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==References== {{reflist|refs= <ref name=4marks>{{cite book | last1 = de Berg | first1 = M. | author1-link = Mark de Berg | last2 = van Kreveld | first2 = M. | author2-link = Marc van Kreveld | last3 = Overmars | first3 = Mark | author3-link = Mark Overmars | last4 = Schwarzkopf | first4 = O. | author4-link = Otfried Cheong | doi = 10.1007/978-3-540-77974-2 | edition = 3rd | page = 58 | publisher = Springer | title = Computational Geometry: Algorithms and Applications | year = 2008}}</ref> <ref name=abbcko>{{cite journal | last1 = Ahn | first1 = Hee-Kap | last2 = Barba | first2 = Luis | last3 = Bose | first3 = Prosenjit | author3-link = Jit Bose | last4 = De Carufel | first4 = Jean-Lou | last5 = Korman | first5 = Matias | last6 = Oh | first6 = Eunjin | arxiv = 1501.00561 | doi = 10.1007/s00454-016-9796-0 | issue = 4 | journal = [[Discrete & Computational Geometry]] | mr = 3561791 | pages = 836–859 | title = A linear-time algorithm for the geodesic center of a simple polygon | volume = 56 | year = 2016}}</ref> <ref name=aggarwal-suri>{{cite journal | last1 = Aggarwal | first1 = Alok | last2 = Suri | first2 = Subhash | author2-link = Subhash Suri | doi = 10.1016/0020-0190(90)90167-V | issue = 1 | journal = [[Information Processing Letters]] | mr = 1069001 | pages = 13–18 | title = Computing the longest diagonal of a simple polygon | volume = 35 | year = 1990}}</ref> <ref name=amp>{{cite journal | last1 = Aichholzer | first1 = Oswin | last2 = Mulzer | first2 = Wolfgang | last3 = Pilz | first3 = Alexander | doi = 10.1007/s00454-015-9709-7 | issue = 2 | journal = [[Discrete & Computational Geometry]] | mr = 3372115 | pages = 368–389 | title = Flip distance between triangulations of a simple polygon is NP-complete | volume = 54 | year = 2015| arxiv = 1209.0579 }}</ref> <ref name=avis-elgindy>{{cite journal | last1 = El Gindy | first1 = Hossam | last2 = Avis | first2 = David | author2-link = David Avis | doi = 10.1016/0196-6774(81)90019-5 | issue = 2 | journal = Journal of Algorithms | pages = 186–197 | title = A linear algorithm for computing the visibility polygon from a point | volume = 2 | year = 1981}}</ref> <ref name=braden>{{cite journal | last = Braden | first = Bart | doi = 10.2307/2686282 | issue = 4 | journal = [[The College Mathematics Journal]] | jstor = 2686282 | pages = 326–337 | title = The surveyor's area formula | url = https://www.maa.org/pubs/Calc_articles/ma063.pdf | archive-url = https://web.archive.org/web/20121107190918/http://www.maa.org/pubs/Calc_articles/ma063.pdf | archive-date = 2012-11-07 | url-status = dead | volume = 17 | year = 1986}}</ref> <ref name=ccksv>{{cite journal | last1 = Cabello | first1 = Sergio | last2 = Cibulka | first2 = Josef | last3 = Kynčl | first3 = Jan | last4 = Saumell | first4 = Maria | last5 = Valtr | first5 = Pavel | arxiv = 1406.1368 | doi = 10.1137/16M1079695 | issue = 5 | journal = [[SIAM Journal on Computing]] | mr = 3708542 | pages = 1574–1602 | title = Peeling potatoes near-optimally in near-linear time | volume = 46 | year = 2017}}</ref> <ref name=chang-yap>{{cite journal | last1 = Chang | first1 = J. S. | last2 = Yap | first2 = C.-K. | doi = 10.1007/BF02187692 | doi-access = free | issue = 2 | journal = [[Discrete & Computational Geometry]] | mr = 834056 | pages = 155–182 | title = A polynomial solution for the potato-peeling problem | volume = 1 | year = 1986}}</ref> <ref name=chazelle>{{cite journal | last = Chazelle | first = Bernard | author-link = Bernard Chazelle | doi = 10.1007/BF02574703 | issue = 5 | journal = [[Discrete & Computational Geometry]] | mr = 1115104 | pages = 485–524 | title = Triangulating a simple polygon in linear time | volume = 6 | year = 1991| doi-access = free }}</ref> <ref name=cmv>{{cite journal | last1 = Cheng | first1 = Siu-Wing | last2 = Mencel | first2 = Liam | last3 = Vigneron | first3 = Antoine | arxiv = 1405.4691 | title = A faster algorithm for computing