L. Guibas, D. Salesin and J. Stolfi, Constructing strongly convex approximate hulls with inaccurate primitives, Algorithmica 9 (1993) 534-560.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....same set with very different tolerance of their simplicity. confused with the concept of algorithmic robustness, which studies how small roundoff errors can accumulate during different steps of an algorithm and produce a false final result. This is the approach of Guibas, Salesin and Stolfi in [12, 13], where the authors define a concept similar to that of tolerance, but from the point of view of algorithmic robustness. The same can be said about the paper [17] by Li and Milenkovic, where the authors propose an algorithm to compute an approximate convex hull taking into account roundoff ....

L. Guibas, D. Salesin and J. Stolfi, Constructing strongly convex approximate hulls with inaccurate primitives, Algorithmica 9 (1993) 534-560.

....above both facets yet remain distant from the precise convex hull. Later, the coplanar point may be far above a new facet. If this occurs, Quickhull generates a warning and reports a wide facet. In R 2 , there are several robust convex hull and Delaunay triangulation algorithms [Fortune 1989] [Guibas et al. 1993] [Li and Milenkovic 1990] In R 3 , Sugihara and Dey et al. produce a topologically robust convex hull and Delaunay triangulation [Dey et al. 1992] Sugihara 1992] Their algorithms are a variation of BeneathBeyond with steps to prevent topological anomalies such as in Figure 5. The output may ....

Guibas, L., Salesin, D., and Stolfi, J. 1993. Constructing strongly convex approximate hulls with inaccurate primitives. Algorithmica 9, 534--560.

....Similar results hold for a floating point arithmetic with chopping. We do not make any assumptions concerning the magnitude of input data and we analyze relative errors. As in [2, 5] the basic primitive operations are evaluations and comparisons of slopes. Related results have been presented in [4, 6] where algorithms for so called ffl strongly ffi hull are provided. A polygon is ffl strongly ffi hull if it is the convex hull of the input points perturbed by at most ffi and remains convex even after perturbing each of its vertices by at most ffl (in the absolute sense) These algorithms use a ....

....is the convex hull of the input points perturbed by at most ffi and remains convex even after perturbing each of its vertices by at most ffl (in the absolute sense) These algorithms use a different set of primitives, or achieve different error estimates than ones presented here. The algorithm in [4] uses a framework of epsilon geometry (see [3] Both papers are concerned with absolute errors. 2 Basic Definitions and Main Result Denote by S(p; q) the slope of the line passing through p and q. In our algorithm we will use an approximation of S(p; q) It is called a computed slope and is ....

L. Guibas, D. Salesin, and J. Stolfi, "Constructing strongly convex approximate hulls with inaccurate primitives," Proceedings of the International Symposium SIGAL '90, LNCS 450, 261-270, 1990.

....subset P 0 P is equally spaced if all points of P 0 are equally spaced along their containing line. A sequence of points that is both collinear and equally spaced is said to be regular. Some techniques for addressing imprecision in geometric problems were introduced by Guibas et al. in [2]. While these methods are not readily applicable to our problem, we adopt some of their notation. In particular, a pointset is regular if each point may be displaced by a distance of at most to yield a regular pointset; i.e. given a fixed 0, a pointset P = fp 1 ; p 2 ; png ae E 2 ....

L. Guibas, D. Salesin, and J. Stolfi, Constructing Strongly Convex Approximate Hulls with Inaccurate Primitives, Algorithmica, 9 (1993), pp. 534--560.

....the first robust geometric algorithm to construct a convex O( hull faster than the best exact arithmetic algorithm for the same problem. Fortune s algorithm [1] is slightly faster and has a little less error (6 ) but it only generates a 6 weakly convex polygon. Guibas, Salesin, and Stolfi [4] have developed a rounded arithmetic algorithm for constructing strongly convex hulls, but it has running time O(n 2 log n) 2 Constructing A Strongly Convex Approximate Hull We will first consider the problem of constructing an ffl strongly convex approximation to the convex hull of a set S of ....

Leonidas Guibas, David Salesin, and Jorge Stolfi. Constructing Strongly Convex Approximate Hulls with Inaccurate Primitives. In Proceedings of the SIGAL International Symposium on Algorithms, Tokyo, Japan, August 16-18, 1990.

....may be just above both facets yet remain distant from the precise convex hull. Later, the coplanar point may be far above a new facet. If this occurs, Quickhull generates a warning and reports a wide facet. In R 2 , there are several robust convex hull and Delaunay triangulation algorithms [23] [29] [34] In R 3 , Sugihara and Dey et al. produce a topologically robust convex hull and Delaunay triangulation [18] 42] Their algorithms are a variation of Beneath Beyond with steps to prevent topological anomalies such as in Figure 3. The output may contain unbounded geometric faults. There ....

L. Guibas, D. Salesin, and J. Stolfi. Constructing strongly convex approximate hulls with inaccurate primitives. Algorithmica, 9:534--560, 1993.

....longer guaranteed) Existing methods for detecting collinearity, such as ones based on Hough transforms [1, 3, 7] are not sensitive to equally spaced constraints and are thus not applicable to our problem. Some algorithms for dealing with imprecision in computational geometry were introduced in [4], but they do not address our problem either. This work builds upon the approach introduced in Robins and Robinson [8] 3 Tools and Techniques Our overall strategy is based on starting with a pair of points and repeatedly extending it into an regular sequence, until it is no longer possible to ....

L. Guibas, D. Salesin, and J. Stolfi, Constructing Strongly Convex Approximate Hulls with Inaccurate Primitives, Algorithmica, 9 (1993), pp. 534--560.

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