950988, 52.087034655727216 5.1488792099405627, 52.086844170233235 5.1489094072021544, 52.086553779430687 5.1488890685141087, 52.086283983197063 5.1488190072122961, 52.086004210880986 5.148699401849246, 52.085884556407109 5.148648968199268, 52.085783737245947 5.148579464526847, 52.085444359574467 5.1483186569530517, 52.08505431888625 5.147909271530807, 52.085063869832084 5.14774867403321, 52.085103993769735 5.1475894195027649, 52.085123664481678 5.1475485048696683, 52.084903807879783 5.1472594002206034, 52.084644382136524 5.1469792136778958, 52.08418409107253 5.1464885615278035, 52.0837237383239 5.1459687419701368, 52.083234543621856 5.145409702023275, 52.082664410911732 5.1448292277490495, 52.082063829526305 5.1443087360821664, 52.082091124779964 5.1440836547198483, 52.081992223858833 5.1440890550147742, 52.08196270884946 5.14405638189055, 52.081944186007604 5.1439888756722212, 52.08194406144986 5.1439872064089114, 52.08192484639585 5.1439289392437786, 52.081920254660311 5.1439031759941996, 52.081906982464716 5.1438652367796749, 52.081898384261621 5.143827152704362, 52.081886463514792 5.1437939475605585, 52.081860758494884 5.143810536588699, 52.081833417158236 5.1438379039788957, 52.081759569933638 5.14407270308584, 52.0816137263635 5.1439596123534246, 52.081454453474372 5.1438598307431391, 52.081304313847795 5.14384896773845, 52.080264462672268 5.1430187125121805, 52.079664091113955 5.1425989381968975, 52.079524534521624 5.14249899610877, 52.079534315969795 5.1424492821097374, 52.079674492839317 5.1419992103874552, 52.079703816364884 5.1418385940623406, 52.079714205814525 5.141648898134008, 52.079727753764018 5.1414623958989978, 52.080252137147674 5.1417998058748831, 52.08029427562046 5.1417563394152745, 52.080314928898588 5.1417286938522011, 52.0803562682122 5.1416860464960337, 52.080404439009726 5.1416505186352879, 52.080450373701751 5.1416298456024379, 52.080458209152553 5.1416284950795994, 52.080495744477957 5.141600257018581, 52.080541761592031 5.141581037081778, 52.080577370766676 5.1415776146752092, 52.080586124956035 5.1415745182313319, 52.080565002281219 5.1411468000151217, 52.080635850084946 5.1411388639826328, 52.081214110314008 5.1410789246463136, 52.081586783519015 5.1409964717458934, 52.081614242866635 5.1412574960850179, 52.081570835318416 5.1413511682767421, 52.08156742547277 5.1413547724810877, 52.081523078051127 5.1414396720759816, 52.081520885843375 5.1414458907124478, 52.0815235725604 5.1414493722841144, 52.081564587075263 5.1415304632391781, 52.081586116692051 5.1416122366208583, 52.081591385416651 5.1417623861789625, 52.081744097638875 5.1417384068481624, 52.081754462670077 5.14239915706246, 52.081888611945665 5.1424242914485125, 52.081887235166505 5.1422738104593009, 52.081907565006986 5.1422072551213205, 52.081948822597042 5.1421398329548538, 52.081990273194968 5.1420943139491024, 52.082000561989844 5.1420720012392849, 52.082041298272088 5.1420040489174426, 52.08205503895892 5.1419854623652519, 52.082057312844228 5.1419532595345077, 52.082057383609936 5.141936854692176, 52.082061406905325 5.1418724298121266, 52.082061399472877 5.1418698709458113, 52.082065169426741 5.1418023992023132, 52.08206505025737 5.1417857583146542, 52.082067978335544 5.1417265709023923, 52.082068552136519 5.1417210444026873, 52.08207146529282 5.1416510321596576, 52.082074348499624 5.1415691960222105, 52.082074102712795 5.1415587870869786, 52.082077217031589 5.141500341455882, 52.082077142713729 5.1414836310842942, 52.082064611044075 5.1414689618560345, 52.08204338257201 5.1414488023146987, 52.0820095549712 5.1414023755017455, 52.08195383178483 5.1413428048418419, 52.0819458400365 5.1413370133377612, 52.081897551489291 5.141270585100548, 52.081845151958987 5.1412304241675884, 52.081783577566966 5.1409387167077512, 52.082063805446388 5.1408189585007031, 52.082534100375206 5.1404983382591407, 52.082604082068428 5.1404395992867649, 52.082693810134288 5.1403690781753832, 52.083284175475136 5.1398683352445742, 52.083963928950048 5.1391394941752653, 52.084103860426694 5.1389694481622428))', 1) );

select naam, shape, shape.Reduce(0.001) as reducedShape from #Shapes

drop table #Shapes

This returns two sets of polygons. First the unreduced set:

Then the reduced set:

These shapes are much simpler and they do have the rough shape correct, but what I would want is to have the border-parts still shared. So they have to be reduced together, in a way.

