A simpler approach to robustness

[mourner]

@Komzpa @fogleman here's another alternative which is much simpler. Needs a higher error threshold, but should still work for most cases in theory.

[fogleman]

Try this set of points. It gives a bad triangulation for me (in Go) unless I filter points within eps squared-distance. Try rendering it if your validate says it's ok.

{{0.226270008640849,-0.5484478681473859},{0.22627000864084906,-0.5484478681473857},{0.766192698520777,-0.06114560279536302},{0.7661926985207771,-0.06114560279536302},{0.40151121510492016,0.08616979557470032},{0.40151121510492027,0.08616979557470034},{-0.41675996433129736,-0.5902787491305856},{-0.4167599643312972,-0.5902787491305853},{-0.2479064469635639,-0.7472011647497873},{-0.24790644696356384,-0.7472011647497872},{0.6078988481689899,-0.8087190266174613},{0.6078988481689901,-0.808719026617461},{0.6844238681986647,-0.22229148851718702},{0.6844238681986647,-0.222291488517187},{0.6486832941181451,0.3706194950394349},{0.6486832941181452,0.3706194950394349},{-0.5361048842131249,-0.16765691382574804},{-0.5361048842131245,-0.167656913825748},{0.4588358986737203,-0.9000280551977525},{0.4588358986737205,-0.9000280551977525},{0.3960651926938643,0.19117525930527385},{0.39606519269386437,0.1911752593052739},{0.30699987842448867,-0.4067155996580057},{0.3069998784244887,-0.4067155996580056},{0.47811583559881354,0.4551485080955586},{0.47811583559881354,0.4551485080955586},{0.5569494202770435,0.3174275448747843},{0.5569494202770439,0.3174275448747845},{-0.4277027605175392,0.09695587866512022},{-0.4277027605175391,0.09695587866512025},{-0.5748114807265807,-0.03838218657575568},{-0.5748114807265806,-0.03838218657575567},{-1.0317070883952917,-0.5245256032470283},{-1.031707088395291,-0.5245256032470283},{0.14712374452633492,0.33141471681448986},{0.147123744526335,0.33141471681448986},{-0.2834737219004291,-0.9271587984120542},{-0.2834737219004289,-0.9271587984120538},{-0.6098149486946731,0.5553773725836295},{-0.6098149486946729,0.5553773725836295},{1.1206314478250745,0.3921423623286639},{1.1206314478250745,0.39214236232866406},{0.4477538973665876,-0.04256704865570235},{0.4477538973665877,-0.04256704865570235},{-0.6156635308889042,-0.10817302193016937},{-0.6156635308889041,-0.10817302193016932},{0.17897362794557034,-0.04224227852769616},{0.17897362794557034,-0.04224227852769614},{-0.9646885789850332,-1.4563419829050452},{-0.9646885789850331,-1.456341982905045},{0.2911613415160255,0.015655417967490592},{0.29116134151602563,0.015655417967490596},{-0.3698918540831971,0.6983267205999204},{-0.3698918540831969,0.6983267205999205},{1.4056553730213062,-0.41615789580202767},{1.4056553730213066,-0.41615789580202767},{0.34141990921721344,-0.5679551502988661},{0.3414199092172136,-0.5679551502988661},{0.2957318137669341,0.8416499601535058},{0.29573181376693425,0.841649960153506},{0.035141462612931273,-0.45835970615650135},{0.03514146261293129,-0.45835970615650123},{-1.3263110033694971,0.8223290351908346},{-1.326311003369497,0.8223290351908346},{-0.18787969354847422,1.4601214758378256},{-0.18787969354847417,1.4601214758378258},{-0.5421684590742957,-0.5196118080038157},{-0.5421684590742956,-0.5196118080038157},{-0.15415956428809274,0.2553265483092856},{-0.15415956428809266,0.25532654830928564},{0.24744639466303925,0.36561549310806263},{0.24744639466303933,0.36561549310806274},{-0.007949225522230624,-0.4463313570187974},{-0.00794922552223062,-0.4463313570187972},{0.4314282749865176,0.6907165244683744},{0.4314282749865177,0.6907165244683744},{0.22721916356346672,-1.145924985720078},{0.22721916356346675,-1.1459249857200775},{0.11627266697915434,0.5679584977485386},{0.11627266697915438,0.5679584977485389},{-0.004760241854834868,1.341758406463988},{-0.004760241854834866,1.3417584064639887},{0.34070213758085,-0.4524446934513693},{0.3407021375808501,-0.45244469345136923},{0.8842875090593054,-0.4369329059094983},{0.8842875090593055,-0.43693290590949824},{0.1514286184534766,-0.17725085421066233},{0.15142861845347666,-0.17725085421066225},{-0.4255258812089902,-0.48986352859695054},{-0.42552588120899015,-0.4898635285969505},{0.9377261482762783,-0.1443481348548356},{0.9377261482762784,-0.14434813485483552},{0.04260345503852292,0.951377045867543},{0.04260345503852292,0.951377045867543},{0.305243584013604,-0.3875472629266138},{0.305243584013604,-0.3875472629266138},{0.03603755940893599,0.34504467425927055},{0.036037559408936,0.34504467425927055},{0.7432869522329792,-0.7836440067269177},{0.7432869522329795,-0.7836440067269175},{-0.2963957383054346,-0.8541077824286829},{-0.2963957383054344,-0.8541077824286829},{-0.5957774790480242,-0.600709712349726},{-0.5957774790480241,-0.6007097123497258},{-0.16224562470708315,0.34537414926581733},{-0.16224562470708306,0.34537414926581733},{-0.7424662163367453,-0.41130625924230096},{-0.742466216336745,-0.41130625924230085},{-0.3624590396531042,-0.10563984421746442},{-0.3624590396531041,-0.10563984421746442},{-0.5392904110560361,-0.08518185259429017},{-0.5392904110560358,-0.08518185259429016},{-0.6778672159722301,0.3431673449069855},{-0.6778672159722301,0.3431673449069856},{0.36715717958832705,-0.5910728761089766},{0.36715717958832716,-0.5910728761089764},{-0.025023155416355747,0.049551540818041445},{-0.025023155416355747,0.04955154081804146},{-0.24819669042158904,1.551076727423892},{-0.24819669042158898,1.5510767274238921},{0.567193157662795,0.11906741314152564},{0.567193157662795,0.11906741314152564},{-0.040143445247768667,0.26972252794743534},{-0.04014344524776866,0.26972252794743534},{-0.2625294670890006,-0.9866393501381076},{-0.2625294670890005,-0.9866393501381073},{0.44843907219373064,0.8048081754922025},{0.44843907219373064,0.8048081754922027},{0.0645600537587031,1.0817638655728792},{0.06456005375870313,1.0817638655728798},{0.7675432088110417,-0.8812717114610312},{0.7675432088110417,-0.8812717114610309},{-0.08286494268897,-0.4289421536808215},{-0.08286494268896998,-0.42894215368082134},{-0.41612370586918423,0.4886715855834002},{-0.41612370586918423,0.48867158558340035},{0.19771717248920714,-0.1094932114101852},{0.19771717248920723,-0.10949321141018517},{0.3325743770435765,0.3050059606614455},{0.3325743770435766,0.3050059606614456},{-0.6076675750885592,-0.2488880571567846},{-0.6076675750885588,-0.24888805715678455},{-0.13216710101702264,-0.5066473875502346},{-0.13216710101702256,-0.5066473875502345},{0.8513876721292416,-0.5489241609365357},{0.8513876721292416,-0.5489241609365356},{-0.382289175026138,-0.47285448091622573},{-0.38228917502613796,-0.4728544809162256},{-0.22454842691828375,0.6151379112650053},{-0.22454842691828367,0.6151379112650056},{-0.8646014175536286,-0.42386569643498184},{-0.8646014175536284,-0.4238656964349818},{0.3117316226386966,0.2627613357418179},{0.3117316226386967,0.262761335741818},{-0.15249103914387663,0.4395379613315442},{-0.15249103914387657,0.4395379613315443},{-0.8535303948590758,-0.5171136892316436},{-0.8535303948590756,-0.5171136892316435},{0.5548908499705427,0.7505471621260598},{0.5548908499705427,0.7505471621260601},{-0.06