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A Bibliography on Digital and Computational Convexity (1961-1988)
February 1989 (vol. 11 no. 2)
pp. 181-190

A bibliography of 370 references of books, papers in serial journals, and conference papers, on convexity in relation to computer science is presented. The subject is divided into five topics: (1) convexity and straightness in digital images; (2) convex hull algorithms and their complexity; (3) other computational problems related to convexity; (4) miscellaneous applications; and (5) general mathematical sources. These references range in time from 1961 to September 1988.

[1] T. A. Anderson and C. E. Kim, "Representation of digital line segments and their preimages,"Comput. Vision, Graphics, Image Processing, vol. 30, no. 3, pp. 279-288, June 1985.
[2] C. Arcelli and A. Massaroti, "Regular Arcs in Digital Contours,"Comput. Graphics Image Processing, vol. 4, no. 4, pp. 339-360, Dec. 1975; Erratum, vol. 5, no. 2, p. 289, June 1976.
[3] C. Arcelli and A. Massaroti, "On the parallel generation of straight lines,"Comput. Graphics Image Processing, vol. 7, no. 1, pp. 67-83, Feb. 1978.
[4] G. Bongiovanni, F. Luccio, and A. Zorat, "The discrete equation of the straight line,"IEEE Trans. Comput., vol. C-24, no. 3, pp. 310-313, Mar. 1975.
[5] R. Brons, "Linguistic methods for the description of a straight line on a grid,"Comput. Graphics Image Processing, vol. 3, no. 1, pp. 48-62, Mar. 1974.
[6] J. M. Chassery, "Discrete convexity; Definition parametrisation and compatibility," inProc. 6th ICPR, Oct. 1982, pp. 645-647.
[7] J. M. Chassery, "Discrete convexity: Definition, parametrisation, and compatibility with continuous convexity,"Comput. Vision, Graphics, Image Processing, vol. 21, no. 3, pp. 326-344, Mar. 1983.
[8] H. U. Döhler and P. Zamperoni, "Compact contour codes for convex binary patterns,"Signal Processing, vol. 8, no. 1, pp. 23-39, Feb. 1985.
[9] L. Dorst, "The accuracy of the digital representation of a straight line," inFundamental Algorithms for Computer Graphics, R. A. Earnshaw, Ed., NATO ASI Series F, Vol. 17. Berlin: Springer-Verlag, 1985, pp. 141-152.
[10] L. Dorst and R. P. W. Duin, "Spirograph theory: A framework for calculations on digitized straight lines,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 5, pp. 632-639, Sept. 1984.
[11] L. Dorst and A. W. M. Smeulders, "The estimation of parameters of digital straight line segments," inProc. 6th ICPR, Oct. 1982, pp. 601-603.
[12] L. Dorst and A. W. M. Smeulders, "Discrete representation of straight lines,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 4, pp. 450-463, July 1984.
[13] L. Dorst and A. W. M. Smeulders, "Best linear unbiased estimators for properties of digitized straight lines,"IEEE Trans. Pattern Anal. Machine Intell., vol. 8, pp. 276-282, Mar. 1986.
[14] H. Freeman, "On the encoding of arbitrary geometric configurations,"IRE Trans. Electon. Comput., vol. EC-10, pp. 260-268, June 1961.
[15] H. Freeman, "Boundary encoding and processing," inPicture Processing and Psychopictorics, B. S. Lipkin and A. Rosenfeld. Eds. New York: Academic, 1970, pp. 241-266.
[16] H. Freeman, "Algorithm for generating a digital straight line on a triangular grid,"IEEE Trans. Comput., vol. C-28, no. 2, pp. 150-152, Feb. 1979.
[17] M. Gaafar, "Convexity verification, block-chords, and digital straight lines,"Comput. Graphics Image Processing, vol. 6, no. 4, pp. 361-370, Aug. 1977.
[18] H. P. A. Haas, "Convexity analysis of hexagonally sampled images," Ph.D. dissertation, Technische Hogeschool Delft, Delft, The Netherlands, 1985.
[19] L. Hodes, "Discrete approximation of continuous convex blobs," SIAM J. Appl. Math, vol. 19, no. 2, pp. 477-485, Sept. 1970.
[20] S. H. Y. Hung, "On the straightness of digital arcs,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-7, no. 2, pp. 203-215, Mar. 1985.
[21] S. H. Y. Hung, and T. Kasvand, "On the chord property and its equivalences," inProc. 7th. ICPR, July-Aug. 1984, pp. 116-119.
[22] L. Janos and A. Rosenfeld, "Some results on fuzzy (digital) convexity,"Pattern Recognition, vol. 15, no. 5, pp. 379-382, 1982.
[23] C. E. Kim, "On the cellular convexity of complexes,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-3, no. 6, pp. 617-625, Nov. 1981 (also Subsection B.1).
[24] C. E. Kim, "On cellular straight line segments,"Comput. Graphics Image Processing, vol. 18, no. 4, pp. 369-381, Apr. 1982.
[25] C. E. Kim, "Digital convexity, straightness and convex polygons,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, no. 6, pp. 618- 626, Nov. 1982.
[26] C. E. Kim, "Three-dimensional digital line segments,"IEEE Trans. Pattern Anl. Machine Intell., vol. PAMI-5, no. 2, pp. 231-234. Mar. 1983.
[27] C. E. Kim, "Three-dimensional digital planes,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 5, pp. 639-645, Sept. 1984.
[28] C. E. Kim and A. Rosenfeld, "On the convexity of digital regions," inProc. 5th ICPR, Dec. 1980, pp. 1010-1015.
[29] C. E. Kim and A. Rosenfeld, "Digital straight lines and convexity of digital regions,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, no. 2, pp. 149- 153, Mar. 1982.
[30] C. E. Kim and J. Sklansky, "Convex digital solids,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, no. 6. pp. 612-618, Nov. 1982.
[31] C. E. Kim and J. Sklansky, "Digital and cellular convexity,"Pattern Recognition, vol. 15, no. 5, pp. 359-367, 1982.
[32] H. Klaasman, "Some aspects of the accuracy of the approximated position of a straight line on a grid,"Comput. Graphics Image Processing, vol. 4, no. 3, pp. 225-235, Sept. 1975
[33] H. C. Lee and K. S. Fu, "Using the FFT to determine digital straight line chain codes,"Comput. Graphics Image Processing, vol. 18, no. 4, pp. 359-368, Apr. 1982.
[34] X. Y. Luo and L. D. Wu, "The generalized chord property of a digital plane element," inProc. 8th ICPR, Oct. 1986, pp. 1159- 1161.
[35] M. D. McIlroy, "A note on discrete representation of lines,"AT&T Tech. J., vol. 64, no. 2, pp. 481-490, Feb. 1984.
[36] M. Minsky and S. Papert,Perceptrons. Cambridge, MA: MIT Press, 1968.
[37] G. U. Montanari, "On limit properties in digitization schemes,"J. ACM, vol. 17, no. 2, pp. 348-360, Apr. 1970.
[38] S. Pham, "Digital straight segments,"Comput. Vision, Graphics, Image Processing, vol. 36, no. 1, pp. 10-30, Oct. 1986.
[39] C. Ronse, "A simple proof of Rosenfeld's characterization of digital straight line segments,"Pattern Recognition Lett., vol. 3, no. 5, pp. 323-326, Sept. 1985.
[40] C. Ronse, "Definitions of convexity and convex hulls in digital images,"Bull. SociétéMathématique de Belgique, vol. 37, no. 2, pp. 71-85, 1985.
[41] C. Ronse, "Criteria for approximation of linear and affine functions,"Arch. Math., vol. 46, pp. 371-384, 1986.
[42] C. Ronse, "A strong chord property for 4-connected convex digital sets,"Comput. Vision, Graphics, Image Processing, vol. 35, no. 2, pp. 259-269, Aug. 1986.
[43] B. Rosenberg, "The analysis of convex blobs,"Comput. Graphics Image Processing, vol. 1, no. 2, pp. 183-192, Aug. 1972.
[44] A. Rosenfeld. "Digital straight line segments,"IEEE Trans. Comput., vol. C-23, no. 2, pp. 1264-1269, Dec. 1974.
[45] A. Rosenfeld, "Measuring the sizes of concavities,"Pattern Recognition Lett., vol. 3, no. 1, pp. 71-75, Jan. 1985.
[46] A. Rosenfeld and C. E. Kim, "How a digital computer can tell whether a line is straight,"Amer. Math. Monthly, vol. 89, no. 4, pp. 230-235, Apr. 1982.
[47] J. Rothstein and C. Weiman, "Parallel and sequential specification of a context sensitive language for straight lines on grids,"Comput. Graphics Image Processing, vol. 5, no. 1, pp. 106-124, Mar. 1976.
[48] J. Serra,Image Analysis and Mathematical Morphology. London: Academic, 1982.