straight skeletons | pages = 44:1–44:21 | journal = [[ACM Transactions on Algorithms]] | volume = 12 | number = 3 | year = 2016 | doi = 10.1145/2898961}}</ref> <ref name=compatible>{{cite journal | last1 = Aronov | first1 = Boris | author1-link = Boris Aronov | last2 = Seidel | first2 = Raimund | author2-link = Raimund Seidel | last3 = Souvaine | first3 = Diane | author3-link = Diane Souvaine | doi = 10.1016/0925-7721(93)90028-5 | issue = 1 | journal = [[Computational Geometry (journal)|Computational Geometry: Theory & Applications]] | mr = 1222755 | pages = 27–35 | title = On compatible triangulations of simple polygons | volume = 3 | year = 1993| doi-access = free }}</ref> <ref name=cross-ratio>{{cite journal | last = Snoeyink | first = Jack | doi = 10.1007/PL00009481 | issue = 4 | journal = [[Discrete & Computational Geometry]] | mr = 1721028 | pages = 619–631 | title = Cross-ratios and angles determine a polygon | volume = 22 | year = 1999| doi-access = free }}</ref> <ref name=csl>{{cite journal | last1 = Chin | first1 = Francis Y. L. | author1-link = Francis Y. L. Chin | last2 = Snoeyink | first2 = Jack | last3 = Wang | first3 = Cao An | doi = 10.1007/PL00009429 | issue = 3 | journal = [[Discrete & Computational Geometry]] | mr = 1672988 | pages = 405–420 | title = Finding the medial axis of a simple polygon in linear time | volume = 21 | year = 1999| doi-access = free }}</ref> <ref name=dfkkm>{{cite journal | last1 = Demaine | first1 = Erik D. | author1-link = Erik Demaine | last2 = Fekete | first2 = Sándor P. | last3 = Keldenich | first3 = Phillip | last4 = Krupke | first4 = Dominik | last5 = Mitchell | first5 = Joseph S. B. | author5-link = Joseph S. B. Mitchell | doi = 10.1145/3504000 | journal = ACM Journal of Experimental Algorithmics | mr = 4390039 | pages = A2.4:1–12 | title = Area-optimal simple polygonalizations: the CG challenge 2019 | volume = 27 | year = 2022| hdl = 1721.1/146480 | hdl-access = free }}</ref> <ref name=dghs>{{cite journal | last1 = Dobkin | first1 = David | author1-link = David P. Dobkin | last2 = Guibas | first2 = Leonidas | author2-link = Leonidas J. Guibas | last3 = Hershberger | first3 = John | author3-link = John Hershberger | last4 = Snoeyink | first4 = Jack | doi = 10.1007/BF01908629 | issue = 1 | journal = [[Algorithmica]] | mr = 1230699 | pages = 1–23 | title = An efficient algorithm for finding the CSG representation of a simple polygon | volume = 10 | year = 1993}}</ref> <ref name=everett-corneil>{{cite journal | last1 = Everett | first1 = Hazel | last2 = Corneil | first2 = Derek | author2-link = Derek Corneil | doi = 10.1016/0925-7721(95)00021-Z | issue = 2 | journal = [[Computational Geometry (journal)|Computational Geometry: Theory & Applications]] | mr = 1353288 | pages = 51–63 | title = Negative results on characterizing visibility graphs | volume = 5 | year = 1995}}</ref> <ref name=fisk>{{cite journal | last = Fisk | first = S. | doi = 10.1016/0095-8956(78)90059-X | doi-access = free | issue = 3 | journal = [[Journal of Combinatorial Theory, Series B]] | page = 374 | title = A short proof of Chvátal's watchman theorem | volume = 24 | year = 1978}}</ref> <ref name=ghosh-goswami>{{cite journal | last1 = Ghosh | first1 = Subir Kumar | last2 = Goswami | first2 = Partha P. | arxiv = 1012.5187 | doi = 10.1145/2543581.2543589 | issue = 2 | journal = [[ACM Computing Surveys]] | pages = 22:1–22:29 | title = Unsolved problems in visibility graphs of points, segments, and polygons | volume = 46 | year = 2013}}</ref> <ref name=ghlst>{{cite journal | last1 = Guibas | first1 = Leonidas | author1-link = Leonidas J. Guibas | last2 = Hershberger | first2 = John | author2-link = John Hershberger | last3 = Leven | first3 = Daniel | last4 = Sharir | first4 = Micha | author4-link = Micha Sharir | last5 = Tarjan | first5 = Robert E. | author5-link = Robert Tarjan | doi = 10.1007/BF01840360 | issue = 2 | journal = [[Algorithmica]] | mr = 895445 | pages = 209–233 | title = Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons | volume = 2 | year = 1987}}</ref> <ref name=grunbaum-shephard>{{cite journal | last1 = Grünbaum | first1 = Branko | author1-link = Branko Grünbaum | last2 = Shephard | first2 = G. C. | author2-link = Geoffrey Colin Shephard | date = February 1993 | doi = 10.2307/2323771 | issue = 2 | journal = [[The American Mathematical Monthly]] | jstor = 2323771 | mr = 1212401 | pages = 150–161 | title = Pick's theorem | volume = 100}}</ref> <ref name=hales>{{cite journal | last = Hales | first = Thomas C. | author-link = Thomas Callister Hales | department = From Insight to Proof: Festschrift in Honour of Andrzej Trybulec | issue = 23 | journal = [[Studies in Logic, Grammar and Rhetoric]] | publisher = University of Białystok | title = Jordan's proof of the Jordan curve theorem | url = https://www.maths.ed.ac.uk/~v1ranick/papers/hales1.pdf | volume = 10 | year = 2007}}</ref> <ref name=malkevitch>{{cite web | last = Malkevitch | first = Joseph | title = Are precise definitions a good idea? | url = https://www.ams.org/publicoutreach/feature-column/fc-2016-01 | publisher = American Mathematical Society | work = AMS Feature Column | year = 2016}}</ref> <ref name=margalit-knott>{{cite journal | last1 = Margalit | first1 = Avraham | last2 = Knott | first2 = Gary D. | doi = 10.1016/0097-8493(89)90059-9 | issue = 2 | journal = Computers & Graphics | pages = 167–183 | title = An algorithm for computing the union, intersection or difference of two polygons | volume = 13 | year = 1989}}</ref> <ref name=mccallum-avis>{{cite journal | last1 = McCallum | first1 = Duncan | last2 = Avis | first2 = David | author2-link = David Avis | doi = 10.1016/0020-0190(79)90069-3 | issue = 5 | journal = [[Information Processing Letters]] | mr = 552534 | pages = 201–206 | title = A linear algorithm for finding the convex hull of a simple polygon | volume = 9 | year = 1979}}</ref> <ref name=meisters>{{cite journal | last = Meisters | first = G. H. | doi = 10.2307/2319703 | issue = 6 | journal = [[The American Mathematical Monthly]] | jstor = 2319703 | mr = 0367792 | pages = 648–651 | title = Polygons have ears | volume = 82 | year = 1975}}</ref> <ref name=milnor>{{cite journal | last = Milnor | first = John W. | doi = 10.2307/1969467 | journal = Annals of Mathematics |series=2nd Series | pages = 248–257 | title = On the total curvature of knots | volume = 52 | year = 1950}}</ref> <ref name=niven-zuckerman>{{cite journal | last1 = Niven | first1 = Ivan | author1-link = Ivan M. Niven | last2 = Zuckerman | first2 = H. S. | doi = 10.1080/00029890.1967.12000095 | journal = [[The American Mathematical Monthly]] | mr = 225216 | pages = 1195–1200 | title = Lattice points and polygonal area | volume = 74 | issue = 10 | jstor = 2315660 | year = 1967}}</ref> <ref name=oks-sharir>{{cite journal | last1 = Oks | first1 = Eduard | last2 = Sharir | first2 = Micha | author2-link = Micha Sharir | doi = 10.1007/s00454-005-1206-y | issue = 2 | journal = [[Discrete & Computational Geometry]] | mr = 2195052 | pages = 223–240 | title = Minkowski sums of monotone and general simple polygons | volume = 35 | year = 2006| doi-access = free }}</ref> <ref name=palfrader-held>{{cite journal | last1 = Palfrader | first1 = Peter | last2 = Held | first2 = Martin | date = February 2015 | doi = 10.1080/16864360.2014.997637 | issue = 4 | journal = Computer-Aided Design and Applications | pages = 414–424 | title = Computing mitered offset curves based on straight skeletons | volume = 12| doi-access = free }}</ref> <ref name=preparata-shamos>{{cite book | last1 = Preparata | first1 = Franco P. | author1-link = Franco P. Preparata | last2 = Shamos | first2 = Michael Ian | author2-link = Michael Ian Shamos | doi = 10.1007/978-1-4612-1098-6 | isbn = 978-1-4612-1098-6 | page = 18 | publisher = Springer-Verlag | series = Texts and Monographs in Computer Science | title = Computational Geometry: An Introduction | url = https://books.google.com/books?id=_p3eBwAAQBAJ&pg=PA18 | year = 1985}}</ref> <ref name=preparata-supowit>{{cite journal | last1 = Preparata | first1 = Franco P. | author1-link = Franco P. Preparata | last2 = Supowit | first2 = Kenneth J. | doi = 10.1016/0020-0190(81)90091-0 | issue = 4 | journal = [[Information Processing Letters]] | pages = 161–164 | title = Testing a simple polygon for monotonicity | volume = 12 | year = 1981}}</ref> <ref name=quintas-supnick>{{cite journal | last1 = Quintas | first1 = L. V. | last2 = Supnick | first2 = Fred | doi = 10.2307/2313333 | issue = 9 | journal = [[The American Mathematical Monthly]] | jstor = 2313333 | mr = 188872 | pages = 977–980 | title = On some properties of shortest Hamiltonian circuits | volume = 72 | year = 1965}}</ref> <ref name=rich2>{{cite book | last1 = Richmond | first1 = Bettina | author1-link = Bettina Richmond | last2 = Richmond | first2 = Thomas | edition = 2nd | isbn = 9781470472047 | page = 421 | publisher = American Mathematical Society | series = Pure and Applied Undergraduate Texts | title = A Discrete Transition to Advanced Mathematics | url = https://books.google.com/books?id=BQDUEAAAQBAJ&pg=PA421 | volume = 63 | year = 2023}}</ref> <ref name=schirra>{{cite conference | last = Schirra | first = Stefan | editor1-last = Halperin | editor1-first = Dan | editor2-last = Mehlhorn | editor2-first = Kurt | book-title = Algorithms – ESA 2008, 16th Annual European Symposium, Karlsruhe, Germany, September 15–17, 2008. Proceedings | doi = 10.1007/978-3-540-87744-8_62 | pages = 744–755 | publisher = Springer | series = Lecture Notes in Computer Science | title = How reliable are practical point-in-polygon strategies? | url = http://wwwisg.cs.uni-magdeburg.de/ag/pointInPolygonReliability/pointPolygon.pdf | volume = 5193 | year = 2008}}</ref> <ref name=snoeyink>{{cite book | last = Snoeyink | first = Jack | editor1-last = Toth | editor1-first = Csaba D. | editor2-last = O'Rourke | editor2-first = Joseph | editor3-last = Goodman | editor3-first = Jacob E. | contribution = Point Location | contribution-url = https://www.csun.edu/~ctoth/Handbook/chap38.pdf | edition = 3rd | pages = 1005–1023 | publisher = Chapman and Hall/CRC Press | title = Handbook of Discrete and Computational Geometry | year = 2017 | isbn = 978-1-498-71139-5}}</ref> <ref name=thomassen>{{cite journal | last = Thomassen | first = Carsten | author-link = Carsten Thomassen (mathematician) | doi = 10.1080/00029890.1992.11995820 | issue = 2 | journal = [[The American Mathematical Monthly]] | jstor = 2324180 | mr = 1144352 | pages = 116–130 | title = The Jordan-Schönflies theorem and the classification of surfaces | volume = 99 | year = 1992}}</ref> <ref name=toussaint>{{cite journal | last = Toussaint | first = Godfried | authorlink = Godfried Toussaint | doi = 10.2307/2324033 | issue = 1 | journal = [[The American Mathematical Monthly]] | jstor = 2324033 | mr = 1083611 | pages = 31–35 | title = Anthropomorphic polygons | volume = 98 | year = 1991}}</ref> <ref name=trefethen-driscoll>{{cite conference | last1 = Trefethen | first1 = Lloyd N. | author1-link = Nick Trefethen | last2 = Driscoll | first2 = Tobin A. | book-title = Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998) | mr = 1648186 | pages = 533–542 | series = Documenta Mathematica | title = Schwarz–Christoffel mapping in the computer era | year = 1998}}</ref> <ref name=urrutia>{{cite book | last = Urrutia | first = Jorge | author1-link = Jorge Urrutia Galicia | editor1-last = Sack | editor1-first = Jörg-Rüdiger | editor1-link = Jörg-Rüdiger Sack | editor2-last = Urrutia | editor2-first = Jorge | contribution = Art gallery and illumination problems | doi = 10.1016/B978-044482537-7/50023-1 | isbn = 0-444-82537-1 | location = Amsterdam | mr = 1746693 | pages = 973–1027 | publisher = North-Holland | title = Handbook of Computational Geometry | year = 2000}}</ref> }}
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