051133138765111,0.10241755750407933},{-0.0605113313876511,0.10241755750407933},{0.5337288423213871,-0.4674709006951539},{0.5337288423213873,-0.4674709006951539},{0.05432726705458686,0.7404240043361822},{0.054327267054586875,0.7404240043361824},{0.18755513858332273,-0.33846461008241124},{0.1875551385833228,-0.33846461008241124},{-0.8591170242442958,0.10096092456106642},{-0.8591170242442956,0.10096092456106642},{-0.6532878500824677,0.06191743854152687},{-0.6532878500824675,0.06191743854152687},{-0.8539614587215372,-0.7324824009962402},{-0.8539614587215372,-0.7324824009962402},{-0.5863802667964559,-1.056546154929931},{-0.5863802667964556,-1.0565461549299304},{-0.1790469166305501,0.2959320232236789},{-0.17904691663055006,0.2959320232236789},{-0.1360834565364501,-0.11972427421383847},{-0.13608345653645007,-0.11972427421383845},{1.000279652308404,0.5677840712010568},{1.0002796523084043,0.5677840712010568},{-0.2539417014734854,-0.24824262411661902},{-0.2539417014734853,-0.24824262411661896},{-0.5513314210236925,0.164455936053998},{-0.5513314210236921,0.16445593605399808},{-0.35669084505120763,-0.5579365995173293},{-0.3566908450512076,-0.557936599517329},{-0.00479028693868494,0.5747959597699825},{-0.004790286938684939,0.5747959597699829},{0.9274618857336762,0.3137388167061812},{0.9274618857336765,0.3137388167061813},{-0.1582654462645559,0.08532244403569378},{-0.1582654462645559,0.08532244403569382},{-0.7338606250043278,0.03884536523072413},{-0.7338606250043278,0.038845365230724134},{0.441630546674704,-0.4757978998267975},{0.4416305466747042,-0.4757978998267975},{-0.340639188849867,-0.016461235375619054},{-0.340639188849867,-0.01646123537561905},{0.6944973204450795,-0.05127049077067958},{0.6944973204450798,-0.051270490770679564},{0.05692195764635159,-0.4860234898913355},{0.05692195764635161,-0.4860234898913355},{-0.34909544551668503,0.07925987763994416},{-0.3490954455166849,0.07925987763994416},{0.020842670418798892,-0.18962128485770935},{0.020842670418798902,-0.1896212848577093},{-0.24296262993119017,-0.7557062436624338},{-0.24296262993119008,-0.7557062436624334},{0.07767785036524773,-0.0756745138376198},{0.07767785036524774,-0.0756745138376198},{-0.5383587124935423,0.3149908402335876},{-0.538358712493542,0.3149908402335876},{-0.3672547557130592,0.8497352282145765},{-0.3672547557130592,0.8497352282145768},{1.0306858576839981,0.6132170100848149},{1.0306858576839986,0.6132170100848152},{0.026403641820751278,-0.11123958700346126},{0.02640364182075129,-0.11123958700346125},{-0.39673068933170313,0.7365210212380586},{-0.3967306893317031,0.7365210212380586},{-0.273859110739041,0.15083421880672626},{-0.2738591107390409,0.15083421880672626},{-0.7502503591118193,-0.6273750425323015},{-0.7502503591118191,-0.6273750425323014},{1.040458273889268,0.3592162639445413},{1.0404582738892683,0.3592162639445414},{-0.30951481303178596,-0.7990197975684153},{-0.30951481303178585,-0.7990197975684152},{-0.3049861667890695,1.6737307580052914},{-0.30498616678906937,1.673730758005292},{0.601935475297747,1.1660575124169412},{0.601935475297747,1.1660575124169419},{0.8838992370838099,0.2656415636074353},{0.8838992370838102,0.2656415636074353},{-0.5085727248068516,-0.23584500534815295},{-0.5085727248068515,-0.2358450053481529},{0.5396217328637709,-0.39810497658583466},{0.5396217328637712,-0.39810497658583466},{0.8665494841240842,0.11624211166929022},{0.8665494841240843,0.11624211166929023},{-0.51942267345288,0.5395224235439922},{-0.5194226734528796,0.5395224235439922},{0.19088288221197763,-0.4663336215970121},{0.19088288221197763,-0.4663336215970119},{-0.23194847381262582,0.21901474700861162},{-0.23194847381262573,0.21901474700861162},{0.8359436402369345,-0.2679779650730807},{0.8359436402369346,-0.2679779650730805},{0.4468309121482219,0.724738511770195},{0.4468309121482219,0.7247385117701953},{0.5963791684457523,0.8746079737915003},{0.5963791684457525,0.8746079737915007},{-0.16268657840268694,-0.10458689278692812},{-0.16268657840268685,-0.10458689278692809},{0.15167543844454376,0.3810633395493045},{0.1516754384445438,0.3810633395493046},{0.3175047149330903,-0.4680659139099735},{0.31750471493309046,-0.4680659139099735},{0.24518019737678892,0.14105859064554405},{0.24518019737678892,0.1410585906455441},{0.1337014618382204,0.216053384319761},{0.1337014618382205,0.21605338431976104},{-0.5196743788563577,-0.24381508621133063},{-0.5196743788563577,-0.24381508621133063},{0.16145768845022127,-0.18548235309792105},{0.16145768845022135,-0.18548235309792097},{0.5267956022472777,-0.07806817831728718},{0.5267956022472777,-0.07806817831728716},{0.2690528801662905,0.007775444056135339},{0.2690528801662905,0.00777544405613534},{0.7565821160819859,-0.3047749278545374},{0.7565821160819859,-0.30477492785453736},{-0.7016467625353928,0.04470959700747512},{-0.7016467625353925,0.04470959700747514},{0.2415239307661166,0.2972238198129453},{0.24152393076611664,0.2972238198129453},{0.2284592008150542,-0.6608245027366711},{0.2284592008150542,-0.6608245027366711},{0.2123088556780684,0.01782161739519142},{0.21230885567806848,0.017821617395191426},{-0.14619514581307758,-0.8833238459080084},{-0.14619514581307758,-0.8833238459080082},{0.1989466009909055,-0.6118402241082294},{0.1989466009909055,-0.6118402241082291},{0.49059993119084305,-0.16493514201871323},{0.4905999311908431,-0.1649351420187132},{-0.4129648372506063,-0.05944366961592451},{-0.4129648372506062,-0.059443669615924496},{0.586485692893329,0.3271185970911774},{0.5864856928933292,0.32711859709117747},{-0.06023227911161408,-0.7107842875157466},{-0.06023227911161407,-0.7107842875157466},{0.6310359079249456,0.29992699270395096},{0.6310359079249456,0.29992699270395107},{-0.6703089300986523,0.6107470941705689},{-0.670308930098652,0.6107470941705689},{0.5005957282133777,0.01407262429060302},{0.500595728213378,0.014072624290603021},{-0.18934890988546538,-0.9372780070318394},{-0.1893489098854653,-0.9372780070318394},{-0.2863087126284564,-0.40444718862380247},{-0.28630871262845636,-0.4044471886238023},{1.190084782443751,0.5322874598725964},{1.1900847824437517,0.5322874598725967},{0.1341442916393324,-0.8420626196661292},{0.13414429163933247,-0.8420626196661289},{-0.7649861084427345,-0.7071073574041574},{-0.7649861084427344,-0.7071073574041573},{-0.362881463482392,0.4530261596665785},{-0.3628814634823919,0.45302615966657866},{0.13437240869925704,0.0763221848731111},{0.13437240869925712,0.0763221848731111},{1.0481657649638807,-0.004257185833033583},{1.0481657649638814,-0.004257185833033581},{-0.7474948815245823,-0.9786844358659653},{-0.7474948815245823,-0.9786844358659653},{0.12735871993303205,-0.3185548367971229},{0.12735871993303208,-0.31855483679712276},{0.36855220211615,-0.5588123239347687},{0.36855220211615003,-0.5588123239347685},{-0.18314335566244416,-0.5442250179734792},{-0.18314335566244408,-0.544225017973479},{0.08693873231351551,-0.6447286294698766},{0.08693873231351551,-0.6447286294698766},{-0.05481436374055537,0.20956141264894845},{-0.05481436374055537,0.2095614126489485},{-0.27114580055426557,0.12928945128646963},{-0.2711458