[49] R. Shoucri, R. Benesch, and S. Thomas, "Note on the determination of a digital straight line from chain codes,"Comput. Vision. Graphics, Image Processing, vol. 29, no. 1, pp. 133-139, Jan. 1983.
[50] J. Sklansky, "Recognizing convex blobs," inProc. 1st IJCAI, May 1969, pp. 107-116.
[51] J. Sklansky, "Recognition of convex blobs,"Pattern Recognition, vol. 2, no. 1, pp. 3-10, 1970.
[52] J. Sklansky, "Measuring concavity on a rectangular mosaic,"IEEE Trans. Comput., vol. C-21, no. 12, pp, 1355-1364, 1972 (also Subsection B.1).
[53] J. Sklansky, R. L. Chazin, and B. J. Hansen, "Minimum-perimeter polygons of digitized silhouettes,"IEEE Trans. Comput., vol. C-21, no. 3, pp. 260-268, Mar. 1972.
[54] J. Sklansky and D. F. Kibler, "A theory of nonuniformly digitized binary pictures,"IEEE Trans. Syst., Man, Cybern., vol. SMC-6, no. 9, pp. 637-647, Sept. 1976.
[55] T. Thong, "A symmetric algorithm for line segment generation,"Comput. Graphics, vol. 6, no. 1, pp. 15-17, 1982.
[56] A. M. Vossespoel and A. W. M. Smeulders, "Statistical properties of digitized line segments," inComput. Graphics 81, London, Oct. 1981, pp. 471-483.
[57] A. M. Vossespoel and A. W. M. Smeulders, "Vector code probability and metrication error in the representation of straight lines of finite length,"Comput. Graphics Image Processing, vol. 20, no. 4, pp. 347-364, Dec. 1982.
[58] L. D. Wu, "On the Freeman's conjecture about the chain code of a line," inProc. 5th ICPR, Dec, 1980, pp. 32-34.
[59] L. D. Wu, "On the chain code of a line,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, no. 3, pp. 347-353, May 1982.
[60] "Corrigendum on convex hull algorithms,"Inform. Processing Lett., vol. 10, no. 3, p. 168, Apr. 1980.
[61] S. G. Akl, "Two remarks on a convex hull algorithm,"Inform. Processing Lett., vol. 8, no. 2, pp. 108-109, Feb. 1979.
[62] S. G. Akl, "A constant-time parallel algorithm for computing convex hulls,"BIT, vol. 22, no. 2, pp. 130-134, 1982.
[63] S. G. Akl, "Optimal parallel algorithms for computing convex hulls and for sorting,"Computing, vol. 33, pp. 1-11, 1984.
[64] S. G. Akl, "Optimal parallel algorithms for selection, sorting and computing convex hulls," inComputational Geometry, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 1-22.
[65] S. G. Akl and G. T. Toussaint, "A fast convex hull algorithm,"Inform. Processing Lett., vol. 7, no. 5, pp. 219-222, Aug. 1978.
[66] S. G. Akl and G. T. Toussaint, "Efficient convex hull algorithms for pattern recognition applications," inProc. 4th IJCPR, Nov. 1978, pp. 483-487.
[67] D. C. S. Allison and M. T. Noga, "Some performance tests of convex hull algorithms,"BIT, vol. 24, no. 1, pp. 2-13, 1984.
[68] K. R. Anderson, "A reevaluation of an efficient algorithm for determining the convex hull of a finite planar set,"Inform. Processing Lett., vol. 7, no. 1, pp. 53-55, Jan. 1978.
[69] A. M. Andrew, "Another efficient algorithm for convex hulls in two dimensions,"Inform. Processing Lett., vol. 9, no. 5, pp. 216- 219, Dec. 1979.
[70] A. Appel and P. M. Will, "Determining the three-dimensional convex hull of a polyhedron,"IBM J. Res. Develop., vol. 20, no. 6, pp. 590-601, Nov. 1976.
[71] C. Arcelli and L. Cordelia, "Concavity point detection by iterative arrays,"Comput. Graphics Image Processing, vol. 3, no. 1, pp. 34-47, Mar. 1974.
[72] C. Arcelli and S. Levialdi, "Concavity extraction by parallel processing,"IEEE Trans. Syst., Man, Cybern., vol. SMC-1, no. 4, pp. 394-396, Oct. 1971.
[73] M. J. Atallah, "Computing the convex hull of line intersections,"J. Algorithms, vol. 7, no. 2, pp. 285-288, June 1986.
[74] B. G. Batchelor, "Two methods for finding convex hulls of planar figures,"Cybern. Syst., vol. 11, no. 1-2, pp. 105-113, 1980.
[75] J. L. Bentley, M. G. Faust, and F. P. Preparata, "Approximation algorithms for convex hulls,"Commun. ACM, vol. 25, no. 1, pp. 64-68, Jan. 1982.
[76] B. K. Bhattacharya and H. ElGindy, "A new linear convex hull algorithm for simple polygons,"IEEE Trans. Inform. Theory, vol. IT-30, no. 1, pp. 85-88, Jan. 1984.
[77] B. K. Bhattacharya and G. T. Toussaint, "Time-and storage-efficient implementation of an optimal convex hull algorithm,"Image Vision Comput., vol. 1, no. 3, pp. 140-144, Aug. 1983.
[78] A. Bykat, "Convex hull of a finite set of points in two dimensions,"Inform. Processing Lett., vol. 7, no. 6, pp. 296-298, Oct. 1978.
[79] D. R. Chand and S. S. Kapur, "An algorithm for convex polytopes,"J. ACM, vol. 17, no. 1, pp. 78-86, Jan. 1970.
[80] G. H. Chen, M. S. Chern, and R. C. T. Lee, "A new systolic architecture for convex hull and half-plane intersection problems,"BIT, vol. 27, no. 2, pp. 141-147, 1987.
[81] A. L. Chow, "A parallel algorithm for determining convex hulls of sets of points in two dimensions," inProc. 19th Annu. Allerton Conf. Communication, Control, Computing, Monticello, IL, 1981, pp. 214-223.
[82] V. U. Degtyar and M. Ya. Finkel'shteyn, "Classification algorithms based on construction of convex hulls of sets,"Eng. Cybern., vol. 12, pp. 150-154, 1974 (also Section D).
[83] F. Dévai and T. Szendrényi, "Comments on convex hull of a finite set of points in two dimensions,"Inform. Processing Lett., vol. 9, no. 3, pp. 141-142, Oct. 1979.
[84] W. F. Eddy, "A new convex hull algorithm for planar sets,"ACM Trans. Math. Software, vol. 3, no. 4, pp. 398-403, Dec. 1977.
[85] E. W. Dijkstra,A Discipline of Programming. Englewood Cliffs, NJ: Prentice-Hall, 1976, ch. 24: "The problem of the convex hull in three dimensions," pp. 168-191; Erratum, Manuscript EWD598-0.
[86] D. J. Evans and S. Mai, "Two parallel algorithms for the convex hull problem in a two dimensional space,"Parallel Comput., vol. 2, no. 4, pp. 313-326, Dec. 1985.
[87] A. Fournier, "Comments on convex hull of a finite set of points in two dimensions,"Inform. Processing Lett., vol. 8, no. 4, p. 173, Apr. 1979.
[88] S. K. Ghosh, "A note on convex hull algorithms,"Pattern Recgonition, vol. 19, no. 1, p. 75, 1986.
[89] S. K. Ghosh and R. K. Shyamasundar, "A linear time algorithm for obtaining the convex hull of a simple polygon,"Pattern Recognition, vol. 16, no. 6, pp. 587-592, 1983.
[90] S. K. Ghosh and R. K. Shyamasundar, "A linear time algorithm for computing the convex hull of an ordered crossing polygon,"Pattern Recognition, vol. 17, no. 3, pp. 351-358, 1984.
[91] M. T. Goodrich, "Finding the convex hull of a sorted point set in parallel,"Inform. Processing Lett., vol. 26, 1987/1988, pp. 173- 179.
[92] R. L. Graham, "An efficient algorithm for determining the convex hull of a finite planar set,"Inform. Processing Lett.vol. 1, no. 4, pp. 132-133, June 1972.
[93] R. L. Graham and F. F. Yao, "Finding the convex hull of a simple polygon,"J. Algorithms, vol. 4, no. 4, pp. 324-331, Dec. 1983.
[94] P. J. Green and B. W. Silverman, "Constructing the convex hull of a set of points in the plane,"Comput. J., vol. 22, no. 3, pp. 262-266, Aug. 1979.
[95] D. Gries and I. Stojmenovic´, "A note on Graham's convex hull algorithm,"Inform. Processing Lett., vol. 25, no. 5, pp. 323-327, July 1987.
[96] C. C. Handley, "Efficient planar convex hull algorithm,"Image Vision Comput., vol. 3, no. 1, pp. 29-35, Feb. 1985.
