Simple polygon (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Simple polygon" in English language version.

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34doi.org

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24ams.org

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2books.google.com

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1ed.ac.uk

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ams.org

mathscinet.ams.org

Everett, Hazel; Corneil, Derek (1995). "Negative results on characterizing visibility graphs". Computational Geometry: Theory & Applications. 5 (2): 51–63. doi:10.1016/0925-7721(95)00021-Z. MR 1353288.
Aronov, Boris; Seidel, Raimund; Souvaine, Diane (1993). "On compatible triangulations of simple polygons". Computational Geometry: Theory & Applications. 3 (1): 27–35. doi:10.1016/0925-7721(93)90028-5. MR 1222755.
McCallum, Duncan; Avis, David (1979). "A linear algorithm for finding the convex hull of a simple polygon". Information Processing Letters. 9 (5): 201–206. doi:10.1016/0020-0190(79)90069-3. MR 0552534.
Meisters, G. H. (1975). "Polygons have ears". The American Mathematical Monthly. 82 (6): 648–651. doi:10.2307/2319703. JSTOR 2319703. MR 0367792.
Thomassen, Carsten (1992). "The Jordan-Schönflies theorem and the classification of surfaces". The American Mathematical Monthly. 99 (2): 116–130. doi:10.1080/00029890.1992.11995820. JSTOR 2324180. MR 1144352.
Niven, Ivan; Zuckerman, H. S. (1967). "Lattice points and polygonal area". The American Mathematical Monthly. 74 (10): 1195–1200. doi:10.1080/00029890.1967.12000095. JSTOR 2315660. MR 0225216.
Aggarwal, Alok; Suri, Subhash (1990). "Computing the longest diagonal of a simple polygon". Information Processing Letters. 35 (1): 13–18. doi:10.1016/0020-0190(90)90167-V. MR 1069001.
Snoeyink, Jack (1999). "Cross-ratios and angles determine a polygon". Discrete & Computational Geometry. 22 (4): 619–631. doi:10.1007/PL00009481. MR 1721028.
Toussaint, Godfried (1991). "Anthropomorphic polygons". The American Mathematical Monthly. 98 (1): 31–35. doi:10.2307/2324033. JSTOR 2324033. MR 1083611.
Grünbaum, Branko; Shephard, G. C. (February 1993). "Pick's theorem". The American Mathematical Monthly. 100 (2): 150–161. doi:10.2307/2323771. JSTOR 2323771. MR 1212401.
Chazelle, Bernard (1991). "Triangulating a simple polygon in linear time". Discrete & Computational Geometry. 6 (5): 485–524. doi:10.1007/BF02574703. MR 1115104.
Urrutia, Jorge (2000). "Art gallery and illumination problems". In Sack, Jörg-Rüdiger; Urrutia, Jorge (eds.). Handbook of Computational Geometry. Amsterdam: North-Holland. pp. 973–1027. doi:10.1016/B978-044482537-7/50023-1. ISBN 0-444-82537-1. MR 1746693.
Aichholzer, Oswin; Mulzer, Wolfgang; Pilz, Alexander (2015). "Flip distance between triangulations of a simple polygon is NP-complete". Discrete & Computational Geometry. 54 (2): 368–389. arXiv:1209.0579. doi:10.1007/s00454-015-9709-7. MR 3372115.
Ahn, Hee-Kap; Barba, Luis; Bose, Prosenjit; De Carufel, Jean-Lou; Korman, Matias; Oh, Eunjin (2016). "A linear-time algorithm for the geodesic center of a simple polygon". Discrete & Computational Geometry. 56 (4): 836–859. arXiv:1501.00561. doi:10.1007/s00454-016-9796-0. MR 3561791.
Guibas, Leonidas; Hershberger, John; Leven, Daniel; Sharir, Micha; Tarjan, Robert E. (1987). "Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons". Algorithmica. 2 (2): 209–233. doi:10.1007/BF01840360. MR 0895445.
Chang, J. S.; Yap, C.-K. (1986). "A polynomial solution for the potato-peeling problem". Discrete & Computational Geometry. 1 (2): 155–182. doi:10.1007/BF02187692. MR 0834056.
Cabello, Sergio; Cibulka, Josef; Kynčl, Jan; Saumell, Maria; Valtr, Pavel (2017). "Peeling potatoes near-optimally in near-linear time". SIAM Journal on Computing. 46 (5): 1574–1602. arXiv:1406.1368. doi:10.1137/16M1079695. MR 3708542.
Chin, Francis Y. L.; Snoeyink, Jack; Wang, Cao An (1999). "Finding the medial axis of a simple polygon in linear time". Discrete & Computational Geometry. 21 (3): 405–420. doi:10.1007/PL00009429. MR 1672988.
Oks, Eduard; Sharir, Micha (2006). "Minkowski sums of monotone and general simple polygons". Discrete & Computational Geometry. 35 (2): 223–240. doi:10.1007/s00454-005-1206-y. MR 2195052.
Trefethen, Lloyd N.; Driscoll, Tobin A. (1998). "Schwarz–Christoffel mapping in the computer era". Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998). Documenta Mathematica. pp. 533–542. MR 1648186.
Quintas, L. V.; Supnick, Fred (1965). "On some properties of shortest Hamiltonian circuits". The American Mathematical Monthly. 72 (9): 977–980. doi:10.2307/2313333. JSTOR 2313333. MR 0188872.
Demaine, Erik D.; Fekete, Sándor P.; Keldenich, Phillip; Krupke, Dominik; Mitchell, Joseph S. B. (2022). "Area-optimal simple polygonalizations: the CG challenge 2019". ACM Journal of Experimental Algorithmics. 27: A2.4:1–12. doi:10.1145/3504000. hdl:1721.1/146480. MR 4390039.
Dobkin, David; Guibas, Leonidas; Hershberger, John; Snoeyink, Jack (1993). "An efficient algorithm for finding the CSG representation of a simple polygon". Algorithmica. 10 (1): 1–23. doi:10.1007/BF01908629. MR 1230699.