005542655,0.12928945128646968},{-0.4451760474692624,0.46862844610576626},{-0.4451760474692623,0.4686284461057663},{0.1341730804119372,-0.5079494612186458},{0.13417308041193723,-0.5079494612186456},{0.3257440025696646,0.4153507171529827},{0.3257440025696647,0.4153507171529827},{-1.2231311278955395,0.5704928559937266},{-1.223131127895539,0.5704928559937269},{-0.07375248343426033,-0.5524759317685063},{-0.0737524834342603,-0.5524759317685063},{-0.6413383012441964,-0.3892879515624541},{-0.6413383012441963,-0.38928795156245405},{-0.000884182358095037,-0.003185720596142992},{-0.0008841823580950368,-0.003185720596142991},{0.737566803637365,-0.7615040446353664},{0.7375668036373654,-0.761504044635366},{0.23446047289831606,0.19035505393365781},{0.23446047289831606,0.19035505393365784},{-0.07211988377390469,-0.13169854040950443},{-0.07211988377390469,-0.13169854040950443},{0.18143877838398617,1.132013860293268},{0.18143877838398625,1.1320138602932683},{-0.22066292105815377,-0.19117568196580417},{-0.22066292105815372,-0.19117568196580417},{-0.4347453028054331,0.5888401578252912},{-0.43474530280543294,0.5888401578252915},{0.24005504098930414,0.8021441938204985},{0.24005504098930416,0.8021441938204986},{-0.34929799898447755,-0.261775797658851},{-0.34929799898447744,-0.26177579765885084},{0.3490077668059596,-0.007752337813972554},{0.3490077668059597,-0.0077523378139725515},{-0.6025788068137587,0.46068756636034236},{-0.6025788068137585,0.4606875663603424},{-0.7122333712891852,0.26308462754739115},{-0.7122333712891852,0.26308462754739115},{0.15764425398809745,0.18964163728856187},{0.15764425398809748,0.18964163728856193},{0.1853787174021873,-0.6789040209134625},{0.18537871740218737,-0.6789040209134621},{0.634911453390334,0.13339968677329644},{0.6349114533903343,0.13339968677329647},{-1.2578415170869763,0.2517963788258869},{-1.2578415170869757,0.2517963788258869},{0.1400845593846478,0.40593141307431857},{0.14008455938464787,0.4059314130743186},{-0.7095485725512902,0.8225233205642902},{-0.7095485725512899,0.8225233205642903},{-1.1960848307098382,0.17404679607890605},{-1.196084830709838,0.17404679607890608},{0.21828979413603433,-0.3280264848946596},{0.2182897941360344,-0.3280264848946595},{0.2662387358530971,0.3568929623829047},{0.26623873585309726,0.3568929623829048},{0.24305026107578037,-0.23724020319018074},{0.24305026107578043,-0.23724020319018066},{-0.3433832627650342,0.3389417719770061},{-0.34338326276503406,0.3389417719770061},{-0.0437269904343551,0.5869495454659391},{-0.04372699043435508,0.5869495454659392},{-0.12109570623011018,-0.8772834803160542},{-0.12109570623011016,-0.8772834803160542},{0.09631218123471452,-0.12108887934946555},{0.09631218123471456,-0.12108887934946555},{-0.41811390046020547,0.8465092639539217},{-0.4181139004602053,0.8465092639539218},{-0.34396631561394114,0.8358904797678759},{-0.343966315613941,0.8358904797678759},{0.43085589801084057,-0.16054297058369527},{0.4308558980108406,-0.1605429705836952},{-0.19787245165430847,0.8949780141072381},{-0.19787245165430842,0.8949780141072381},{-0.5907860100454578,0.18974221311023962},{-0.5907860100454575,0.18974221311023964},{-0.5306691342020886,-0.7275053842709899},{-0.5306691342020886,-0.7275053842709899},{-0.345074608245379,1.207589321519286},{-0.34507460824537883,1.207589321519286},{-0.32302823411726667,0.08250252511437048},{-0.32302823411726667,0.0825025251143705},{-0.1000939664088763,-1.056428113867832},{-0.10009396640887627,-1.056428113867832},{0.0057223538613018765,-0.07997801149692216},{0.005722353861301878,-0.07997801149692216},{-1.0232923766303312,0.22905472765407248},{-1.0232923766303312,0.22905472765407253},{-0.04071787429636753,0.03839904161757046},{-0.04071787429636751,0.03839904161757047},{-0.5114614823431506,-0.0673439850879256},{-0.5114614823431503,-0.06734398508792559},{-0.033395285925899576,-0.25197193535594753},{-0.03339528592589957,-0.2519719353559475},{-1.3238866550876203,-0.34335648499193994},{-1.3238866550876196,-0.3433564849919398},{0.3098949809621799,-0.692558554406312},{0.30989498096218,-0.6925585544063119},{-0.7778172969650805,-0.7251725696504421},{-0.7778172969650804,-0.7251725696504421},{0.5832467520992983,-0.0005585979375463679},{0.5832467520992983,-0.0005585979375463677},{0.6402717430536337,-0.24460516745019825},{0.6402717430536337,-0.24460516745019825},{0.3744231501345624,0.23752933224278633},{0.37442315013456257,0.23752933224278638},{-0.5526534599107001,0.2959174882702319},{-0.5526534599106999,0.29591748827023195},{0.0870980709703463,0.011155933053077993},{0.08709807097034632,0.011155933053077997},{0.10294466025799387,0.6246279155358483},{0.10294466025799387,0.6246279155358484},{0.7907530514131953,0.7968130944966136},{0.7907530514131955,0.796813094496614},{-0.06771348768905705,-0.19742894579933645},{-0.06771348768905704,-0.19742894579933642},{1.7336246702438183,-0.08111369728186346},{1.7336246702438185,-0.08111369728186343},{0.39279504341227045,-0.2803428186493195},{0.39279504341227056,-0.2803428186493194},{-0.3837990187335033,0.5817465996045292},{-0.38379901873350314,0.5817465996045292},{-0.15897299229161954,0.2123178635236439},{-0.15897299229161949,0.21231786352364398},{1.2871753315186103,-0.2936546706485327},{1.2871753315186105,-0.2936546706485326},{-0.28157817609809926,0.015215204873323618},{-0.28157817609809926,0.015215204873323621},{-0.8407785771058587,0.11715953275528568},{-0.8407785771058583,0.11715953275528568},{0.057427665729494065,0.17741033446395021},{0.057427665729494086,0.17741033446395027},{-0.3919333534914909,-0.8777063099779623},{-0.3919333534914909,-0.8777063099779623},{1.046062759037447,0.12566529633175702},{1.0460627590374476,0.1256652963317571},{0.05208282489856039,0.23074154552008772},{0.05208282489856039,0.23074154552008772},{0.3090093991217477,-0.28949051651550656},{0.3090093991217478,-0.2894905165155065},{-0.903992079888195,-0.08968028913527537},{-0.903992079888195,-0.08968028913527537},{0.1114034542194284,-0.1420055490952354},{0.11140345421942845,-0.1420055490952354},{0.49928483909803145,-1.031860401303775},{0.49928483909803145,-1.031860401303775},{-0.25021332122685536,-0.23430348924020267},{-0.2502133212268553,-0.23430348924020258},{0.45788605189844944,0.008986832993373578},{0.45788605189844944,0.008986832993373583},{0.9922986143818168,-0.3970601247358978},{0.9922986143818171,-0.3970601247358978},{0.3242247399299542,0.00883592005445788},{0.3242247399299542,0.008835920054457881},{0.6104748391149722,-0.1588370496187479},{0.6104748391149722,-0.15883704961874784},{-0.2328772934092499,-0.28654852459626834},{-0.23287729340924987,-0.28654852459626823},{0.2591579326588679,-0.48250620169929226},{0.2591579326588679,-0.4825062016992922},{0.030769057057074042,-0.6677902182695195},{0.030769057057074042,-0.6677902182695192},{0.5724668628416123,0.17684659209108886},{0.5724668628416124,0.17684659209108886},{-0.1936816938025718,0.017884183939394893},{-0.19368169380257177,0.017884183939394897},{0.3927424946727771,-0.3589320240798228},{0.3927424946727773,-0.35893202407982266},{-0.13217719866296695,0.4509072577920714},{-0.13217