[97] A. Hübler, R. Klette, and K. Voß, "Determination of the convex hull of a finite set of planar points within linear time,"Elektron. Informationsverarb. Kybernet, vol. 17, no. 2-3, pp. 121-139, 1981.
[98] R. A. Jarvis, "On the identification of the convex hull of a finite set of points in the plane,"Inform. Processing Lett., vol. 2, no. 1, pp. 18-21, Mar. 1973.
[99] G. H. Johansen and C. Gram, "A simple algorithm for building the 3-D convex hull,"BIT, vol. 3, no. 2, pp. 146-160, 1983.
[100] A. Józwik, "A method for solving then-dimensional convex hull problem,"Pattern Recognition Lett., vol. 2, no. 1, pp. 23-25, Oct. 1983.
[101] M. Kallay, "Convex hull made easy,"Inform. Processing Lett., vol. 22, no. 3, p. 161, Mar. 1986.
[102] B. S. Kang, "Computer construction of the convex hull of a finite set of points in space (Chinese. English summary),"J. Northwest Univ., vol. 15, no. 3, pp. 17-23, 1985.
[103] D. G. Kirkpatrick and R. Seidel, "The ultimate planar convex hull algorithm?"SIAM J. Comput., vol. 15, no. 1, pp. 287-299, Feb. 1986.
[104] R. Klette, "On the approximation of convex hulls of finite grid point sets,"Pattern Recognition Lett., vol. 2, no. 1, pp. 19-22, Oct. 1983.
[105] J. Koplowitz, and D. Jouppi, "A more efficient covex hull algorithm,"Inform. Processing Lett., vol. 7, no. 1, pp. 56-57, Jan. 1978.
[106] D. T. Lee, "On finding the convex hull of a simple polygon,"Int. J. Comput. Inform. Sci., vol. 12, no. 2, pp. 87-98, Apr. 1983.
[107] D. Nath, S. N. Maheshwari, and P. C. P. Bhatt, "Parallel algorithms for the convex hull in two dimensions," inProc. Conf. Anal. Problem Classes Programming Parallel Comput., 1981, pp. 358- 372.
[108] A. Maus, "Delaunay triangulation and the convex hull ofnpoints in expected linear time,"BIT, vol. 24, no. 2, pp. 151-163, 1984.
[109] D. McCallum and D. Avis, "A linear algorithm for finding the convex hull of a simple polygon,"Inform. Processing Lett., vol. 9, no. 5, pp. 201-206, Dec. 1979.
[110] M. M. McQueen and G. T. Toussaint, "On the ultimate convex hull algorithm in practice,"Pattern Recognition Lett., vol. 3, no. 1, pp. 29-34, Jan. 1985.
[111] A. A. Melkman, "On-line construction of the convex hull of a simple polyline,"Inform. Processing Lett., vol. 25, no. 1, pp. 11- 12, Apr. 1987.
[112] Y. J. Mu, "Computer construction of the convex hull of finite point sets (Chinese. English summary)"J. Northwest Univ., vol. 12, no. 2, pp. 28-34, 1982.
[113] M. Orlowski, "On the conditions for success of Sklansky's convex hull algorithm,"Pattern Recognition, vol. 16, no. 6, pp. 579-586, 1983.
[114] M. Orlowski, "A convex hull algorithm for planar simple polygons,"Pattern Recognition, vol. 18, no. 5, pp. 361-366, 1985.
[115] M. H. Overmars and J. van Leeuwen, "Further comments on Bykats convex hull alogrithm,"Inform. Processing Lett., vol. 10, no. 4-5, pp. 209-212, July 1980.
[116] F. P. Preparata, "An optimal real-time algorithm for planar convex hulls,"Commun. ACM, vol. 22, no. 7, pp. 402-405, July 1979.
[117] F. P. Preparata and S. J. Hong, "Convex hulls of finite sets of points in two and three dimensions,"Commun. ACM, vol. 20, pp. 87-93, 1977.
[118] D. Rutovitz, "An algorithm for in-line generation of a convex cover,"Comput. Graphics Image Processing, vol. 4, no. 1, pp. 74-78, Mar. 1975.
[119] A. A. Schäffer and C. J. Van Wyk, "Convex hulls of piecewise-smooth Jordan curves,"J. Algorithms, vol. 8, no. 1, pp. 66-94, Mar. 1987.
[120] R. Seidel, "A convex hull algorithm optimal for point sets in even dimensions," Dept. Comput. Sci. Univ. British Columbia, Rep. 81/14, 1981.
[121] R. Seidel, "Constructing higher-dimensional convex hulls at logarithmic cost by face," inProc. 18th Annu. ACM Symp. Theory of Computing, 1986, pp. 404-413.
[122] J. Sklansky, "On filling cellular concavities,"Comput. Graphics&Image Processing, vol. 4, no. 3, pp. 236-247, Sept. 1975.
[123] J. Sklansky, "Finding the convex hull of a simple polygon,"Pattern Recognition Lett., vol. 1, no. 2, pp. 79-83, Dec. 1982.
[124] J. Sklansky, L. P. Cordella, and S. Levialdi, "Parallel detection of concavities in cellular blobs,"IEEE Trans. Comput., vol. C- 25, no. 2, pp. 187-196, Feb. 1976.
[125] S. Y. Shin and T. C. Woo, "Finding the convex hull of a simple polygon in linear time,"Pattern Recognition, vol. 19, no. 6, pp. 453-458, 1986.
[126] E. Soisalon-Soininen, "On computing approximate convex hulls,"Inform. Processing Lett., vol. 16, no. 3, pp. 121-126, Apr. 1983.
[127] S. N. Weiss, "A formal framework for the study of concurrent program testing," inProc. 2nd Workshop on Software Test., Analysis, and Verification(Banff, AB, Can.), July 1988, pp. 106-113.
[128] I. Stojmenovic´and D. J. Evans, "Comments on two parallel algorithms tor the convex hull problem,"Parallel Comput., vol. 5, no. 3, pp. 373-375, Nov. 1987.
[129] G. Swart, "Finding the convex hull facet by facet,"J. Algorithms, vol. 6, no. 1, pp. 17-48, Mar. 1985.
[130] G. T. Toussaint, "A historical note on convex hull finding algorithms,"Pattern Recognition Lett., vol. 3, no. 1, pp. 21-28, Jan. 1985.
[131] G. T. Toussaint, "An optimal algorithm for computing the relative convex hull of a set of points in a polygon," inSignal Processing III: Theories and Applications. 3rd European Signal Processing Conf., Sept. 1986, pp. 853-856.
[132] G. T. Toussaint and D. Avis, "On a convex hull algorithm for polygons and its application to triangulation problems,"Pattern Recognition, vol. 15, no. 1, pp. 23-29, 1982.
[133] G. T. Toussaint and H. ElGindy, "A counterexample to an algorithm for computing monotone hulls of simple polygons,"Pattern Recognition Lett., vol. 1, no. 4, pp. 219-222, May 1983.
[134] M. Yau and S. N. Srihari, "Digital convex hulls from hierarchical data structures," inProc. Canadian Man-Comput. Commun. Soc. Conf., 1981, pp. 163-171 (also Section A).
[135] Z. Y. Zhou, "A real time algorithm for two-dimensional convex hull problem (Chinese. English summary),"Chinese J. Comput., vol. 8, no. 2, pp. 136-143, 1985.
[136] D. Avis, "Comments on a lower bound for convex hull determination,"Inform. Processing Lett., vol. 11, no. 3, p. 126, Nov. 1980.
[137] D. Avis, "On the complexity of finding the convex hull of a set of points,"Discr. Appl. Math., vol. 4, no. 2, pp. 81-86, Apr. 1982.
[138] J. Bentley, H. Kung, M. Schkolnick, and C. Thompson, "On the average number of maxima in a set of vectors and applications,"J. ACM, vol. 11, no. 1, pp. 536-543, 1978.
[139] J. L. Bentley and M. I. Shamos, "Divide and conquer for expected linear time,"Inform. Processing Lett., vol. 7, no. 2, pp. 87-91, Feb. 1978.
[140] H. Carnal, "Die konvexe Hülle vonnrotationssymmetrisch verteilten Punkten,"Z. Wahrscheinlichkeits, vol. 15, pp. 168-176, 1970.
[141] L. Devroye, "A note on finding convex hulls via maximal vectors,"Inform. Processing Lett., vol. 11, no. 1, pp. 53-56, Aug. 1980.
[142] L. Devroye, "How to reduce the average complexity of convex hull algorithms,"Comput. Math. Applicat., vol. 7, pp. 299-308, 1981.
[143] L. Devroye, "On the computer generation of random convex hulls,"Comput. Math. Applicat., vol. 8, pp.1-13, 1982.
[144] L. Devroye and G. T. Toussaint, "A note on linear expected time algorithms for finding convex hulls,"Computing, vol. 16, no. 4, pp 361-366, 1981.
