Negative buffer with join-style mitre

[theroggy]

Quite a specific case: for a specific polygon, when I apply a negative buffer (distance -5) with join style mitre (mitre distance 2), a large part of the polygon disappears...

In the image below the input polygon is in blue, the result after applying the negative buffer is in red.

Code to reproduce:

from matplotlib import pyplot as plt
import shapely
import shapely.plotting

wkt = "Polygon ((192800.25198371690930799 231454.62886510850512423, 192799.81520632578758523 231453.52218602373613976, 192786.04915788403013721 231446.86360824486473575, 192801.88253643843927421 231411.54299454658757895, 192801.30145057078334503 231410.01465837462455966, 192716.32490501765278168 231371.78896312581491657, 192712.28734987965435721 231375.44304183250642382, 192714.54021742971963249 231382.17160624865209684, 192768.56934017801540904 231524.5083285111177247, 192778.11818941161618568 231550.19523288929485716, 192780.08499048536759801 231555.39736354001797736, 192780.06706917562405579 231555.429495604155818, 192813.87713734642602503 231646.39144207796198316, 192813.24304402875714004 231647.81024954235181212, 192828.236274086026242 231663.98016347750672139, 192829.7379972608468961 231662.84963450999930501, 192829.76923481578705832 231662.90687218552920967, 192835.13797317413263954 231672.21670686689321883, 192838.74942462120088749 231678.48658785136649385, 192889.72698129829950631 231765.04056633179425262, 192899.79063106325338595 231784.68724321207264438, 192904.71836394618730992 231797.77362817942048423, 192904.44099068827927113 231798.57972623527166434, 192908.84998118507792242 231809.34114382942789234, 192915.39578192730550654 231828.9553750800259877, 192918.00878075163927861 231829.40077260686666705, 192914.46051785934832878 231832.14893700383254327, 192912.85541633720276877 231837.50681109874858521, 192913.43023715176968835 231839.38160613141371869, 192910.59184958104742691 231838.42826746855280362, 192902.21572010856471024 231844.74922290549147874, 192853.78836480996687897 231890.11989867241936736, 192853.77580221343669109 231890.11864241276634857, 192848.4450350079277996 231895.12149176179082133, 192838.21739705553045496 231889.40967127529438585, 192836.12850935195456259 231887.15921214708941989, 192835.26215201613376848 231882.38847108458867297, 192831.76194672874407843 231880.03587408812018111, 192833.35543169380980544 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192752.4831609778048005 231679.49890663541737013, 192734.39380021544639021 231695.12015135888941586, 192682.75085649755783379 231741.08141903163050301, 192682.68559480312978849 231741.46570078661898151, 192698.44373878868645988 231769.83035996064427309, 192716.76689904610975645 231795.61679986893432215, 192716.82813857996370643 231795.62128870908054523, 192727.60947156630572863 231816.16498723489348777, 192731.27823051571613178 231824.56638075172668323, 192667.52885671347030438 231854.40085114433895797, 192666.95976365191745572 231855.99384012760128826, 192667.82814148627221584 231857.8061069123505149, 192630.66964961175108328 231875.35511270837741904, 192590.32536901682033204 231769.69199562008725479, 192589.5981729646155145 231769.30065908713731915, 192495.7756118583783973 231790.15011711075203493, 192415.0532187680946663 231813.00525250378996134, 192414.27045788787654601 231808.13575167927774601, 192407.87309215069399215 231807.15003862322191708, 192389.07855140746687539 231844.59912353061372414, 192387.93428563565248623 231864.21510819019749761, 192411.18594264448620379 231995.28533796977717429, 192408.17658207967178896 232019.8239289904886391, 192407.47137072047917172 232021.58199111130670644, 192407.01404671400086954 232025.16104855330195278, 192352.96504584528156556 232156.7300528778869193, 192351.01467031831271015 232161.49096327423467301, 192350.15414678974775597 232163.58223557041492313, 192303.26592349063139409 232278.21738771288073622, 192303.93884741986403242 232279.7927760501333978, 192539.61663765838602558 232372.60537935988395475, 192559.49825207740650512 232379.86063926786300726, 192560.66032974197878502 232379.36802874502609484, 192560.74785376954241656 232379.1715125321643427, 192560.51012587067089044 