ams.org

Malkevitch, Joseph (2016). "Are precise definitions a good idea?". AMS Feature Column. American Mathematical Society.

arxiv.org

Aichholzer, Oswin; Mulzer, Wolfgang; Pilz, Alexander (2015). "Flip distance between triangulations of a simple polygon is NP-complete". Discrete & Computational Geometry. 54 (2): 368–389. arXiv:1209.0579. doi:10.1007/s00454-015-9709-7. MR 3372115.
Ahn, Hee-Kap; Barba, Luis; Bose, Prosenjit; De Carufel, Jean-Lou; Korman, Matias; Oh, Eunjin (2016). "A linear-time algorithm for the geodesic center of a simple polygon". Discrete & Computational Geometry. 56 (4): 836–859. arXiv:1501.00561. doi:10.1007/s00454-016-9796-0. MR 3561791.
Cabello, Sergio; Cibulka, Josef; Kynčl, Jan; Saumell, Maria; Valtr, Pavel (2017). "Peeling potatoes near-optimally in near-linear time". SIAM Journal on Computing. 46 (5): 1574–1602. arXiv:1406.1368. doi:10.1137/16M1079695. MR 3708542.
Cheng, Siu-Wing; Mencel, Liam; Vigneron, Antoine (2016). "A faster algorithm for computing straight skeletons". ACM Transactions on Algorithms. 12 (3): 44:1–44:21. arXiv:1405.4691. doi:10.1145/2898961.
Ghosh, Subir Kumar; Goswami, Partha P. (2013). "Unsolved problems in visibility graphs of points, segments, and polygons". ACM Computing Surveys. 46 (2): 22:1–22:29. arXiv:1012.5187. doi:10.1145/2543581.2543589.

books.google.com

Preparata, Franco P.; Shamos, Michael Ian (1985). Computational Geometry: An Introduction. Texts and Monographs in Computer Science. Springer-Verlag. p. 18. doi:10.1007/978-1-4612-1098-6. ISBN 978-1-4612-1098-6.
Richmond, Bettina; Richmond, Thomas (2023). A Discrete Transition to Advanced Mathematics. Pure and Applied Undergraduate Texts. Vol. 63 (2nd ed.). American Mathematical Society. p. 421. ISBN 9781470472047.