[145] B. Efron, "The convex hull of a random set of points,"Biometrika, vol. 52, pp. 331-334, 1985.
[146] P. van Erode Boas, "On theΩ(nlogn) lower bound for convex hull and maximal vector determination,"Inform. Processing/ Lett., vol. 10, no. 3, pp. 132-136, Apr. 1980.
[147] J. W. Jaromczyk, "Linear decision trees are too weak for convex hull problems,"Inform, Processing Lett., vol. 12, no. 3, pp. 138- 141, June 1981.
[148] M. Kallay, "The complexity of incremental convex hull algorithms inRd," Inform. Processing Lett., vol. 19, no. 4, p. 197, Nov. 1984.
[149] A. Klapper, "A lower bound on the complexity of the convex hull problem for simple polyhedra,"Inform. Processing Lett., vol. 25, no. 3, pp. 159-161, May 1987.
[150] H. Raynaud, "Sur l'enveloppe convexe des nuages de points aléatoires dansRnI,"J. Appl. Probability, vol. 7, pp. 35-48, 1970.
[151] A. Rényi and R. Sulanke,Über die konvexe Hülle vonnzufällig gewählten Punkten, I,"Z. Wahrscheinlichkeits, vol. 2, pp. 75- 84, 1963, II, vol. 3, pp. 138-147, 1964.
[152] A. Rényi and R. Sulanke "Zufällige konvexe Polygone in einem Ringgebeit,"Z. Wahrscheinlichkeits, vol. 9, pp. 146-157, 1968.
[153] A. C. Yao, "A lower bound to finding convex hulls,"J. ACM, vol. 28, no. 4, pp. 780-787, Oct. 1981.
[154] H. Ziezold, "Über die Eckenzahl zufälliger konvexer Polygone,"Izv. Akad. Nauk. Armanj. SSR. Ser. Mat., vol. 5, pp. 296-312, 1970.
[155] A. Aggarwal, B. Chazelle, L. Guibas, C.Ó'Dúnlaig, and C. Yap, "Parallel computational geometry,"Algorithmica, vol. 3, no. 3, pp. 293-327, 1988.
[156] A. Aggarwal, M. M. Klawe, S. Moran, P. Shor, and R. Wilberg, "Geometric applications of a matrix-searching algorithm,"Algorithmica, vol. 2, no. 2, pp. 195-208, 1987.
[157] M. J. Atallah and M. T. Goodrich, "Parallel algorithms for some functions of two convex polygons," inProc. 24th Annu. Allerton Conf. Communication, Control, Computing, Monticello, IL, 1986, pp. 758-767.
[158] G. D. Chakerian and L. H. Lange, "Geometric extremum problems,"Math, Mag., vol. 44, no. 1, pp. 57-69, Jan 1971.
[159] B. M. Chazelle, "A theorem on polygon cutting with applications," inProc. IEEE 23rd Ann. Symp. Foundations of Computer Science, 1982, pp. 339-349.
[160] B. M. Chazelle and D. P. Dobkin, "Detection is easier than computation," inProc. 12th Annu. ACM Symp. Theory of Computing, 1980, pp. 146-153.
[161] F. Chin, J. Sampson, and C. A. Wang, "A unifying approach for a class of problems in the computational geometry of polygons,"Visual Comput., vol. 1, no. 2, pp. 124-132, 1985.
[162] L. Devroye, "Recent results of the average time behavior of some algorithms in computational geometry," inComput. Science and Statisitcs: Proc. 13th Symp. Interface, W. F. Eddy, Ed. Berlin: Springer-Verlag, 1981, pp. 76-82.
[163] L. Devroye, "Expected time analysis of algorithms in computational geometry," inComputational Geometry, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 135- 151 (also Subsection B.2).
[164] D. P. Dobkin and L. Snyder, "On a general method for maximizing and minimizing among certain geometric problems," inProc. IEEE 20th Annu. Symp. Foundations of Computer Science, 1979, pp. 9-17.
[165] H. Edelsbrunner and L. J. Guibas, "Topologically sweeping an arrangement," inProc. 18th Annu. ACM Symp. Theory of Computing, 1986, pp. 389-403.
[166] H. ElGindy, D. Avis, and G. T. Toussaint, "Applications of a two-dimensional hidden-line algorithm to other geometric problems,"Computing, vol. 31, no. 3, pp. 191-202, 1983.
[167] W. Henze, "Zur VLSI-Kompliziertheit geometrischer Berechnungsprobleme," Sektion Mathematik, Humboldt, Univ,, Berlin, 1985.
[168] A. Inselberg, T. Chomut, and M. Rei, "Convexity algorithms in parallel coordinates,"J. ACM, vol. 34, no. 4, pp. 765-801, Oct. 1987.
[169] D. T. Lee and F. P. Preparata, "Computational geometry-A survey,"IEEE Trans. Comput., vol. C-33, no. 12, pp. 1072-1101, Dec. 1984, Correction, vol. C-34, no. 6, p. 584, June 1985.
[170] G. Nagy, "Advances in computational geometry," inProc. 21st Midwest Symp. Circuits and Systems, 1978, pp. 598-603.
[171] F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction. New York: Springer-Verlag, 1985.
[172] R. Seidel, "A method for proving lower bounds for certain geometrical problems," inComputational Geometry,, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 319- 334.
[173] M. I. Shamos, "Geometric complexity," inProc. Seventh Annu. ACM SIGACT Conf., May 1975, pp. 224-233.
[174] M. I. Shamos, and D. Hoey, "Closest-point problems," inProc. IEEE 16th Annu. Symp. Foundations of Computer Science, 1975, pp. 151-162.
[175] G. T. Toussaint, "Pattern recognition and geometric complexity," in Proc. 5th ICPR, Dec. 1980, pp. 1324-1347.
[176] G. T. Toussaint, "Computational geometric problems in pattern recognition," inPattern Recognition Theory and Applications, J. Kittler, K. S. Fu, and L. F. Pau, Eds. Dordrecht, The Netherlands: Reidel, 1982, pp. 73-91.
[177] G. T. Toussaint, "Complexity, convexity, and unimodality,"Int. J. Comput. Inform. Sci., vol. 13, no. 3, pp. 197-217, June 1984.
[178] G. T. Toussaint, Ed.,Computational Geometry. Amsterdam, The Netherlands: North-Holland, 1985.
[179] G. T. Toussaint, "New results in computational geometry relevant to pattern recognition in practice," inPattern Recognition in Practice II, E. S. Gelsema and L. N. Kanal, Eds. Amsterdam, The Netherlands: North-Holland, 1986, pp. 135-146.
[180] W. Altherr, "An algorithm for enumerating all vertices of a convex polyhedron,"Computing, vol. 15, no. 3, pp. 181-193, 1975.
[181] M. L. Balinski, "An algorithm for finding all vertices of convex polyhedral sets,"J. SIAM, vol. 9, no. 1, pp. 72-88, Mar. 1961.
[182] I. Bárány and Z. Füredi, "Computing the volume is difficult,"Discr. Comput. Geom., vol. 2, no. 4, pp. 319-326, 1987.
[183] B. K. Bhattacharya and G. T. Toussaint, "A counterexample to a diameter algorithm for convex polygons,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, no. 3, pp. 306-309, May 1982.
[184] C. A. Burdet, "Generating all the faces of a polyhedron,"SIAM J. Appl. Math., vol. 26, no. 3, pp. 479-489, May 1974.
[185] J. Cohen and T. Hickey, "Two algorithms for determining volumes of convex polyhedra,"J. ACM, vol. 26, no. 3, pp. 401-414, July 1979.
[186] M. E. Dyer and L. G. Proll, "An algorithm for determining all extreme points of a convex polytope,"Math. Program., vol. 12. pp. 81-96, 1977.
[187] G. Elekes, "A geometric inequality and the complexity of computing volume,"Discr. Comput. Geom., vol. 1, no. 4, pp. 289- 292, 1986.
[188] J. B. Lasserre, "An analytical expression and an algorithm for the volume of a convex polyhedron inRn,"J. Optimization Theory Applicat., vol. 39, no. 3, pp. 363-377, Mar. 1983.
[189] M. Manas, "Methods for finding all vertices of a convex polyhedron,"Ekonom. I Mat. Obzor, vol. 5, pp. 325-342, 1969.
[190] M. Manas and J. Nedoma, "Finding all vertices of a convex polyhedron,"Numerische Mathematik, vol. 12, no. 3, pp. 226- 229, 1968.
[191] T. H. Mattheiss and D. Rubin, "A survey and comparison of methods for finding all vertices of convex polyhedral sets,"Math. Oper. Res., vol. 5, no. 2, pp. 167-185, May 1980.
[192] T. H. Mattheiss and B. K. Schmidt, "Computational results on an algorithm for finding all vertices of a polytope,"Math. Program., vol. 18, pp. 308-329, 1980.