719866296687,0.4509072577920715},{0.7771200989698435,0.07094000492318109},{0.7771200989698438,0.07094000492318112},{-0.043208921594939775,-0.7058014850795868},{-0.043208921594939755,-0.7058014850795865},{-0.44161734737621083,0.17508260808335738},{-0.44161734737621083,0.17508260808335738},{0.3111521947954433,0.5211230285003844},{0.3111521947954433,0.5211230285003846},{-0.5089025606249975,-0.08897969566205755},{-0.5089025606249975,-0.08897969566205753},{-0.785274533858358,0.2966023384405856},{-0.785274533858358,0.2966023384405857},{0.13643734685972797,-0.5487534801505365},{0.136437346859728,-0.5487534801505362},{-0.5113536157192956,-0.38818343681854633},{-0.5113536157192953,-0.3881834368185463},{0.6482527388360249,-0.3660801422494009},{0.6482527388360252,-0.3660801422494007},{0.1219550825441264,0.2636220365395331},{0.12195508254412644,0.2636220365395332},{0.830646565838305,0.05595258169938715},{0.8306465658383052,0.055952581699387154},{0.02087272912166732,-0.2757601788166507},{0.02087272912166733,-0.2757601788166507},{-0.8969757534742673,-1.0096320440536182},{-0.8969757534742671,-1.0096320440536182},{0.281470556211261,-0.5392051870077439},{0.281470556211261,-0.5392051870077438},{0.09939015666169382,-0.0010699511947921958},{0.09939015666169386,-0.0010699511947921952},{-0.002256115172019346,-0.04020319566150099},{-0.0022561151720193458,-0.04020319566150097},{0.4504785560293585,0.373102472756903},{0.4504785560293585,0.3731024727569031},{0.5231672603524817,0.16985255790851625},{0.5231672603524821,0.16985255790851628},{-0.7514640400004967,0.07080018087746165},{-0.7514640400004965,0.07080018087746165},{0.13303832542382837,0.2602273203264872},{0.1330383254238284,0.2602273203264874},{0.19343395931079577,-0.5502548672222486},{0.1934339593107958,-0.5502548672222483},{-0.20823169078587966,-0.925945416171643},{-0.20823169078587964,-0.925945416171643},{-1.0354112179615744,0.9009086420084467},{-1.035411217961574,0.9009086420084467},{-0.13833287790394402,0.33595123313495734},{-0.13833287790394397,0.3359512331349575},{-0.48681401106341476,0.012840401303908289},{-0.4868140110634147,0.012840401303908292},{-0.38580806564875847,-0.3414309718415358},{-0.3858080656487583,-0.3414309718415357},{-0.387387928447792,0.3363647167396555},{-0.387387928447792,0.3363647167396555},{-0.7289577885281368,0.11000344782305926},{-0.7289577885281364,0.11000344782305929},{0.5996652640170703,-0.3788676471009784},{0.5996652640170704,-0.37886764710097826},{0.1184108904136601,-0.36481788339618465},{0.11841089041366011,-0.36481788339618465},{-0.030883796635844396,-0.2470002368704879},{-0.030883796635844393,-0.24700023687048783},{0.003754694361758959,-0.19869298401291166},{0.0037546943617589594,-0.1986929840129116},{0.11693502055240339,0.2098964093295748},{0.11693502055240342,0.20989640932957487},{-0.44372931923544234,0.056472315155220026},{-0.44372931923544234,0.05647231515522005},{-0.2835673309912712,-0.5631986234801009},{-0.2835673309912712,-0.5631986234801006},{0.6006827467154858,-0.5932750105917384},{0.6006827467154859,-0.593275010591738},{0.24363277450292076,-0.14517064380485928},{0.24363277450292084,-0.14517064380485925},{-0.4381173292277971,0.8515765445495456},{-0.4381173292277971,0.8515765445495457},{-0.4772264554892779,-0.4558040067081244},{-0.4772264554892779,-0.4558040067081244},{0.42511520260261526,-0.11760098022868892},{0.4251152026026154,-0.11760098022868892},{-0.317536469473846,-0.6047699984659938},{-0.31753646947384584,-0.6047699984659937},{-0.47946248289928994,-0.6870741625598951},{-0.47946248289928994,-0.6870741625598947},{0.24756054302633185,0.738575212829874},{0.24756054302633188,0.738575212829874},{0.30991707565082616,-0.1730076242522987},{0.3099170756508263,-0.17300762425229868},{0.1762415438802143,-0.45603299469545666},{0.17624154388021437,-0.4560329946954566},{-0.5684090790521096,-0.5323520385817601},{-0.5684090790521092,-0.5323520385817597},{1.1773067064626908,-0.31618798230516987},{1.177306706462691,-0.3161879823051697},{-0.2853416740347503,-0.7541701445620144},{-0.28534167403475025,-0.7541701445620143},{-0.3324739283651593,-0.041138670378205386},{-0.33247392836515915,-0.041138670378205386},{1.2664180977863824,-0.7401911722318033},{1.2664180977863828,-0.740191172231803},{0.4182693143279388,-0.7039334975576141},{0.41826931432793885,-0.703933497557614},{0.3813359912592416,-1.0453256669790556},{0.3813359912592416,-1.0453256669790554},{0.6509129030314083,-0.5412696201327558},{0.6509129030314084,-0.5412696201327558},{0.12018094767199916,0.5279211204926886},{0.12018094767199916,0.5279211204926887},{-0.45305717081196895,0.008198588994697165},{-0.45305717081196883,0.008198588994697166},{1.1671283999119613,-0.15065449704305311},{1.167128399911962,-0.1506544970430531},{-0.9008096320814036,0.1402761647761295},{-0.9008096320814036,0.14027616477612953},{-0.33154219658246964,0.2612070104089204},{-0.3315421965824696,0.2612070104089204},{-0.03280139984795011,-0.46647401981355685},{-0.032801399847950094,-0.46647401981355685},{0.01502591710973531,-0.5159959791954403},{0.015025917109735313,-0.51599597919544},{0.08126445056757484,-0.059451961687364746},{0.08126445056757486,-0.05945196168736473},{-0.4257412994811337,-0.20546840486340784},{-0.4257412994811336,-0.20546840486340776},{0.38799639318217627,0.3512270928822726},{0.3879963931821764,0.35122709288227266},{0.21154693848150546,-0.03634275654418231},{0.21154693848150552,-0.0363427565441823},{-0.23511045964865424,-0.3182820554745927},{-0.23511045964865424,-0.3182820554745926},{-0.27930734350964126,-0.34019779603069944},{-0.27930734350964115,-0.3401977960306993},{-0.7191434211894179,0.018581718879366438},{-0.7191434211894179,0.018581718879366448},{-0.020348708221664874,-0.11541476308320475},{-0.020348708221664864,-0.11541476308320471},{-0.869130537954744,0.5168791425703672},{-0.8691305379547439,0.5168791425703672},{-0.30797478551715907,0.16894312777393505},{-0.30797478551715896,0.16894312777393514},{-0.3412253953512523,-0.13703919671643483},{-0.3412253953512523,-0.1370391967164348},{-0.2363788997551411,0.020160959823633195},{-0.2363788997551411,0.020160959823633202},{-1.1342573157600304,-1.0490903515949865},{-1.1342573157600302,-1.0490903515949863},{-0.7951801524174422,-0.39048765852721024},{-0.7951801524174421,-0.39048765852721024},{-0.37682393173602985,-0.7154876526440125},{-0.37682393173602974,-0.7154876526440123},{-0.7261698499159233,0.25576182656428276},{-0.7261698499159229,0.25576182656428287},{0.6047122068958138,0.3531321759458359},{0.604712206895814,0.35313217594583596},{-0.3347865534686024,-0.44639370766792674},{-0.3347865534686024,-0.4463937076679267},{-0.3162737402922597,-0.6054254978296343},{-0.3162737402922597,-0.6054254978296342},{-0.38296113359720985,1.055727844318872},{-0.38296113359720985,1.0557278443188722},{-0.002541168924166004,-0.08959542143473792},{-0.0025411689241660036,-0.08959542143473788},{-0.46847678028199197,0.3128229066138286},{-0.4684767802819919,0.3128229066138288},{-0.7474510887594696,-0.11273520921655422},{-0.7474510887594695,-0.11273520921655422},{-0.10138857243233154,0.