csun.edu

Snoeyink, Jack (2017). "Point Location" (PDF). In Toth, Csaba D.; O'Rourke, Joseph; Goodman, Jacob E. (eds.). Handbook of Discrete and Computational Geometry (3rd ed.). Chapman and Hall/CRC. pp. 1005–1023.

doi.org

Milnor, John W. (1950). "On the total curvature of knots". Annals of Mathematics. 2nd Series. 52: 248–257. doi:10.2307/1969467.
Preparata, Franco P.; Shamos, Michael Ian (1985). Computational Geometry: An Introduction. Texts and Monographs in Computer Science. Springer-Verlag. p. 18. doi:10.1007/978-1-4612-1098-6. ISBN 978-1-4612-1098-6.
Everett, Hazel; Corneil, Derek (1995). "Negative results on characterizing visibility graphs". Computational Geometry: Theory & Applications. 5 (2): 51–63. doi:10.1016/0925-7721(95)00021-Z. MR 1353288.
Aronov, Boris; Seidel, Raimund; Souvaine, Diane (1993). "On compatible triangulations of simple polygons". Computational Geometry: Theory & Applications. 3 (1): 27–35. doi:10.1016/0925-7721(93)90028-5. MR 1222755.
McCallum, Duncan; Avis, David (1979). "A linear algorithm for finding the convex hull of a simple polygon". Information Processing Letters. 9 (5): 201–206. doi:10.1016/0020-0190(79)90069-3. MR 0552534.
de Berg, M.; van Kreveld, M.; Overmars, Mark; Schwarzkopf, O. (2008). Computational Geometry: Algorithms and Applications (3rd ed.). Springer. p. 58. doi:10.1007/978-3-540-77974-2.
Meisters, G. H. (1975). "Polygons have ears". The American Mathematical Monthly. 82 (6): 648–651. doi:10.2307/2319703. JSTOR 2319703. MR 0367792.
Thomassen, Carsten (1992). "The Jordan-Schönflies theorem and the classification of surfaces". The American Mathematical Monthly. 99 (2): 116–130. doi:10.1080/00029890.1992.11995820. JSTOR 2324180. MR 1144352.
Margalit, Avraham; Knott, Gary D. (1989). "An algorithm for computing the union, intersection or difference of two polygons". Computers & Graphics. 13 (2): 167–183. doi:10.1016/0097-8493(89)90059-9.
Niven, Ivan; Zuckerman, H. S. (1967). "Lattice points and polygonal area". The American Mathematical Monthly. 74 (10): 1195–1200. doi:10.1080/00029890.1967.12000095. JSTOR 2315660. MR 0225216.
Aggarwal, Alok; Suri, Subhash (1990). "Computing the longest diagonal of a simple polygon". Information Processing Letters. 35 (1): 13–18. doi:10.1016/0020-0190(90)90167-V. MR 1069001.
Snoeyink, Jack (1999). "Cross-ratios and angles determine a polygon". Discrete & Computational Geometry. 22 (4): 619–631. doi:10.1007/PL00009481. MR 1721028.
Toussaint, Godfried (1991). "Anthropomorphic polygons". The American Mathematical Monthly. 98 (1): 31–35. doi:10.2307/2324033. JSTOR 2324033. MR 1083611.
Fisk, S. (1978). "A short proof of Chvátal's watchman theorem". Journal of Combinatorial Theory, Series B. 24 (3): 374. doi:10.1016/0095-8956(78)90059-X.
Preparata, Franco P.; Supowit, Kenneth J. (1981). "Testing a simple polygon for monotonicity". Information Processing Letters. 12 (4): 161–164. doi:10.1016/0020-0190(81)90091-0.
Schirra, Stefan (2008). "How reliable are practical point-in-polygon strategies?" (PDF). In Halperin, Dan; Mehlhorn, Kurt (eds.). Algorithms – ESA 2008, 16th Annual European Symposium, Karlsruhe, Germany, September 15–17, 2008. Proceedings. Lecture Notes in Computer Science. Vol. 5193. Springer. pp. 744–755. doi:10.1007/978-3-540-87744-8_62.
Braden, Bart (1986). "The surveyor's area formula" (PDF). The College Mathematics Journal. 17 (4): 326–337. doi:10.2307/2686282. JSTOR 2686282. Archived from the original (PDF) on 2012-11-07.