232380.45790198497707024, 192560.76279075685306452 232380.91628111110185273, 192561.9358490142330993 232381.38550441362895072, 192562.92666004609782249 232382.89265358890406787, 192563.46525952045340091 232383.33036459251889028, 192561.17257465189322829 232383.85829763329820707, 192535.92900264158379287 232436.80534718171111308, 192527.55848618701566011 232455.13268773836898617, 192525.60437112807994708 232459.04091785062337294, 192525.85061900209984742 232459.3889639642147813, 192519.63208731100894511 232474.30764635978266597, 192519.63840958767104894 232474.332343098212732, 192558.30220923901651986 232505.25689741817768663, 192570.90570758713874966 232515.71038722453522496, 192461.07175790265318938 232651.28163093799958006, 192420.5935977183689829 232624.11501415411476046, 192417.98881937187979929 232624.91207459970610216, 192381.75821330811595544 232714.11673245165729895, 192379.23003117376356386 232711.90619371365755796, 192373.32804879525792785 232716.01500624587060884, 192375.23590001702541485 232721.02311570360325277, 192376.00231167644960806 232723.19220530576421879, 192378.47354798138258047 232726.4740071187261492, 192394.23271510089398362 232733.7350568154361099, 192406.3676703511737287 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192707.28671687084715813 232920.6749988810333889, 192770.76497748770634644 232842.53522798043559305, 192813.31242550519527867 232789.1887326360156294, 192836.56705439355573617 232763.47255525083164684, 192850.7138776911306195 232745.41449224983807653, 192863.24628754629520699 232730.08600688909064047, 192899.5329030393040739 232684.81279991441988386, 192903.63645668761455454 232679.61563416908029467, 192907.76439408725127578 232674.37203801280702464, 192911.63812869536923245 232669.06902891132631339, 192911.76885447942186147 232663.99686849268618971, 192910.56288243364542723 232662.17068225200637244, 192909.09648780227871612 232659.91269405858474784, 192906.72686511883512139 232657.74261854845099151, 192905.5437751499703154 232656.66093402204569429, 192844.50352501097950153 232608.28318247699644417, 192830.5920382282929495 232596.32768666232004762, 192826.24092836008640006 232592.7713931166799739, 192785.86718021632987075 232560.91476437554229051, 192785.16370083412039094 232560.35990728120668791, 192725.61632455958169885 232513.03404491452965885, 192710.28221539524383843 232501.03300255941576324, 192707.55067027756012976 232498.89384072029497474, 192706.69442835947847925 232498.77967513116891496, 192698.59283302642870694 232491.53488776518497616, 192698.39844891024404205 232491.3648016634688247, 192680.03065662924200296 232476.84750989897293039, 192631.37415711453650147 232438.37984671094454825, 192633.61069369336473756 232437.98288048247923143, 192633.62898876107647084 232437.95215415078564547, 192633.63484389637596905 232437.96630640444345772, 192633.51028010400477797 232438.37277772690868005, 192657.53590486120083369 232457.81729268192430027, 192672.38375702747725882 232470.46101024863310158, 192737.07912954624043778 232521.2723982373427134, 192737.95294938643928617 232522.07560637325514108, 192738.50536789436591789 232522.56883718390599824, 192740.96218751720152795 232524.24037199580925517, 192743.58999999999650754 232526.03798784568789415, 192743.58999999999650754 232526.58831015991745517, 192745.80613698324305005 232528.45187989578698762, 192746.50882385979639366 232529.04646109903114848, 192789.98717906084493734 232563.60489585704635829, 192800.37103793551796116 232571.95995458585093729, 192800.81439930238411762 232572.31464367933222093, 192826.49502517431392334 232592.05445165128912777, 192832.76172504608985037 232598.01180805807234719, 192841.92215053900144994 232605.16041212165146135, 192845.80953415669500828 232608.19963931367965415, 192849.52673673687968403 232606.86063317104708403, 192855.49209751808666624 232579.64054153926554136, 192919.50241922790883109 232581.84642961548524909, 192918.88445933244656771 232588.02602856984594837, 192917.52506321200053208 232611.41771144230733626, 192916.30898886188515462 232646.25466488435631618, 192917.50606367166619748 232651.16367754968814552, 192917.38954608884523623 232656.19335320743266493, 192917.99913125287275761 232659.54607160922023468, 