O'Rourke, J., "An on-line algorithm for fitting straight lines between data ranges," Communications of the ACM, vol. 24, No. 9, September 1981, pp. 574-578.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....criteria are discussed in [8, 14, 16, 17, 28] In some cases, the data points to be approximated are not defined precisely, but are themselves approximated by simple objects such as polygons or circles. Naturally, in such cases, we may still want to find the best approximating line. In [25], O Rourke examined the problem of finding a line consistent with a set of data ranges, i.e. a line intersecting a set of vertical line segments. Morris and Norback [23] gave some characterizations of both the unweighted and weighted versions of the linear approximation of points. Following their ....

J. O'Rourke. An on-line algorithm for fitting straight lines between data ranges, Communications of the ACM 24 (1981), 574--578.

....P and Q we may ask whether Q can be translated by an arbitrary amount in a specified direction without colliding with P. The CS lines provide an answer to this question. 6. 3 Range fitting and linear separability Both of these problems involve finding a line that separates two convex polygons [12]. The critical support lines provide one solution to these problems. Consider Figure 6, where L(p i , q j ) and L(p i 2 ,q j 2 ) are the two CS lines. Denote their intersection by l . We can choose as our separating line that line that goes through l and bisects angle p i l q j 2 . ....

J. O'Rourke, "An on-line algorithm for fitting straight lines between data ranges", Comm. ACM, Vol. 24, September 1981, pp. 574-578.

....translates have a line transversal but the entire family has no line transversal. A line which intersects every member in a family of objects is known as a line stabber or line transversal. Recently, computer scientists have been very interested in algorithms for finding such line stabbers, see [1, 2, 3, 5, 6, 7, 8, 14, 24, 25]. Mathematicians have also shown renewed interest in transversal problems, see [11, 15, 16, 17, 18, 19, 26, 30, 31] In [8] Edelsbrunner et al. presented an O(n log n) algorithm for constructing a representation of the line stabbers of n line segments in the plane. This was generalized by ....

O'Rourke, J., An on-line algorithm for fitting straight lines between data ranges, Comm. ACM 24 pp. 574-578 (1981).

....the individual algorithms used are characterized and classified, the properties of these heuristic combinations are not. Criteria much like our fattening [5, 26, 29] may then be used a posteriori to test the quality of the resulting approximations. Imai and Iri [16, 17, 18] and other researchers [2, 4, 8, 13, 23, 25, 31] have chosen mathematical criterion for the approximations and then sought efficient algorithms to find best approximations. The algorithms they have developed, however, have quadratic or greater running times especially for those that use original data points as vertices of the approximation. ....

Joseph O'Rourke. An on-line algorithm for fitting straight lines between data ranges. Communications of the Association for Computing Machinery, 24(9):574--578, September 1981.

....both the mathematics [Gr58] Le80] and computer science [AB87] AW87] AW88] Ed85] We88] literatures. In the computer science literature the more aggressive term stabber is traditionally used for transversal. Transversals in the plane find application in several areas including line fitting [O R81] and updating triangulations [ET85] Edelsbrunner, Overmars and Wood [EOW81] developed a method for solving planar visibility problems that yields a procedure for computing transversals for F, a family of simple objects, in O(n 2 log n) time, where n is the cardinality of F. By simple objects it ....

....that have an O(1) storage description each and which are such that, for every pair of objects, constant time suffices to compute such basic op 2 erations as their intersection, common tangents, etc. O(n log n) time is sufficient for the special cases of unsorted vertical line segments [O R81], for line segments with arbitrary directions [EMPRWW82] for a set of n translates of a simple object in the plane [Ed85] and for n circles of equal radius [BL83] Given a family K of n convex cones, determining whether K admits a common transversal can be accomplished in O(n log n a(n) time, ....

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O'Rourke, J., "An on-line algorithm for fitting straight lines between data ranges," Communications of the ACM, vol. 24, No. 9, September 1981, pp.574-578.

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O'Rourke, J., "An on-line algorithm for fitting straight lines between data ranges," Communications of the ACM, vol. 24, No. 9, September 1981, pp. 574-578.

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J. O'Rourke, "An on-line algorithm for fitting straight lines between data ranges", Comm. ACM 24 (1981) 574-478.

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J. O'Rourke. An on-line algorithm for fitting straight lines between data ranges. Communications of the Association for Computing Machinery, 24(9):574--578, Sept. 1981.

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JOSEPH O'ROURKE. An on-line algorithm for fitting straight lines between data ranges. Communications of the ACM, 24(9):574--578, 1981.

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O'Rourke, J., "An on-line algorithm for fitting straight lines between data ranges," Communications of the ACM, vol. 24, No. 9, September 1981, pp. 574-578.

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