Grünbaum, Branko; Shephard, G. C. (February 1993). "Pick's theorem". The American Mathematical Monthly. 100 (2): 150–161. doi:10.2307/2323771. JSTOR 2323771. MR 1212401.
Chazelle, Bernard (1991). "Triangulating a simple polygon in linear time". Discrete & Computational Geometry. 6 (5): 485–524. doi:10.1007/BF02574703. MR 1115104.
Urrutia, Jorge (2000). "Art gallery and illumination problems". In Sack, Jörg-Rüdiger; Urrutia, Jorge (eds.). Handbook of Computational Geometry. Amsterdam: North-Holland. pp. 973–1027. doi:10.1016/B978-044482537-7/50023-1. ISBN 0-444-82537-1. MR 1746693.
Aichholzer, Oswin; Mulzer, Wolfgang; Pilz, Alexander (2015). "Flip distance between triangulations of a simple polygon is NP-complete". Discrete & Computational Geometry. 54 (2): 368–389. arXiv:1209.0579. doi:10.1007/s00454-015-9709-7. MR 3372115.
Ahn, Hee-Kap; Barba, Luis; Bose, Prosenjit; De Carufel, Jean-Lou; Korman, Matias; Oh, Eunjin (2016). "A linear-time algorithm for the geodesic center of a simple polygon". Discrete & Computational Geometry. 56 (4): 836–859. arXiv:1501.00561. doi:10.1007/s00454-016-9796-0. MR 3561791.
Guibas, Leonidas; Hershberger, John; Leven, Daniel; Sharir, Micha; Tarjan, Robert E. (1987). "Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons". Algorithmica. 2 (2): 209–233. doi:10.1007/BF01840360. MR 0895445.
El Gindy, Hossam; Avis, David (1981). "A linear algorithm for computing the visibility polygon from a point". Journal of Algorithms. 2 (2): 186–197. doi:10.1016/0196-6774(81)90019-5.
Chang, J. S.; Yap, C.-K. (1986). "A polynomial solution for the potato-peeling problem". Discrete & Computational Geometry. 1 (2): 155–182. doi:10.1007/BF02187692. MR 0834056.
Cabello, Sergio; Cibulka, Josef; Kynčl, Jan; Saumell, Maria; Valtr, Pavel (2017). "Peeling potatoes near-optimally in near-linear time". SIAM Journal on Computing. 46 (5): 1574–1602. arXiv:1406.1368. doi:10.1137/16M1079695. MR 3708542.
Chin, Francis Y. L.; Snoeyink, Jack; Wang, Cao An (1999). "Finding the medial axis of a simple polygon in linear time". Discrete & Computational Geometry. 21 (3): 405–420. doi:10.1007/PL00009429. MR 1672988.
Cheng, Siu-Wing; Mencel, Liam; Vigneron, Antoine (2016). "A faster algorithm for computing straight skeletons". ACM Transactions on Algorithms. 12 (3): 44:1–44:21. arXiv:1405.4691. doi:10.1145/2898961.
Palfrader, Peter; Held, Martin (February 2015). "Computing mitered offset curves based on straight skeletons". Computer-Aided Design and Applications. 12 (4): 414–424. doi:10.1080/16864360.2014.997637.
Oks, Eduard; Sharir, Micha (2006). "Minkowski sums of monotone and general simple polygons". Discrete & Computational Geometry. 35 (2): 223–240. doi:10.1007/s00454-005-1206-y. MR 2195052.
Quintas, L. V.; Supnick, Fred (1965). "On some properties of shortest Hamiltonian circuits". The American Mathematical Monthly. 72 (9): 977–980. doi:10.2307/2313333. JSTOR 2313333. MR 0188872.
Demaine, Erik D.; Fekete, Sándor P.; Keldenich, Phillip; Krupke, Dominik; Mitchell, Joseph S. B. (2022). "Area-optimal simple polygonalizations: the CG challenge 2019". ACM Journal of Experimental Algorithmics. 27: A2.4:1–12. doi:10.1145/3504000. hdl:1721.1/146480. MR 4390039.
Dobkin, David; Guibas, Leonidas; Hershberger, John; Snoeyink, Jack (1993). "An efficient algorithm for finding the CSG representation of a simple polygon". Algorithmica. 10 (1): 1–23. doi:10.1007/BF01908629. MR 1230699.
Ghosh, Subir Kumar; Goswami, Partha P. (2013). "Unsolved problems in visibility graphs of points, segments, and polygons". ACM Computing Surveys. 46 (2): 22:1–22:29. arXiv:1012.5187. doi:10.1145/2543581.2543589.