[193] W. E. Snyder and D. A. Tang, "Finding the extrema of a region,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-2, no. 3, pp. 266-269, May 1980.
[194] W. E. Snyder and D. A. Tang, "Comments on "A counterexample to a diameter algorithm for convex polygons,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, no. 3, p. 309, May 1982.
[195] T. Speevak, "An efficient algorithm for obtaining the volume of a special kind of pyramid and application to convex polyhedra,"Math. Computat., vol. 46, no. 174, pp. 531-536, Apr. 1986.
[196] T. Bailey and J. Cowles, "A convex hull inclusion test,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 2, pp. 312- 316, Mar, 1987.
[197] J. L. Bentley and W. Carruthers, "Algorithms for testing the inclusion of points in polygons," inProc. 18th Annu. Allerton Conf. Communication, Control. Computing, Monticello, IL, 1980, pp. 11-19.
[198] D. Cole, "Searching and storing similar lists,"J. Algorithms, vol. 7, no. 2, pp. 202-220, June 1986.
[199] H. Edelsbrunner, L. J. Guibas, and J. Stolfi, "Optimal point location in a monotone subdivision,"SIAM J. Comput., vol. 15, no. 2, pp. 317-340, May 1985.
[200] D. G. Kirkpatrick, "Optimal search in planar subdivisions,"SIAM J. Comput, vol. 12, no. 1, pp. 28-35, Feb. 1983.
[201] D. T. Lee and F. P. Preparata, "Location of a point in a planar subdivision and its applications,"SIAM J. Comput., vol. 6, no. 3, pp. 594-606, Sept. 1977.
[202] R. J. Lipton and R. E. Tarjan, "Applications of a planar separator theorem," inProc. IEEE 18th Annu. Symp. Foundations of Computer Science, 1977, pp. 162-170.
[203] S. Nordbeck and B. Rysted, "Computer cartography point-inpolygon programs,"BIT, vol. 7, no. 1, pp. 39-64, 1967 (also Section D).
[204] F. P. Preparata, "A new approach to planar point location,"SIAM J. Comput., vol. 10, no. 3, pp. 473-482, Aug. 1981.
[205] K. B. Salomon, "An efficient point-in-polygon algorithm,"Comput. Geosci., vol. 4, pp. 173-178, 1978.
[206] N. Sarnak and R. E. Tarjan, "Planar point location using persistent search trees,"Commun. ACM, vol. 29, no. 7, pp. 669-679, July 1986.
[207] M. Boyer and L. Paquette, "An algorithm to decide if the intersection of convex polyhedral cones has non empty interior,"BIT, vol. 16, no. 4, pp. 459-461, 1976 (also Section D).
[208] B. Chazelle and D. P. Dobkin, "Intersection of convex objects in two and three dimensions,"J. ACM, vol. 34, no. 1, pp. 1-27, Jan. 1987.
[209] F. Chin and C. A. Wang, "Optimal algorithm for the intersection and minimum distance problems between planar polygons,"IEEE Trans. Comput., vol. C-32, no. 12, pp. 1203-1207, Dec. 1983 (also Subsection C.5).
[210] P. G. Comba, "A procedure for detecting intersections of three-dimensional objects,"J. ACM, vol. 15, no. 3, pp. 354-366, July 1968.
[211] D. P. Dobkin and D. G. Kirkpatrick, "Fast detection of polyhedral intersections,"Theoret. Comput. Sci., vol. 27, no. 3, pp. 241- 253, Dec. 1983.
[212] S. Hertel, M. Mäntilä, K. Mehlhorn, and J. Nievergelt, "Space sweep solves intersection of convex polyhedra,"Acta Inform., vol. 21, no. 5, pp. 501-519, 1984.
[213] S. Kundu, "A newO(nlogn) algorithm for computing the intersection of convex polygons,"Pattern Recognition, vol. 20, no. 4, pp. 419-424, 1987.
[214] K. Maruyama, "A procedure to determine intersections between polyhedral objects,"Int. J. Comput. Inform. Sci., vol. 1, no. 3, pp. 255-266, Sept. 1972.
[215] K. Melhorn and K. Simon, "Intersecting two polyhedra one of which is convex," inFoundations of Computation Theory, Cottbus, GDR, L. Budach, Ed. (Lecture Notes in Computer Science Vol. 199). Berlin: Springer-Verlag, 1985, pp. 534-542.
[216] D. E. Muller and F. P. Preparata, "Finding the intersection of two convex polyhedra,"Theoret. Comput. Sci., vol. 7, no. 2, pp. 217- 236, Oct. 1978.
[217] J. Nievergelt and F. P. Preparata, "Plane-sweep algorithms for intersecting geometric figures,"Commun. ACM, vol. 25, no. 10, pp. 739-747, 1982.
[218] J. O'Rourke, C. B. Chien, T. Olson and D. Naddor, "A new linear algorithm for intersecting convex polygons,"Comput. Graphics Image Processing, vol. 19, no. 4, pp. 384-391, Aug. 1982.
[219] M. I. Shamos and D. Hoey, "Geometric intersection problems,"Proc. IEEE 7th Annu. Symp. Foundations of Computer Science, 1976, pp. 208-215.
[220] S. Storøy, "An algorithm for finding a vector in the intersection of open convex polyhedral cones,"BIT, vol. 13, no. 1, pp. 114- 119, 1973 (also Section D).
[221] G. T. Toussaint, "A simple linear algorithm for intersecting convex polygons,"Visual Comput., vol. 1, no. 2, pp. 118-123, 1985.
[222] M. J. Atallah, "A linear time algorithm for the Hausdorff distance between convex polygons,"Inform. Processing Lett., vol. 17, no. 4, pp. 207-209, Nov. 1983.
[223] M. J. Atallah and M. T. Goodgrich, "Parallel algorithms for some functions of two convex polygons,"Algorithmica, vol. 3, no. 4, pp. 535-548, 1988 (also Subsection C. 10).
[224] D. Avis, G. T. Toussaint, and B. K. Bhattacharya, "On the multimodality of distances in convex polygons,"Comput. Math. Applicat., vol. 8, no. 2, pp. 153-156, 1982.
[225] A. Baltsan and M. Sharir, "On the shortest path between two convex polyhedra,"J. ACM, vol. 35, no. 2, pp. 267-287, Apr. 1988.
[226] B. K. Bhattacharya and G. T. Toussaint, "Efficient algorithms for computing the maximum distance between two finite planar sets,"J. Algorithms, vol. 4, no. 2, pp. 121-136, June 1983.
[227] B. K. Bhattacharya and G. T. Toussaint, "On geometric algorithms that use the furthest-point Voronoi diagram," inComputational Geometry, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 43- 61.
[228] F. Chin and C. A. Wang, "Minimum vertex distance between separable convex polygons,"Inform. Processing Lett., vol. 18, no. 1, pp. 41-45, Jan. 1984.
[229] A. K. Dewdney and J. K. Vranch, "A convex partition ofR3with applications to Crum's problem and Knuth's post-office problem,"Utilitas Math., vol. 12, pp. 193-199, 1977.
[230] H. Edelsbrunner, "Computing the extreme distances between two convex polygons,"J. Algorithms, vol. 6, no. 2, pp. 213-224, June 1985.
[231] A. Fournier and Z. Kedem, "Comments on the all nearest-neighbor problem for convex polygons,"Inform. Processing Lett., vol. 9, no. 3, pp. 105-107, Oct. 1979.
[232] D. T. Lee and F. P. Preparata, "The all nearest-neighbor problem for convex polygons,"Inform. Processing Lett., vol. 7, no. 4, pp. 189-192, June 1978.
[233] M. McKenna and G. T. Toussaint, "Finding the minimum vertex distance between two disjoint convex polygons in linear time,'"Comput. Math. with Applicat., vol. 11, no. 12, pp. 1227-1242, 1985.
[234] J. T. Schwartz, "Finding the minimum distance between two convex polygons,"Inform. Processing Lett., vol. 13, no. 4-5, pp. 168-170, Dec. 1981.
[235] G. T. Toussaint, "An optimal algorithm for computing the minimum vertex distance between two crossing convex polygons,"Computing, vol. 32, no. 4, pp. 357-364, 1984.
[236] G. T. Toussaint and B. K. Bhattacharya, "Optimal algorithms for computing the minimum distance between two finite planar sets,"Pattern Recognition Lett., vol. 2, no. 2, pp. 79-82, Dec. 1983.
[237] G. T. Toussaint and J. A. McAlear, "A simpleO(nlogn) algorithm for finding the maximum distances between two finite planar sets,"Pattern Recognition Lett., vol. 1, no. 1, pp. 21-24, Oct. 1982.
[238] C. C. Yang and D. T. Lee, "A note on the all nearest-neighbor problem for convex polygons,"Inform. Processing Lett., vol. 8, no. 4, pp. 193-194, Apr. 1979.
