Halperin and Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. CGTA: Computational Geometry: Theory and Applications, 10, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....algorithm is very complex or not readily available. Other experiences suggest that property (iii) is the exception rather than the rule. In any case, users must weigh these considerations (cf. Sch94] A weaker form of the [BMS95] approach is illustrated by work of Halperin and co workers [HS98, Raa99] Again, the algorithm must explicitly detect the presence of degeneracies but now, we explicitly perturb the input to remove all degeneracies. Their problem may be framed as follows: given a sequence S = O 1 , On ) of geometric objects, let A i (i = 1, n) be the ....

D. Halperin and C.R. Shelton. A perturbation scheme for spherical arrangements with applications to molecular modeling. Computational Geometry: Theory and Applications, 10(4):273--288, 1998.

.... between O(n 2 logn) and O(n 2 e ) for arbitrarily small positive e. All these algorithms make use of a vertical decomposition scheme. Since it was reported that using vertical decompositions of spherical planar maps in the context of molecular modelling leads to numerical problems [13], we decided to search for a data structure which does not distinguish a specific direction. Again, we are not aware of an implementation of any of these algorithms for non linear input objects. 1.3 Outline of paper We begin our presentation by recalling some characteristic properties of ....

Halperin, D., & Shelton, C. (1997). A perturbation scheme for spherical arrangements with application to molecular modeling, Proc. 13th Annu. ACM Sympos. Comput. Geom. (pp. 183--192).

....to some subset of C ij . A solution S, if it exists, is called an invariant of M . 1 A preliminary version of this paper was published earlier as part of a conference proceedings [22] 2 A third module of RAPID, currently under development, involves the computation of molecular surfaces (see [21, 31]) Although at this stage the two modules of RAPID work independently, we plan to support their interaction as the system develops. For example, the invariant identification module will be able to request from the conformational search module conformations that contain certain features of the ....

D. Halperin, C. Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. This proceedings, 1997

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D. Halperin and C. R. Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. Comput. Geom. Theory Appl., 10:273-287, 1998.

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D. Halperin and C. R. Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. Comput. Geom. Theory Appl., 10:273--287, 1998.

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D. Halperin and C. Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. Comput. Geom. Theory Appl., 10:273-287, 1998.

....more di#cult to handle robustly than addition, subtraction and multiplication. Furthermore, implementing such predicates using exact number types, would require the representation of irrational numbers. The perturbation scheme that we follow, controlled perturbation, was first presented in [14] as a method to speed up molecular surface computation. The use of exact computation turned out to be too slow for real time manipulation, so a finite precision method was needed. Controlled perturbation was devised to handle the robustness issues caused by the use of finite precision arithmetic, ....

....issues caused by the use of finite precision arithmetic, and to remove all the degeneracies. It was extended in [23] were it was applied to arrangements of polyhedral surfaces. Those arrangements require complex calculations in order to achieve a good perturbation bound. In [23] as in [14]) the resolution bound (Section 4) is assumed to be given. The resolution bound is a key element in the scheme. In this work we describe a method for obtaining good resolution bounds, which we anticipate will lead to a better understanding of the method and will open the way to applying the ....

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D. Halperin and C. R. Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. Comput. Geom. Theory Appl., 10:273--287, 1998.

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D. Halperin and C. Shelton. A perturbation scheme for spherical arrangements with applicati on to molecular modeling. Comput. Geom. Theory Appl., 10:273-287, 1998.

.... surface area contributions from pairs of atoms and approximates the error introduced by ignoring three way contributions [13] 2) a method that computes the surface area as a sum over the surface contribution of each atom computed approximately using arrangements of great circles on a sphere [27]. One possible extension of our work would be to use the ChainTree to help select better simulation steps. Indeed, the rejection rate in MCS becomes so high for compact conformations that simulation comes to a quasi standstill. This is a known weakness of MCS, which makes it less useful around ....

D. Halperin and C. Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. Comp. Geo.: Theory and Applications, 10(4):273--288, 1998.

....problems are not unique to geometric algorithms, such as the fact that the standard asymptotic measures of algorithm performance may hide prohibitively large constants. This pitfall has been observed many times in geometry, for example in the context of range searching [37] vertical decomposition [50], and construction of Minkowski sums [4] the latter example will be described in more detail in the sequel. Sometimes the worst case resource bounds are deterringly high since they cover the treatment of even the most pathological non realistic input instances. This has led to the study of ....

....means to overcome degeneracies [32] 34] 78] provided that exact arithmetic is available. If one insists on using only xed precision arithmetic then several methods that approximate the geometric objects were proposed to guarantee robustness and or remove degeneracies; see for example, 43] [50], 53] 61] 75] Because of all the diculties in implementing geometric algorithms (as discussed above) several computational geometry groups have decided to put up a carefully designed and implemented library with an emphasis on robustness and generality [63] This resulted in Cgal: The ....

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D. Halperin and C. R. Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. Comput. Geom. Theory Appl., 10:273{ 287, 1998.

....need only be present in conformations of some K of the N molecules. Although at this stage the two modules of RAPID work independently, we plan to support their interaction as the system develops. A third module of RAPID, currently under development, involves the computation of molecular surfaces [9,13]. Related Work We offer below a brief overview of related work. The interested reader can find an extensive survey in [10,16] As far as conformational search is concerned, both systematic and randomized techniques are being investigated [18] Randomized methods obtain conformations by applying ....

D. Halperin and C. Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. In ACM Conference on Computational Geometry, pages 183--192, Nice, France, 1997.

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Halperin and Shelton. A perturbation scheme for spherical arrangements with application to molecular modeling. CGTA: Computational Geometry: Theory and Applications, 10, 1998.

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