ed.ac.uk

maths.ed.ac.uk

Hales, Thomas C. (2007). "Jordan's proof of the Jordan curve theorem" (PDF). From Insight to Proof: Festschrift in Honour of Andrzej Trybulec. Studies in Logic, Grammar and Rhetoric. 10 (23). University of Białystok.

handle.net

hdl.handle.net

Demaine, Erik D.; Fekete, Sándor P.; Keldenich, Phillip; Krupke, Dominik; Mitchell, Joseph S. B. (2022). "Area-optimal simple polygonalizations: the CG challenge 2019". ACM Journal of Experimental Algorithmics. 27: A2.4:1–12. doi:10.1145/3504000. hdl:1721.1/146480. MR 4390039.

jstor.org

Meisters, G. H. (1975). "Polygons have ears". The American Mathematical Monthly. 82 (6): 648–651. doi:10.2307/2319703. JSTOR 2319703. MR 0367792.
Thomassen, Carsten (1992). "The Jordan-Schönflies theorem and the classification of surfaces". The American Mathematical Monthly. 99 (2): 116–130. doi:10.1080/00029890.1992.11995820. JSTOR 2324180. MR 1144352.
Niven, Ivan; Zuckerman, H. S. (1967). "Lattice points and polygonal area". The American Mathematical Monthly. 74 (10): 1195–1200. doi:10.1080/00029890.1967.12000095. JSTOR 2315660. MR 0225216.
Toussaint, Godfried (1991). "Anthropomorphic polygons". The American Mathematical Monthly. 98 (1): 31–35. doi:10.2307/2324033. JSTOR 2324033. MR 1083611.
Braden, Bart (1986). "The surveyor's area formula" (PDF). The College Mathematics Journal. 17 (4): 326–337. doi:10.2307/2686282. JSTOR 2686282. Archived from the original (PDF) on 2012-11-07.
Grünbaum, Branko; Shephard, G. C. (February 1993). "Pick's theorem". The American Mathematical Monthly. 100 (2): 150–161. doi:10.2307/2323771. JSTOR 2323771. MR 1212401.
Quintas, L. V.; Supnick, Fred (1965). "On some properties of shortest Hamiltonian circuits". The American Mathematical Monthly. 72 (9): 977–980. doi:10.2307/2313333. JSTOR 2313333. MR 0188872.

maa.org

Braden, Bart (1986). "The surveyor's area formula" (PDF). The College Mathematics Journal. 17 (4): 326–337. doi:10.2307/2686282. JSTOR 2686282. Archived from the original (PDF) on 2012-11-07.

uni-magdeburg.de

wwwisg.cs.uni-magdeburg.de

Schirra, Stefan (2008). "How reliable are practical point-in-polygon strategies?" (PDF). In Halperin, Dan; Mehlhorn, Kurt (eds.). Algorithms – ESA 2008, 16th Annual European Symposium, Karlsruhe, Germany, September 15–17, 2008. Proceedings. Lecture Notes in Computer Science. Vol. 5193. Springer. pp. 744–755. doi:10.1007/978-3-540-87744-8_62.

web.archive.org

Braden, Bart (1986). "The surveyor's area formula" (PDF). The College Mathematics Journal. 17 (4): 326–337. doi:10.2307/2686282. JSTOR 2686282. Archived from the original (PDF) on 2012-11-07.