[239] B. M. Chazelle, "Convex decomposition of polyhedra, inProc. 13th Annu. ACM SIGACT Symp., 1981.
[240] B. M. Chazelle, "A decision procedure for optimal polyhedron partitioning,"Inform. Processing Lett., vol. 16, no. 2, pp. 75-78, Feb. 1983.
[241] B. M. Chazelle, "Convex partitions of polyhedra: A lower bound and worst-case optimal algorithm,"SIAM J. Comput., vol. 13, no. 3, p. 448- 507, Aug. 1984.
[242] B. M. Chazelle and D. P. Dobkin, "Decomposing a polygon into its convex parts," inProc. 11th Annu. ACM Symp. Theory. of Computing, 1979, pp. 38-48.
[243] B. M. Chazelle and D. P. Dobkin, "Optimal convex decompositions," inComputational Geometry, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 63-133.
[244] D. P. Dobkin, D. L. Souvaine, and C. J. Van Wyk, "Decomposition and intersection of simple splinegons,"Algorithmica, vol. 3, no. 4, pp. 473-485, 1988 (also Subsection C.4).
[245] D. H. Greene, "The decomposition of polygons into convex parts," inAdvances in Computing Research, vol. 1, F. P. Preparata, Ed. JAI Press, 1983, pp. 235-259.
[246] T. C. Hu and M. T. Shing, "AnO(n)algorithm to find a near-optimum partition of a convex polygon,"J. Algorithms, vol. 2, no. 2, pp. 122-138, June 1981.
[247] J. M. Keil, "Decomposing a polygon into simpler components,"SIAM J. Comput., vol. 14, no. 4, pp. 799-817, Nov. 1985.
[248] J. M. Keil and J. R. Sack, "Minimum decompositions of polygonal objects," inComputational Geometry, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 197-216.
[249] C. Levcopoulos and A. Lingas, "Bounds on the length of convex partitions of polygons," inFoundations of Software Technology and Theoretical Computer Science, 4th. Conf., Bangalore, India, Dec. 1984 (Lecture Notes in Computer Science Vol. 181). Berlin: Springer-Verlag, 1984, pp. 279-295.
[250] A. Lubiw, "Decomposing polygonal regions into convex quadrilaterals," inProc. Ist Annu. ACM Symp. Computational Geometry, June 1985, pp. 97-106.
[251] J. O'Rourke and K. J. Supowit, "Some NP-hard polygon decomposition problems,"IEEE Trans. Inform. Theory, vol. IT-29, no. 2, pp. 181-190, Mar. 1983.
[252] J. R. Sack, "AO(nlogn) algorithm for decomposing rectilinear polygons into convex quadrilaterals," inProc. 20th Annu. Allerton Conf. Communications, Control and Computing, Monticello, IL, 1982, pp. 64-74.
[253] J. R. Sack and G. T. Toussaint, "A linear-time algorithm for decomposing rectilinear star-shaped polygons into convex quadrilaterals," inProc. 19th Annu. Allerton Conf. Communication, Control and Computing, Monticello, IL, 1981, pp. 21-30.
[254] B. Schachter, "Decomposition of polygons in convex sets,"IEEE Trans. Comput., vol. C-27, no. 11, pp. 1078-1082, Nov. 1978.
[255] S. B. Tor and A. E. Middleditch, "Convex decomposition of simple polygons,"ACM Trans. Graphics, vol. 3, no. 4, pp. 244-265, Oct. 1984.
[256] A. Aggarwal, J. S. Chang, and C. K. Yap, "Minimum area cirumscribing polygons,"Visual Comput., vol. 1, no. 2, pp. 112- 117, 1985.
[257] N. A. A. De Pano and A. Aggarwal, "Finding restrictedk-envelopes for convex polygons," inProc. 22nd Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL, 1984, pp. 81-90.
[258] D. Dori and M. Ben-Bassat, "Circumscribing a convex polygon by a polygon of fewer sides with minimal area addition,"Comput. Vision, Graphics, Image Processing, vol. 24, no. 2, pp. 131-159, Nov.1983.
[259] J. Elzinga and D. Hearn, "The minimum sphere covering a convex polyhedron,"Naval Res. Logistics Quart., vol. 21, pp. 715-718, 1974.
[260] H. Freeman and R. Shapira, "Determining the minimal-area enclosing rectangle for an arbitrary closed curve,"Commun. Assoc. Comput. Mach., vol. 18, pp. 409-413, 1975.
[261] V. Klee, "A linear-time algorithm that finds all local minima among triangles containing a given convex polygon,"Proc. Vth Symp. Operations Res., Köln, Aug. 1980.
[262] V. Klee and M. C. Laskowski, "Finding the smallest triangles containing a given convex polygon,"J. Algorithms, vol. 6, no. 3, pp. 359-375, Sept. 1985.
[263] J. O'Rourke, "The complexity of computing minimum convex covers for polygons," inProc. 20th Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL, 1982, pp. 75-84.
[264] J. O'Rourke, "Finding minimal enclosing boxes,"Int. J. Comput. Inform. Sci., vol. 14, no. 3, pp. 183-199, June 1985.
[265] J. O'Rourke, "Counterexamples to a minimal circumscription algorithm,"Comput. Vision Graphics, Image Processing, vol. 30, no. 3, pp. 364-366, June 1985.
[266] J. O'Rourke, A. Aggarwal, S. Maddila, M. Baldwin, "An optimal algorithm for finding minimal enclosing triangles,"J. Algorithms, vol. 7, no. 2, pp. 258-269, June 1986.
[267] G. T. Toussaint, "Solving geometric problems with the "rotating calipers," inProc. IEEE MELECON 83, Athens, Greece, May 1983.
[268] T. C. Woo and H. C. Lee, "On the time complexity for circumscribing a convex polygon,"Comput. Vision, Graphics, Image Processing, vol. 30, no. 3, pp. 362-363, June 1985.
[269] J. S. Chang and C. K. Yap, "A polymomial solution for potatopeeling and other polygon inclusion and enclosure problems," inProc. IEEE 25th Annu. Symp. Foundations of Computer Science, 1984, pp. 408-416.
[270] J. S. Chang and C. K. Yap, "A polymomial solution for the potato-peeling problem,"Distr. Comput. Geom., vol. 1, no. 2, pp. 155-182, 1986.
[271] V. Chvátal and G. Klincsek, "Finding largest convex subsets," inProc. 11th Southeastern Int. Conf. Combinatorics, Graph Theory, and Computing, Vol. II, Boca Raton, FL;Congr. Numer., vol. 29, pp. 453-460, 1980.
[272] J. E. Goodman, "On the largest convex polygon contained in a non-convexn-gon, or how to peel a potato,"Geometriae Dedicata, vol. 11, pp. 99-106, 1981.
[273] D. Wood and C. K. Yap, "Computing a convex skull of an orthogonal polygon," inProc. 1st Annu. ACM Symp. Computational Geometry, June 1985, pp. 311-315.
[274] V. Akman,Unobstructed Shortest Paths in Polyhedral Environments(Lecture Notes in Computer Science Vol. 251). Berlin: Springer-Verlag, 1987.
[275] J. Hershberger and L. J. Guibas, "AnO(n2) shortest path algorithm for a non-rotating convex body,"J. Algorithms, vol. 9, no. 1, pp. 18-46, Mar. 1988.
[276] K. Kedem and M. Sharir, "An efficient algorithm for planning collision-free translational motion of a convex polygonal object in 2- dimensional space amidst polygonal obstacles," inProc. 1st Annu. ACM Symp. Computational Geometry, June 1985, pp. 75-80.
[277] D. Leven and M. Sharir, "Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams,"Discr. Comput. Geom., vol. 2, no. 1, pp. 9- 31, 1987.
[278] D. Leven and M. Sharir, "On the number of critical free contacts of a convex polygonal object moving in two-dimensional polygonal space,"Discr. Comput. Geom., vol. 2, no. 3, pp. 255-270, 1987.
[279] J. O'Rourke, "Convex hulls, Voronoi diagrams, and terrain navigation," inProc. 9th Pecora Symp. Spatial Information Technologies for Remote Sensing Today and Tomorrow, R. M. Haralick, Ed. Washington, DC: IEEE Computer Society Press, 1984, pp. 358-361.
[280] H. Rohnert, "Shortest paths in the planes with convex polygonal obstacles,"Inform. Processing Lett., vol. 23, pp. 71-76, Aug. 1986.
[281] H. Rohnert, "Time and space efficient algorithms for shortest paths between convex polygons,"Inform. Processing Lett., vol. 27, no. 4, pp. 175-179, Apr. 1988.
[282] M. Sharir, "On shortest paths amidst convex polyhedra,"SIAM J. Comput., vol. 16, no. 3, pp. 561-572, June 1987.