192922.39653397185611539 232663.95994400134077296, 192925.12685555423377082 232665.2275933074997738, 192960.08149505700566806 232664.04156093398341909, 192922.19341563477064483 232667.21885490595013835, 192909.53603150777053088 232675.14850377454422414, 192868.37171355160535313 232724.70790923503227532, 192847.13947025814559311 232752.03375615930417553, 192830.2759766562958248 232774.70624178560683504, 192827.72400038444902748 232780.88987659817212261, 192823.86363902481389232 232806.93704885718761943, 192820.24017160257790238 232837.29365370573941618, 192819.12932134311995469 232853.61698112945305184, 192820.09673285990720615 232869.01323250317364, 192821.28074574892525561 232880.06742180325090885, 192824.1307107700558845 232898.55826628542854451, 192829.96705342881614342 232902.89904613792896271, 192870.05982268255320378 232909.17086822880082764, 192884.65518619923386723 232931.03106220325571485, 192888.17992303089704365 232934.60867008741479367, 192883.52317678884719498 232941.84378319612005726, 192883.83850210611126386 232943.36052349352394231, 192916.7698694329301361 232965.36021374762640335, 192918.21366124899941497 232965.0968009339121636, 192925.63976374012418091 232954.71494442282710224, 192947.68821440875763074 232970.23499845754122362, 192942.1701671862101648 232986.24941871801274829, 192924.76053885917644948 233021.07964552222983912, 192924.96754859320935793 233021.89091663362341933, 192948.8933581218298059 233038.52788951082038693, 192950.67605876186280511 233038.1777009878132958, 192971.55617653668741696 233005.97581951369647868, 192981.81405613015522249 232983.90794663460110314, 192984.59929442885913886 232980.04247964563546702, 192995.5841574429650791 232981.26558414089959115, 192999.9692972571356222 232982.47234742311411537, 193023.59184762451332062 232993.35375672130612656, 193036.73519013344775885 232998.62738291773712263, 193046.10733076045289636 233001.84925563159049489, 193042.52411234023747966 233008.89743443831684999, 193031.50505202397471294 233038.46160773732117377, 193032.01802369666984305 233039.67745134286815301, 193056.35700390723650344 233050.41648024873575196, 193058.42658363949158229 233049.4689355660811998, 193060.46776817011414096 233042.78869528393261135, 193067.39254103956045583 233046.55884940174291842, 193069.16645849181804806 233045.99623190480633639, 193091.66301979203126393 233000.35797202377580106, 193094.40377602443913929 233001.71837972523644567, 193082.89317181007936597 233024.72046754890470766, 193083.38796979136532173 233026.23089765457552858, 193099.60730838170275092 233034.54490507373702712, 193103.42132690502330661 233036.27148405590560287, 193101.73627185504301451 233060.55023581147543155, 193172.30919041112065315 233094.16163518626126461, 193173.79342635755892843 233093.64592746019479819, 193178.11859773710602894 233084.86102381374803372, 193181.13606766925659031 233058.56592869080486707, 193232.38928018801379949 233065.46942262188531458, 193228.53661313591874205 233094.60521720329415984, 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193115.85938445702777244 232655.54939408323843963, 193114.35118856074404903 232655.65627410737215541, 193111.14082265429897234 232656.32387313377694227, 193092.35532254326972179 232657.19830279378220439, 193075.37623333823285066 232658.41294083429966122, 193074.64658911045989953 232659.16945603408385068, 193072.97890219095279463 232706.44946311510284431, 193072.89611109610996209 232707.2664804985106457, 193062.0684238221438136 232712.54804872375098057, 193057.07905715482775122 232727.18641666768235154, 193041.0641354170802515 232723.78144231621990912, 193040.13154645578470081 232724.32151934591820464, 193039.38962966474355198 232726.62605734285898507, 193038.45235872775083408 232726.31297734499094076, 193038.37509640704956837 232726.16950883864774369, 193026.51480092728161253 232722.0030688317201566, 193024.87509790837066248 232722.82657911806018092, 193007.96391928123193793 232777.0904308422759641, 192994.52893738783313893 232820.72051213454687968, 192994.01243347881245427 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poly = shapely.from_wkt(wkt)
poly_bufm = shapely.buffer(
    poly, distance=-5, join_style="mitre", mitre_limit=2.0,
)