I think you have to break them up into polylines first (from edge to edge), then Reduce the lines and then reassembling them to polygons again. I have no idea how to do this in T-SQL though.

Any ideas?

Edit: I've accepted alphadaogg's answer. Both current answers weren't entirely covincing to me, but alphadogg has certainly put in the most effort and I really appreciate any sharing of thoughts. So the bounty goes to him.

I will follow-up with a self-answer later if I find a satisfying method.

Follow-up: I e-mailed with Isaac Kunen, Program Manager on the SqlServer Geo team. His helpfull response is below:

Your problem is not at all rare, but it isn't something we directly support: it's an operation that requires knowledge of the topology of your figures, and we don't have anything like this built in. Essentially, you don't want to store separate polygons for each neighborhood. Rather, you want to store curves representing portions of boundaries, and reuse these boundaries for multiple polygons. When you generalize, you generalize the shared boundary, and all dependent polygons are affected.

You could build this yourself---as the posters in the thread you cite hint---but it may be real effort to do so.

I don't know the third-party software you're using, but this is the other option. If you don't want a full-fledged GIS, you could use a package like the FME from Safe Software (http://www.safe.com). The FME doesn't do general-purpose topology, but I believe it has enough functionality to do what you're looking for. See: http://www.safe.com/products/desktop/under-the-hood.php#3b.

I hope this helps.

Cheers,

-Isaac

Answer 1

I'm not sure how you'd get the "shared" LineStrings from your shapes. Secondly, once you reduce a "subset" of the shape since your endpoints may move from the original and you will not be able to make them match up after reduction.

The nutshell of what I would do is basically use boolean operations to play with the reduced shapes.

First, do what you do, namely create a temporary table of reduced shapes (called #ReducedShapes).

Then, I would create a second temp table and find the areas of overlap (using STIntersection) between all shapes. In this table, I would basically have columns naam1, naam2 and intsec, the last one being of type shape. Something like (untested):

INSERT INTO #IntSecs(naam1, naam2, intsec)
SELECT s1.naam, s2.naam, s1.naam.STIntersection(s2.naam)
FROM #ReducedShapes s1, #ReducedShapes s2 
WHERE s1.naam.STIntersection(s2.naam) IS NOT NULL

This gets you a list of where pairs of shapes overlap. In fact, you have two rows for each overlap. For example, if A and B overlap you'd have and . I would make a pass and delete one of the two for each occurence.

Lastly, for each overlap, I would subtract (STDifference) the intersection from only one of the two regions in the pair from the #ReducedShapes table. Imagine you have two squares A and B, half-overlapping. The operation would involve A.STDifference(B) meaning you keep all of B and half of A. I would insert the modified shapes into a third table (say #ModifiedShapes).

Two problems: a) as you can see from your "orange" and "blue" shapes, they did not reduce similarly, so you'll get one of two possible reductions depending on how you deal with who "wins". b) a more complicated form of the problem is that, depending on the complexity of the initial shapes, you may get overlap between three or more regions. You'll have to determine your own way to establish which one shape "wins" in that intersection, based on your particular needs. It's not clear if there are constraints. Could be as simple as arbitrarily picking a winner by ordering, or more complicated since accuracy is important.

The above concept unfortunately does not address the issue of gaps. This one's a little more complicated and I am not 100% sure how to resolve it. But, if you create a third table that subtracts (STDifference again) all the modified shapes #ModifiedShapes from all the original shapes in #Shapes (testing for overlap before actually subtracting, of course), you'd be left with the remainder shapes in the gaps. You'd want to aggregate the adjoining shapes and assign a "winning color", possibly merging it back in with the related shape.

This answer is long and I will leave it like this. I may be barking up the wrong tree. Based on your feedback/questions, I would add to the post.

Answer 2

Wow, that's a pretty cool set of features.

Taking a look at some of the other methods available, here are a few ideas that come to mind:

On the unreduced shapes, use .STIntersects (returns a boolean) and .STIntersection (returns a shape) to find out if and where two shapes intersect.

For two adjacent map regions, I would assume that .STIntersection should return the line segment that borders both.

Then you can reduce these line segments and re-assemble the reduced shapes.

Answer 3

Isaac is right that you could reduce the features to lines, and use them as shared boundaries.

But the software he mentions - FME - has a transformer called the Generalizer which will simplify them as you wish while still retaining them as polygons. The option to use is called 'Preserve Shared Boundaries'. You can download FME from [here][1] and request a 14-day eval license to try it out.

Answer 4

This isn't strictly speaking an answer to your question, but if your ultimate objective is to render maps in the browser, then you should look into Mike Bostock's TopoJSON project.

TopoJSON, like GeoJSON, is a javascript-friendly spatial file format. Unlike GeoJSON, TopoJSON contains just the topology so that shared borders are only represented once. This results in (a) more compact data and (b) seamless simplification.

There's a great introduction here, including live visualizations of the algorithm used to infer topology: http://bost.ocks.org/mike/topology/

The project wiki is here: https://github.com/mbostock/topojson