[283] M. Sharir and A. Schorr, "On shortest paths in polyhedral spaces,"SIAM J. Comput., vol. 15, no. 1, pp. 193-215, Feb. 1986.
[284] A. Aggarwal, H. Booth, J. O'Rourke, S. Suri, and C. K. Yap, "Finding minimal convex nested polygons," inProc. 1st Annu. ACM Symp. Computational Geometry, June 1985, pp. 296-304.
[285] V. Akman, "An algorithm for determining an opaque minimal forest of a convex polygon,"Inform. Processing Lett., vol. 24, no. 3, pp. 193-198, Feb. 1987.
[286] D. Avis, H. ElGindy, and R. Seidel, "Simple on-line algorithms for convex polygons," inComputational Geometry, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 23-42.
[287] D. Avis and D. Rappaport, "Computing the largest empty convex subset of a set of points," inProc. 1st. Annu. ACM Symp. Computational Geometry, June 1985, pp. 161-167.
[288] B. S. Baker, S. J. Fortune, and S. R. Mahaney, "Polygon containment under translation,"J. Algorithms, vol. 7, no. 4, pp. 532- 548, Dec. 1986.
[289] Y. Ben-Haim, "Convex sets and nondestructive assay,"SIAM J. Alg. Discr. Methods, vol. 6, no. 4, pp. 688-706, Oct. 1985.
[290] H. J. Bernstein, "Determining the shape of a convexn-sided polygon by using 2n+ktactile probes,"Inform. Processing Lett., vol. 22, no. 5, pp. 255-260, Apr. 1986.
[291] J. E. Boyce, D. P. Dobkin, R. L. Drysdale, and L. J. Guibas, "Finding external polygons,"SIAM J. Comput., vol. 14, no. 1, pp. 134-147, Feb. 1985.
[292] B. M. Chazelle, "The polygon containment problem," inAdvances in Computing Research, vol. 1, F. P. Preparata, Ed. JAI Press, 1983, pp. 1-33.
[293] B. M. Chazelle, "On the convex layers of a planar set,"IEEE Trans. Inform. Theory, vol. IT-31, no. 4, pp. 509-517, July 1985.
[294] R. Cole and C. K. Yap, "Shape from probing,"J. Algorithms, vol. 8, no. 1, pp. 19-38, Mar. 1987.
[295] R. Cole, M. Sharir, and C. K. Yap, "Findingk-convex hulls," inProc. 16th Annu. ACM SIGACT Symp., 1984, pp. 154-166.
[296] R. Cole, M. Sharir, and C. K. Yap, "Onk-hulls and related problems,"SIAM J. Comput., vol. 16, no. 1, pp. 61-77, Feb. 1987.
[297] G. Davis, "Computing separating planes for pairs of disjoint convex polyhedra," inProc. 1st. Annu. ACM Symp. Computational Geometry, June 1985, pp. 8-14.
[298] D. P. Dobkin, R. L. Drysdale, and L. J. Guibas, "Finding smallest polygons," inAdvances in Computing Research, vol. 1, F. P. Preparata, Ed. JAI Press, 1983, pp. 181-214.
[299] D. P. Dobkin, H. Edelsbrunner, and C. K. Yap, "Probing convex polytopes," inProc. 18th Annu. ACM Symp. Theory of Computing, 1986, pp. 424-432.
[300] D. P. Dobkin and D. G. Kirkpatrick, "A linear algorithm for determining the separation of convex polyhedra,"J. Algorithms, vol. 6, no. 3, pp. 381-392, Sept. 1985.
[301] D. Dori and M. Ben-Bassat, "Efficient nesting of congruent convex figures,"Commun. ACM, vol. 27, no. 3, pp. 228-235, Mar. 1984.
[302] H. Edelsbrunner and S. S. Skiena, "Probing convex polygon with X-rays,"SIAM J. Comput., vol. 17, no. 5, pp. 870-882, Oct. 1988.
[303] L. J. Guibas and R. Seidel, "Computing convolutions by reciprocal search,"Discr. Comput. Geom., vol. 2, no. 2, pp. 175-193, 1987.
[304] D. S. Hochbaum and W. Maass, "Fast approximation algorithms for a nonconvex covering problem,"J. Algorithms, vol. 8, no. 3, pp. 305-323, Sept. 1987.
[305] J. M. Keil, "Minimally covering a horizontally convex orthogonal polygon," inProc. 2nd Annu. ACM Symp. Computational Geometry, 1986, pp. 43-51.
[306] R. Klette and E. V. Krishnamurthy, "Algorithms for testing convexity of digital polygons,"Comput. Graphics Image Processing, vol. 16, no. 2, pp. 177-184, June 1981.
[307] D. T. Lee and I. M. Chen, "Display of visible edges of a set of convex polygons," inComputational Geometry, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 249-265.
[308] D. T. Lee and C. B. Silio, "An optimal illumination region algorithm for convex polygons,"IEEE Trans. Comput., vol. C-31, no. 12, pp. 1225-1227, Dec. 1982.
[309] W. Maass, "On the complexity of nonconvex covering,"SIAM J. Comput., vol. 15, no. 2, pp. 453-467, May 1986.
[310] M. McKenna and R. Seidel, "Finding the optimal shadow of a convex polytope," inProc. 1st. Annu. ACM Symp. Computational Geometry, June 1985, pp. 24-28.
[311] A. Mesa Henriquez, "CONVY: An algorithm for the nonoverlapping covering of polygons by convex sets (Spanish, English summary),"Investigación Oper., vol. 6 no. 2-3, pp. 79-94, 1985.
[312] A. Mesa Henriquez, "HODY: An algorithm for constructing the hodograph of convex polygons (Spanish. English summary),"Investigación Oper., vol. 6, no. 2-3, pp. 95-110, 1985.
[313] T. M. Nicholl, D. T. Lee, Y. Z. Liao, and C. K. Wong, "On the X-Y convex hull of a set of X-Y polygons,"BIT, vol. 23, pp. 456- 471, 1983.
[314] T. Ottmann, E. Soisalon-Soininen, and D. Wood," On the definition and computation of rectilinear convex hulls,"Inform. Sci., vol. 33, no. 3, pp. 157-171, 1984.
[315] M. H. Overmars and J. van Leeuwen, "Dynamically maintaining configurations in the plane," inProc. 12th Annu. ACM Symp. Theory, of Computing, 1980, pp. 135-145.
[316] M. H. Overmars and J. van Leeuwen, "Maintenance of configurations in the plane,"J. Comput. Sys. Sci., vol. 23, no. 2, pp. 166-204, Oct. 1981.
[317] J. Pach, "On an isoperimetric problem,"Studia Sci. Math. Hungar. vol. 13, no. 1-2, pp. 43-45, 1978.
[318] J. Pach, "Covering the plane with convex polygons,"Discr. Comput. Geom., vol. 1, no. 1, pp. 73-81, 1986.
[319] G. J. E. Rawlins and D. Wood, "Optimal computation of finitely oriented convex hulls,"Inform. Computat., vol. 72, no. 2, pp. 150-166, Feb. 1987.
[320] S. S. Venkatesh and D. Psaltis, "Linear and logarithmic capacities in associative neural networks,"IEEE Trans. Inform. Theory, vol. 35, pp. 558-568, 1989.
[321] J. R. Sack, "A simple hidden-line algorithm for rectilinear polygons," inProc. 21st Annu. Allerton Conf. Communication, Control and Computing, Monticello, IL, 1983, pp. 437-446.
[322] R. L. Shuo-Yen, "Reconstruction of polygons from projections,"Inform. Processing Lett., vol. 28, no. 5, pp. 235-240, Aug. 1988.
[323] S. P. Smith and A. K. Jain, "Testing for uniformity in multidimensional data,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 1, pp. 73-81, Jan. 1984 (also Section D).
[324] G. T. Toussaint, "A simple proof of Pach's extremal theorem for convex polygons,"Pattern Recognition Lett., vol. 1, no. 2, pp. 85-86, Dec. 1982.
[325] P. Widmayer, Y. F. Wu, and C. K. Wong, "On some distance problems in fixed orientations,"SIAM J. Comput., vol. 16, no. 4, pp. 728-746, Aug. 1987.
[326] D. Wood, "An isothetic view of computational geometry," inComputational Geometry, G. T. Toussaint, Ed. Amsterdam, The Netherlands: North-Holland, 1985, pp. 429-459.
[327] D. Wood and C. K. Yap, "The orthogonal convex skull problem,"Discr. Comput. Geom., vol. 3, no. 4, pp. 349-365, 1988.
[328] c. Arcelli and G. Sanniti de Baja, "Polygonal covering and concavity tree of binary digital pictures," inAdvances in Measurement and Control, MECO'78, Int. Symp. Measurement and Control, M. H. Hamza and S. G. Tzafestas, Eds., Athens, Panhellenic Soc. Mech. Elec. Eng., June 1978, pp, 292-297.