print(f"poly.is_valid: {poly.is_valid}")
print(f"poly_bufm.is_valid: {poly_bufm.is_valid}")

shapely.plotting.plot_polygon(poly)
shapely.plotting.plot_polygon(poly_bufm, color="red")
plt.show()

[pramsey]

But with a non-mitre end-cap? (I kind of wonder what a mitre even means in the case of polygon buffer/unbuffer)

[theroggy]

As far as I know an end-cap is irrelevant for a polygon as it doesn't have any endings?

Regarding join-cap mitre (distance) for polygon buffer: look at the bottom of the following page for some examples/illustrations: geofileops.buffer

[pramsey]

You specified mitre in your description so I wondered if you were seeing it having an effect. I agree, for polygons it should be a no-op.

[theroggy]

You specified mitre in your description so I wondered if you were seeing it having an effect. I agree, for polygons it should be a no-op.

The mitre join-style is definitely important, and does have an impact on the output as shown in the examples for geofileops.buffer. Only the end-style is a no-op for polygons. If join-style mitre isn't specified, the problem doesn't occur.

[mwtoews]

Interestingly, this issue only happens with mitre_limit exactly 2.0. A brute-force check with other limits does not yield the bad result. Not even 1.999999999999 or 2.000000000001 trigger this error, so there could be logic quirks based on mitre_limit==2.0

[pramsey]

Or an interaction with some element of the input that is itself has a size of exactly 2?

[mwtoews]

Actually, it more complicated. Other combinations trigger the same error, e.g., here's a few others:

for distance in np.round(np.linspace(-0.1, -10.1, 101), 1):
    for mitre_limit in np.round(np.linspace(0.1, 5.1, 51), 1):
        g = shapely.buffer(poly, join_style="mitre", distance=distance, mitre_limit=mitre_limit)
        if g.area < 700000.0:
            print(f"> {distance=}, {mitre_limit=}, {g.area:.1f}")

distance=-2.5, mitre_limit=2.9, 122669.6
distance=-3.4, mitre_limit=1.8, 120603.6
distance=-3.9, mitre_limit=3.2, 119437.9
distance=-5.0, mitre_limit=2.0, 116924.9
distance=-5.1, mitre_limit=1.7, 116704.2
distance=-5.4, mitre_limit=2.0, 116008.0
distance=-9.6, mitre_limit=0.9, 107042.7

[theroggy]

I did some random tests with some other mitre limits than 2, and also noticed that it is quite specific.

The combinations with other distances leading to the issue is an interesting find indeed...

[theroggy]

Probably not super relevant, but something I forgot to mention... the input polygon is the result of a +5 meter buffer on a polygon, with a mitre limit of 1.5...