6540514477632215},{-0.10138857243233154,0.6540514477632217},{0.7025815823095183,-0.6472293123262207},{0.7025815823095184,-0.6472293123262207},{0.7918249248447928,-0.19424553454596438},{0.7918249248447932,-0.19424553454596438},{0.054665259285737594,-0.1426160884627486},{0.05466525928573761,-0.14261608846274854},{0.8678958225451003,0.7680573370722297},{0.8678958225451004,0.7680573370722298},{0.2527320686719843,-0.10300747956510839},{0.25273206867198444,-0.10300747956510836},{0.013030931888632663,0.2996259196764839},{0.013030931888632665,0.2996259196764839},{1.2101948699429645,0.7680276029628541},{1.210194869942965,0.7680276029628543},{0.001739080834353146,0.7050842932559666},{0.0017390808343531463,0.7050842932559666},{0.7920805263720672,-0.5649631474553106},{0.7920805263720672,-0.5649631474553105},{0.25575043599568525,0.0889317006762374},{0.25575043599568525,0.08893170067623742},{0.09261316731698108,0.2703067174076892},{0.0926131673169811,0.27030671740768925},{-0.5747802180771169,0.08613851106223658},{-0.5747802180771168,0.08613851106223662},{0.40507673833837643,-0.8945358512704514},{0.40507673833837643,-0.8945358512704511},{0.3856111747477545,-0.11976774680260635},{0.3856111747477546,-0.11976774680260632},{-0.25578702556512617,0.3677566511805598},{-0.255787025565126,0.36775665118055983},{-0.20976738975410314,0.6671667928732408},{-0.20976738975410314,0.6671667928732408},{-0.21007992057543357,0.11101431938197523},{-0.21007992057543348,0.11101431938197523},{-0.5538419739084758,-0.050566470413442005},{-0.5538419739084757,-0.05056647041344199},{-0.26983745787555147,-0.005254721629673997},{-0.2698374578755514,-0.0052547216296739965},{-0.31654388864740896,0.4356887820490702},{-0.3165438886474089,0.43568878204907036},{-0.6124922582532396,-0.22656761299178974},{-0.6124922582532395,-0.22656761299178974},{0.5136728866074527,-0.14672923625352396},{0.513672886607453,-0.14672923625352388},{-0.06100014188022765,-0.07483055132359873},{-0.06100014188022765,-0.07483055132359868},{0.0632389321030824,-0.3727037315430909},{0.06323893210308244,-0.3727037315430909},{-0.6239765829480394,-0.43378186506793615},{-0.6239765829480394,-0.43378186506793603},{-0.2962023614106011,-0.24082492622254642},{-0.296202361410601,-0.24082492622254636},{-0.08363974045743232,0.4635673337808054},{-0.08363974045743229,0.4635673337808054},{-0.07869730556773968,0.7594146318238462},{-0.07869730556773967,0.7594146318238463},{0.559161552723403,0.26005051714491845},{0.5591615527234033,0.2600505171449186},{0.009099193447173748,-0.8925628969298484},{0.00909919344717375,-0.892562896929848},{-0.01551647656911137,-0.38885814801603924},{-0.015516476569111365,-0.38885814801603924},{-0.01567035614455939,-0.3579485826040038},{-0.015670356144559385,-0.35794858260400375},{0.446781462990565,-0.052239411468506664},{0.446781462990565,-0.05223941146850665},{1.0710389841912518,-0.2731132034289364},{1.0710389841912522,-0.2731132034289364},{0.23533790163003582,-0.23476194158747798},{0.23533790163003585,-0.23476194158747793},{0.07915424936926652,0.6036539628377416},{0.07915424936926652,0.6036539628377419},{0.6311044368999582,-0.6562564634414947},{0.6311044368999585,-0.6562564634414947},{-0.21077148265812098,0.032523815759867236},{-0.2107714826581209,0.03252381575986725},{-0.7231240597670221,-0.006544627251553192},{-0.7231240597670221,-0.006544627251553192},{-0.08060584759784664,0.13336777305165762},{-0.08060584759784663,0.13336777305165762},{0.48597827619774187,-0.6069162101181359},{0.48597827619774203,-0.6069162101181359},{-0.4507483055292626,0.19434862886898324},{-0.4507483055292625,0.19434862886898324},{0.2827195867383647,-0.22519487430374507},{0.2827195867383647,-0.22519487430374502},{-0.8215093346304647,-0.03268014435976413},{-0.8215093346304647,-0.03268014435976413},{-0.11933763497114419,0.25235131805383626},{-0.11933763497114419,0.25235131805383626},{-0.050641541900826315,-0.05481336786080909},{-0.05064154190082631,-0.05481336786080908},{0.37639163137503584,-0.04913023720926801},{0.37639163137503595,-0.049130237209268006},{0.2754899163868257,-1.2892018379461803},{0.27548991638682585,-1.28920183794618},{0.19113786193208002,-0.49992907513642937},{0.1911378619320801,-0.4999290751364293},{-0.18408107881733532,-0.6738283284096425},{-0.18408107881733524,-0.6738283284096425},{0.26736586776080096,0.35645201936711196},{0.2673658677608011,0.35645201936711196},{1.1765511302564113,-0.5480893596413949},{1.176551130256412,-0.5480893596413949},{1.1542398998705217,-0.3147952918363603},{1.1542398998705217,-0.3147952918363603},{-0.6689853024562176,0.8040377543458188},{-0.6689853024562172,0.804037754345819},{0.24120212235388105,-0.07423471553787372},{0.2412021223538811,-0.0742347155378737},{0.5689391732853385,-0.4334628652354342},{0.5689391732853388,-0.43346286523543415},{-0.4229071860412019,0.11827577249881677},{-0.4229071860412019,0.11827577249881677},{-0.5721332694193333,0.26812444739865027},{-0.5721332694193333,0.26812444739865043},{-0.14648803653271852,0.4305316791577641},{-0.1464880365327185,0.43053167915776425},{0.05374623984152754,-0.4459959249147729},{0.053746239841527564,-0.4459959249147729},{0.5896530144495327,0.07735649659442079},{0.589653014449533,0.07735649659442081},{-0.25257596915203095,-0.1831343633500895},{-0.2525759691520309,-0.18313436335008942},{0.6519199000082152,0.8113502122689806},{0.6519199000082153,0.811350212268981},{-0.20987680281715365,0.31018961232143716},{-0.2098768028171536,0.3101896123214372},{0.488852615545995,-0.7694857263920457},{0.488852615545995,-0.7694857263920457},{0.32498664525642773,0.35466894818618966},{0.3249866452564279,0.3546689481861898},{-0.21867254773101694,0.33653237135631914},{-0.21867254773101685,0.3365323713563192},{-0.1628632057456908,0.12513912098254698},{-0.16286320574569077,0.12513912098254704},{-0.2482127546806861,0.054592620932045616},{-0.24821275468068604,0.05459262093204564},{0.19972864932719311,0.48470032915534},{0.19972864932719311,0.4847003291553401},{0.5194203708908046,0.6086898891039105},{0.519420370890805,0.6086898891039109},{0.19766219439600413,-0.624494348335875},{0.1976621943960042,-0.6244943483358748},{-0.6659766058933296,0.5642507949642299},{-0.6659766058933294,0.56425079496423},{0.6380303702196312,0.7911458327140173},{0.6380303702196312,0.7911458327140173},{-0.2639580944341406,1.0973674142268384},{-0.26395809443414053,1.0973674142268388},{-0.013043068475538544,-0.18048505417693753},{-0.013043068475538539,-0.1804850541769375},{-0.6177459783187123,-0.2779905668540201},{-0.6177459783187123,-0.27799056685401996},{0.6541020344580163,0.582124792529954},{0.6541020344580166,0.5821247925299543},{-1.0384774049322054,0.8009193618277922},{-1.0384774049322048,0.8009193618277922},{-0.1554306169575903,0.44885645072316704},{-0.15543061695759022,0.4488564507231671},{-0.21901225075291414,0.029572470395186623},{-0.21901225075291408,0.029572470395186626},{0.06665349581693292,0.2278463140029154},{0.06665349581693296,0.22784631400291547},{-0.18730209014152358,-0.44204961843797247},{-0.1873020901415235,-0.44204961843797247},{-0.8954194222707068,-0