[329] F. Aurenhammer, "On-line sorting of twisted sequences in linear time,"BIT, vol. 28, no. 2, pp. 194-204, 1988.
[330] J. Bajon, M. Cattoën, and S. D. Kim, "A concavity characterization method for digital objects,"Signal Processing, vol. 9, no. 3, pp. 151-161, Oct. 1985.
[331] B. G. Batchelor, "Shape description using concavity trees," inAdvances in Measurement and Control, MECO'78, Int. Symp. Measurement and Control, M. H. Hamza and S. G. Tzafestas, Eds. Athens, Panhellenic Soc. Mech. Elec. Eng., June 1978, pp. 385- 390.
[332] B. G. Batchelor, "Using concavity trees for shape description, "IEE J. Comput. Digital Techniques, vol. 2, no. 4, pp. 157-168, Aug. 1979
[333] B. G. Batchelor, "Hierarchical shape description based upon convex hulls of concavities,J. Cybern., vol. 10, pp. 205-210, 1980.
[334] B. G. Batchelor, "Shape descriptors for labelling concavity trees,"J. Cybern., vol. 10, pp. 233-237, 1980.
[335] C. E. Blair and R. G. Jeroslow, "Extension of a theorem of Balas,"Discr. Appl. Math., vol. 9, no. 1, pp. 11-26, Sept. 1984.
[336] K. Q. Brown, "Voronoi diagrams from convex hulls,"Inform. Processing Lett., vol. 9, no. 5, pp. 223-228, Dec. 1979.
[337] L. Calabi and W. E. Hartnett, "Shape recognition, prairie fires, convex deficiencies and skeletons,"Amer. Math. Monthly, vol. 75, pp. 335-342, 1968.
[338] J. M. Chassery and C. Garbay, "Iterative process for colour image segmentation using a convexity criterion," inApplications of Digital Image Processing, A. Oosterlinck and A. G. Tescher, Eds;Proc. SPIE, vol. 397, pp. 165-172, 1983.
[339] H. Edelsbrunner and J. W. Jaromczyk, "How ofeen can you see yourself in a convex configuration of mirrors?" inProc. 17th Southeastern Int. Conf. Combinatorics, Graph Theory, Computing, Boca Raton, FL;Congr. Numer., vol. 53, pp. 193-200, 1986.
[340] H. Edelsbrunner, D. G. Kirkpatrick, and R. Seidel, "On the shape of a set of points in the plane,"IEEE Trans. Inform. Theory, vol. IT-29, no. 4, pp. 551-559, July 1983.
[341] R. J. Gardner, "Symmetrals and X-rays of planar convex bodies,"Arch. Math., vol. 41, pp. 183-189, 1983.
[342] V. Di Gesu, and M. C. Maccarone, "Description of fuzzy images by convex hull techniques," inProc. 8th ICPR, Oct. 1986, pp. 1276-1278.
[343] R. N. Goldman and T. D. DeRose, "Recursive subdivision without the convex hull property,Comput. Aided Geom. Design, vol. 3, no. 4, pp. 247-265, 1987.
[344] H. P. A. Haas, E. Backer, and I. J. Boxma, "Convex hull nearest neighbor rule," inProc. 5th. ICPR, Dec. 1980, pp. 87-90.
[345] M. Jourlin and B. Laget, "Convexity and symmetry: Part 1," inImage Analysis and Mathematical Morphology, Volume 2: Theoretical Advances, J. Serra, Ed. London: Academic, 1988, pp. 343-357.
[346] V. Klee, "On the complexity ofd-dimensional Voronoi diagrams,"Arch. Math., vol. 34, pp. 75-80, 1980.
[347] R. A. Jarvis, "Computing the shape hull of point in the plane," inProc. IEEE Comput. Conf. Pattern Recognition Image Processing, 1977, pp. 231-241.
[348] M. Krivánek and J. Morávek, "Clustering to minimize the sum of volumes of convex hulls of clusters is NP-complete," inFoundations of Computation Theory, Cottbus, GDR, L. Budach, Ed. (Lecture Notes in Computer Science Vol. 199). Berlin: Springer-Verlag, 1985, pp. 234-241.
[349] G. Matheron and J. Serra, "Convexity and symmetry: Part 2," inImage Analysis and Mathematical Morphology, Volume 2: Theoretical Advances, J. Serra, Ed. London: Academic, 1988, pp. 359-375.
[350] L. O'Gorman and A. C. Sanderson, "The wedge filter technique for convex boundary estimation,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-7, no. 3, pp. 326-332, May 1985.
[351] P. M. Pardalos, "Quadratic problems defined on a convex hull of points,"BIT, vol. 28, no. 2, pp. 323-328, 1988.
[352] J. Pecht, "On the index of concavity of neighborhood templates,"Acta Cybern., vol. 7, no. 4, pp. 373-376, 1986.
[353] J. Piper and E. Granum, "Computing distance transformations in convex and non convex domains,"Pattern Recog., vol. 20, pp. 599-615, 1987.
[354] A. Rosenfeld and P. De La Torre, "Histogram concavity analysis as an aid in threshold selection,"IEEE Trans. Systems, Man. Cybern., vol. SMC-13, no. 3, pp. 231-235, Mar.-Apr. 1983.
[355] G. T. Toussaint, "The convex hull as a tool in pattern recognition," inProc. AFOSR Workshop Communication Theory and Applications, Provincetown, MA, Sept. 1978, pp. 43-46.
[356] G. T. Toussaint, "On the application of the convex hull to histogram analysis in threshold selection,"Pattern Recognition Lett, vol. 2, no. 2, pp. 75-77, Dec. 1983.
[357] P. Zamperoni, "Analysis and synthesis of binary images by means of convex blobs," inProc. Int. Conf. Digital Signal Processing, Florence, Italy, Aug.-Sept. 1978, pp. 181-188.
[358] P. Zamperoni, "Bilddarstellung durch konvexe Elementarmuster," inBildverarbeitung und Musterekennung, DAGM Symp., E. Triendl, Ed. (Informatik-Fachberichte, vol. 17). Berlin: Springer-Verlag, 1978, pp. 145-154.
[359] P. Zamperoni, "Sequential growth of convex regions for grey-scale image analysis," inProc. 6th ICPR, Oct. 1982, pp. 912-914.
[360] V. Boltjansky, and I. T. Gohberg,Results and Problems in Combinatorial Geometry. New York: Cambridge University Press, 1985.
[361] A. Brønsted,An Introduction to Convex Polytopes(Graduate Texts in Mathematics, Vol. 90). Berlin: Springer-Verlag, 1983.
[362] H. S. M. Coxeter,Regular Polytopes. 2nd ed. New York: Dover, 1973.
[363] L. Danzer, B. Grünbaum, and V. Klee, "Helly's theorem and its relatives," inConvexity, Proc. 7th Symp. Pure Math. Amer. Math. Soc., V. L. Klee, Ed., AMS, Providence, RI, 1963, pp. 101-180.
[364] B. Grünbaum,Convex Polytopes. New York: Wiley-Interscience, 1967.
[365] S. R. Lay,Convex Sets and their Applications. New York: Wiley, 1982.
[366] L. A. Lyusternik,Convex Figures and Polyhedra. New York: Dover, 1963.
[367] P. McMullen and G. C. Shephard,Convex Polytopes and the Upper Bound Conjecture. New York: Cambridge University Press, 1971.
[368] J. Stoer and C. Witzgall,Convexity and Optimization in Finite Dimensions I. Berlin: Springer-Verlag, 1970.
[369] H. S. Witsenhausen, "Some aspects of convexity useful in information theory,"IEEE Trans. Inform. Theory, vol. IT-26, no. 3, pp. 265-271, May 1980.
[370] I. M. Yaglom and V. G. Boltyanskii,Convex Figures. New York: Holt, Rinehart&Winston, 1961.
[371] C. A. Berenstein, L. N. Kanal, D. Lavine, and E. Olson, "A geometric approach to subpixel registration accuracy,"Comput. Vision Graphics Image Processing, vol. 40, no. 3, pp. 334-360, 1987.
[372] [b] C. A. Berenstein and D. Lavine, "On the number of digital straight lines,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-10, no. 6, pp. 880-887, Nov. 1988.
[373] [c] M. E. Houle and G. T. Toussaint, "Computing the width of a set,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-10, no. 5, pp. 761-765, Sept. 1988.
[374] [d] M. Reichling, "On the detection of a common intersection ofkconvex obiects in the plane,"Inform. Processing Lett., vol. 29, no. 1, pp. 25-29, Sept. 1988

Index Terms:
computerised picture processing; bibliography; computational convexity; straightness; digital images; convex hull; computational complexity; computational geometry; picture processing
Citation:
C. Ronse, "A Bibliography on Digital and Computational Convexity (1961-1988)," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 2, pp. 181-190, Feb. 1989, doi:10.1109/34.16713
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