.09622762051569644},{-0.8954194222707068,-0.09622762051569644},{0.6876813467148475,-0.1006745035590906},{0.6876813467148476,-0.10067450355909059},{0.8020144882556199,-0.4557444532553835},{0.80201448825562,-0.4557444532553834},{0.11678579588295551,0.4778013596576872},{0.11678579588295553,0.4778013596576872},{-0.6173779479953273,-0.1463086195272349},{-0.6173779479953271,-0.1463086195272348},{0.04109570275886973,-0.38022576288843984},{0.04109570275886973,-0.3802257628884398},{0.8314003498756972,-0.48166469434786263},{0.8314003498756976,-0.4816646943478625},{-0.3417449594665635,0.2351852756985343},{-0.34174495946656336,0.23518527569853434},{-0.747231864230736,-0.05533196936496787},{-0.7472318642307357,-0.055331969364967856},{0.44786515872763016,-0.8581662077619436},{0.4478651587276303,-0.8581662077619435},{0.2394196493059546,0.5685962507505915},{0.23941964930595466,0.5685962507505915},{-0.47370747024486054,-0.518217306207919},{-0.4737074702448605,-0.5182173062079186},{-0.24686466238928517,0.5140980999371543},{-0.24686466238928517,0.5140980999371544},{0.4465869335283311,-0.37822156772624715},{0.4465869335283311,-0.378221567726247},{0.7216840280411014,-0.12155234552799939},{0.7216840280411017,-0.12155234552799934},{0.015204864396908546,0.6376683618342354},{0.015204864396908548,0.6376683618342357},{-0.42393694982300156,-0.5218089477315881},{-0.42393694982300145,-0.5218089477315878},{0.07415078821601045,0.6371956908817733},{0.07415078821601047,0.6371956908817734},{-0.1903574628038755,-0.38684400671343444},{-0.19035746280387544,-0.38684400671343444},{-0.3773559131237457,0.0068579608273421355},{-0.3773559131237457,0.006857960827342137},{0.08501466839094085,0.27421860297639405},{0.08501466839094089,0.2742186029763941},{1.3703190609240201,-0.6705242349995242},{1.3703190609240201,-0.6705242349995238},{0.22067502222484947,-0.42972719575427676},{0.22067502222484955,-0.4297271957542766},{0.4496324731373458,-0.5997904924904096},{0.44963247313734583,-0.5997904924904094},{0.4606769016215748,-0.4028663766293615},{0.4606769016215748,-0.4028663766293614},{0.20461881450521396,0.23845839738985905},{0.20461881450521396,0.2384583973898591},{-0.177021903697815,0.0017472361069717779},{-0.17702190369781493,0.0017472361069717785},{0.33088666738271627,0.39635242461181414},{0.33088666738271644,0.39635242461181425},{-0.5126793030962896,-0.9816818891160128},{-0.5126793030962894,-0.9816818891160127},{-0.20315580021343643,0.25993483522132416},{-0.2031558002134364,0.2599348352213242},{0.01157315314252727,-0.0752286580183012},{0.011573153142527272,-0.07522865801830117},{-0.2122874953702656,1.0455265018271471},{-0.2122874953702656,1.0455265018271478},{-0.4118959539781374,0.2565463745780656},{-0.41189595397813733,0.2565463745780657},{-0.40504807761153394,-0.826767279687959},{-0.40504807761153383,-0.8267672796879587},{0.8728370056581523,-0.8489146211330629},{0.8728370056581523,-0.8489146211330626},{-0.15484731030271964,0.2978543674333216},{-0.15484731030271962,0.2978543674333217},{0.9598395979151622,-0.021475535817715843},{0.9598395979151622,-0.021475535817715833},{-0.3813769756912948,0.7192828208488169},{-0.38137697569129464,0.719282820848817},{0.21951101473819934,0.6480843500744788},{0.21951101473819934,0.6480843500744791},{-0.3113427744080721,0.045948715073330315},{-0.31134277440807195,0.045948715073330336},{-0.16009981684527497,-0.17250123317199526},{-0.16009981684527497,-0.17250123317199526},{0.25568807750253153,0.30423782531372767},{0.2556880775025317,0.30423782531372784},{0.2534978588720535,0.41258202395216825},{0.25349785887205356,0.4125820239521684},{-0.22823188438717018,0.3555909158613313},{-0.22823188438717018,0.3555909158613314},{-0.043847734475191566,0.546988883272136},{-0.04384773447519155,0.5469888832721362},{0.0022848127328267687,0.16581911916150355},{0.0022848127328267695,0.16581911916150358},{-0.9664510167365821,0.5772556019222926},{-0.9664510167365818,0.5772556019222929},{0.19331577714046103,0.16819098929912168},{0.1933157771404611,0.16819098929912168},{0.880938028512706,1.3996876457175011},{0.8809380285127063,1.3996876457175018},{-0.6403207225525454,0.2297596920614577},{-0.640320722552545,0.22975969206145774},{-0.926993144927124,-0.7404608887419831},{-0.9269931449271237,-0.7404608887419828},{-0.30368277421537726,-0.5055446699316368},{-0.3036827742153772,-0.5055446699316366},{0.5466694604144853,0.07004761038909013},{0.5466694604144854,0.07004761038909016},{0.25500851421300097,-0.29367076034138706},{0.25500851421300114,-0.29367076034138695},{0.15138727668563495,-0.0049418965549759275},{0.151387276685635,-0.004941896554975927},{-0.43887856303510187,0.8136477342030863},{-0.4388785630351018,0.8136477342030866},{-0.33880265875092413,-0.31551224415527107},{-0.33880265875092397,-0.315512244155271},{1.377423681456482,0.012704561359672462},{1.377423681456482,0.012704561359672462},{-0.041263422421853435,0.4035844851267748},{-0.041263422421853414,0.40358448512677497},{-0.08610165644909173,-0.7986737010728233},{-0.08610165644909172,-0.7986737010728232},{0.3836918938530838,0.8390085156051033},{0.38369189385308383,0.8390085156051033},{-0.17307936456124118,-0.06474709047756155},{-0.1730793645612411,-0.06474709047756153},{-0.02753475823767776,-0.15870621273858665},{-0.02753475823767775,-0.15870621273858657},{-0.5116996522331295,-0.4553457116638264},{-0.5116996522331294,-0.45534571166382637},{0.6086269804673172,0.015815755110900165},{0.6086269804673176,0.015815755110900165},{-0.3066696359213093,-0.6490796718967194},{-0.3066696359213093,-0.6490796718967194},{0.2573582808012723,0.49429943061451787},{0.25735828080127243,0.4942994306145179},{-0.5573569025227104,0.10864971359925568},{-0.5573569025227101,0.1086497135992557},{0.10100854569812368,-0.5775400700305715},{0.10100854569812368,-0.5775400700305712},{0.16011849083924728,-0.5182501761924749},{0.1601184908392473,-0.5182501761924749},{1.1626364195660153,-0.027141868869618918},{1.162636419566016,-0.027141868869618915},{-0.45286020053725284,0.46618578082394724},{-0.4528602005372528,0.4661857808239473},{0.32258327609642495,-0.2102016160014837},{0.3225832760964251,-0.21020161600148368},{-0.4469041249092892,-0.30385833257152894},{-0.4469041249092891,-0.30385833257152894},{0.8377224062973287,-0.5225876068528582},{0.8377224062973289,-0.5225876068528581},{-0.35063350958529577,-0.44521824304962737},{-0.3506335095852957,-0.44521824304962726},{0.042917945172412694,-0.2699072536318396},{0.0429179451724127,-0.2699072536318395},{0.28617439894992625,-0.6241441143108587},{0.28617439894992625,-0.6241441143108584},{-0.21331655993940007,1.1315954154549954},{-0.21331655993940002,1.1315954154549959},{-0.7071603986591413,-0.0587365030909921},{-0.7071603986591409,-0.0587365030909921},{-0.43104678259786616,-0.4031905103539523},{-0.4310467825978661,-0.40319051035395215},{0.479647329346727,-0.6208557999362405},{0.47964732934672716,-0.6208557999362404},{-0.27104983788326825,0.005338803231299233},{-0.2710498378832682,0.0053388032312992354},{-0.0041329173810210895,0.3935166528530436},{-0.004132917381021089,0.39351665285304366}}```

[fogleman]

This smaller set of points made pseudoAngle return exactly 1 for me in Go.

{{0.226270008640849, -0.5484478681473859}, {0.22627000864084906, -0.5484478681473857}, {0.766192698520777, -0.06114560279536302}, {0.7661926985207771, -0.06114560279536302}, {0.40151121510492016, 0.08616979557470032}, {0.40151121510492027, 0.08616979557470034}, {-0.41675996433129736, -0.5902787491305856}, {-0.4167599643312972, -0.5902787491305853}, {-0.2479064469635639, -0.7472011647497873}, {-0.24790644696356384, -0.7472011647497872}, {0.6078988481689899, -0.8087190266174613}, {0.6078988481689901, -0.808719026617461}, {0.6844238681986647, -0.22229148851718702}, {0.6844238681986647, -0.222291488517187}, {0.6486832941181451, 0.3706194950394349}, {0.6486832941181452, 0.3706194950394349}, {-0.5361048842131249, -0.16765691382574804}, {-0.5361048842131245, -0.167656913825748}, {0.4588358986737203, -0.9000280551977525}, {0.4588358986737205, -0.9000280551977525}, {0.3960651926938643, 0.19117525930527385}, {0.39606519269386437, 0.1911752593052739}, {0.30699987842448867, -0.4067155996580057}, {0.3069998784244887, -0.4067155996580056}, {0.47811583559881354, 0.4551485080955586}, {0.47811583559881354, 0.4551485080955586}, {0.5569494202770435, 0.3174275448747843}, {0.5569494202770439, 0.3174275448747845}, {-0.4277027605175392, 0.09695587866512022}, {-0.4277027605175391, 0.09695587866512025}, {-0.5748114807265807, -0.03838218657575568}, {-0.5748114807265806, -0.03838218657575567}, {-1.0317070883952917, -0.5245256032470283}, {-1.031707088395291, -0.5245256032470283}, {0.14712374452633492, 0.33141471681448986}, {0.147123744526335, 0.33141471681448986}, {-0.2834737219004291, -0.9271587984120542}, {-0.2834737219004289, -0.9271587984120538}, {-0.6098149486946731, 0.5553773725836295}, {-0.6098149486946729, 0.5553773725836295}, {1.1206314478250745, 0.3921423623286639}, {1.1206314478250745, 0.39214236232866406}, {0.4477538973665876, -0.04256704865570235}, {0.4477538973665877, -0.04256704865570235}, {-0.6156635308889042, -0.10817302193016937}, {-0.6156635308889041, -0.10817302193016932}, {0.17897362794557034, -0.04224227852769616}, {0.17897362794557034, -0.04224227852769614}, {-0.9646885789850332, -1.4563419829050452}, {-0.9646885789850331, -1.456341982905045}, {0.2911613415160255, 0.015655417967490592}, {0.29116134151602563, 0.015655417967490596}, {-0.3698918540831971, 0.6983267205999204}, {-0.3698918540831969, 0.6983267205999205}, {1.4056553730213062, -0.41615789580202767}, {1.4056553730213066, -0.41615789580202767}, {0.34141990921721344, -0.5679551502988661}, {0.3414199092172136, -0.5679551502988661}, {0.2957318137669341, 0.8416499601535058}, {0.29573181376693425, 0.841649960153506}, {0.035141462612931273, -0.45835970615650135}, {0.03514146261293129, -0.45835970615650123}, {-1.3263110033694971, 0.8223290351908346}, {-1.326311003369497, 0.8223290351908346}, {-0.18787969354847422, 1.4601214758378256}, {-0.18787969354847417, 1.4601214758378258}, {-0.5421684590742957, -0.5196118080038157}, {-0.5421684590742956, -0.5196118080038157}, {-0.15415956428809274, 0.2553265483092856}, {-0.15415956428809266, 0.25532654830928564}, {0.24744639466303925, 0.36561549310806263}, {0.24744639466303933, 0.36561549310806274}, {-0.007949225522230624, -0.4463313570187974}, {-0.00794922552223062, -0.4463313570187972}, {0.4314282749865176, 0.6907165244683744}, {0.4314282749865177, 0.6907165244683744}, {0.22721916356346672, -1.145924985720078}, {0.22721916356346675, -1.1459249857200775}, {0.11627266697915434, 0.5679584977485386}, {0.11627266697915438, 0.5679584977485389}, {-0.004760241854834868, 1.341758406463988}, {-0.004760241854834866, 1.3417584064639887}, {0.34070213758085, -0.4524446934513693}, {0.3407021375808501, -0.45244469345136923}, {0.8842875090593054, -0.4369329059094983}, {0.8842875090593055, -0.43693290590949824}, {0.1514286184534766, -0.17725085421066233}, {0.15142861845347666, -0.17725085421066225}, {-0.4255258812089902, -0.48986352859695054}, {-0.42552588120899015, -0.4898635285969505}, {0.9377261482762783, -0.1443481348548356}, {0.9377261482762784, -0.14434813485483552}, {0.04260345503852292, 0.951377045867543}, {0.04260345503852292, 0.951377045867543}, {0.305243584013604, -0.3875472629266138}, {0.305243584013604, -0.3875472629266138}, {0.03603755940893599, 0.34504467425927055}, {0.036037559408936, 0.34504467425927055}, {0.7432869522329792, -0.7836440067269177}, {0.7432869522329795, -0.7836440067269175}}

[mourner]

@fogleman both cases are passing in the JS version. I guess JS does the angle calculation differently and never reaches 1.

[fogleman]

That's weird.

The pseudoAngle arguments are:

dx = -0.0710337425925249
dy = 6.938893903907228e-18

I tried your function in node and Chrome with this input and it does produce 1. So I guess you never have those same arguments for some reason.

[fogleman]

@mourner Are you sure it never happens? JS doesn't seem to mind going out of bounds:

[mourner]

@fogleman hmm, I actually didn't check pseudoangle. I only saw that the samples produce triangulations that pass validation. Let me try it.

[mourner]

@fogleman yeah, you're right. It reached 1, it just didn't affect anything, just silently grew the hash. Fixed just in case in https://github.com/mapbox/delaunator/commit/d7a7ce61389cb27e4290769f3ab76255fa884e1c

[fogleman]

@mourner You didn't render the first test case I posted, did you? :)

It computes the right area, but it's wrong. The hull doubles over on itself. Here are renders from Go:

Incorrect:

Correct:

I didn't render anything from JS but yours is producing a hull with 16 points which matches the incorrect version.

[mourner]

@fogleman whoa that indeed looks bad! The corresponding tests fail when I add abs to triangle areas. Will look into it.

[mourner]

@fogleman fixed for now in https://github.com/mapbox/delaunator/commit/77a7992772f98dc42cf7a28735532b709ba772ec but I'd love to explore what exactly happens in the algorithm for the hull to go like that.

[fogleman]

So, my robust code actually does work. I just had another bug earlier that threw me off. The only time my robust code skips a point now is when it's really close to one of the initial 3 points (i0, i1, i2). So I probably just need a robust version of circumradius, or comparing circumradii.

[mourner]

It's indeed a robustness issue — a point tries to determine orientation vs a near-zero segment, and decides it's on the other side than it actually is.

[
-0.0041329173810210895,
0.3935166528530436,
-0.004132917381021089,
0.39351665285304366
]

[MaxGraey]

@mourner Proper comparison two floats is really tricky. May be better use more robust comparison instead current, like this:

function equals(a, b) {
  return Math.abs(a - b) <= Number.EPSILON; // 2.220446049250313e-16
}

function almostEquals(a, b) {
  if (a === b) return true;
  var eps = Math.max(Math.abs(a), Math.abs(b)) * Number.EPSILON;
  return Math.abs(a - b) <= eps;
}

const a = 0.10000000000000001;
const b = 0.10000000000000011;
console.log(equals(a, b)); // true
console.log(almostEquals(a, b)); // false

[fogleman]

I was wrong - it still skips more points than that. But it never produces the doubled-over hull (yet), so it's doing something better. Still working on it...

[fogleman]

@MaxGraey that's probably not sufficient for this. We need consistent geometry predicates for multiple different queries.

[munrocket]

I think you can use double.js when you divide to small number for good robustness and peformance.