Segal, M. and S'equin, C. H. Consistent calculations for solids modeling, Proceedings of the First Annual Conference on Computational Geometry, Baltimore, Maryland, 1985, 29-38.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....likely, but we focus our attention on gaps for ease of exposition. Concept Reality Figure 1: Gaps along Boundary Curve Interoperability for Distributed Design Systems 3 3 Related Work The problem of accuracy in geometric modeling for CAD has attracted considerable attention in the last decade [5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 25, 27, 30], with attention both to errors inherent to floating point arithmetic and to numerical approximations in algorithms. However, the use of associated tolerances within modeling implementations has received scant attention in the literature (Please see, for example [26] compared to their ....

Segal, M. and S'equin, C. H. Consistent calculations for solids modeling, Proceedings of the First Annual Conference on Computational Geometry, Baltimore, Maryland, 1985, 29-38.

....to detect and analyze gaps and even, in some elementary cases, to propose fixes. Prior to the work reported here, no adequate diagnostic tool has existed to assess gaps within STEP. 3 Related Work This CAD modeling robustness problem has attracted considerable attention in the last decade [7, 11, 13, 14, 15, 17, 24, 29], where some of these authors [14, 17, 24] have discussed that a numerical method had solved exactly a problem close to the given problem, as is considered in backward error analysis 8 . The necessary characterization of ill conditioned problems and the development of responsive methods have not ....

Segal, M. and S'equin, C. H. Consistent calculations for solids modeling, Proceedings of the First Annual Conference on Computational Geometry, Baltimore, Maryland, 1985, 29-38.

....another situation in which there is no subtle infeasibility. A number of algorithms set aside strict accuracy in favor of good error bounds in all but pathological cases. This author [12] gives such an algorithm for constructing unions and intersections of polygonal regions. Segal and Sequin [20] have a similar result. Fortune [5] gives a robust algorithm for maintaining point set triangulations which has optimal time in all cases and good error bounds in non pathological cases. Fortune and this author [6] give optimal running time algorithms for constructing arrangements of lines and ....

Mark Segal and Carlo H. Sequin. Consistent calculations for solids modeling. In Proceedings of the Symposium on Computational Geometry, pages 29--37, ACM, June 1985.

....arithmetic. The author has also created line arrangement and plane arrangement algorithms that satisfy this definition [14] For a discussion of the more general problem of improving the reliability geometric computations using rounded arithmetic, see [8, 9] Problems addressed include polygon [19, 13] and polyhedron [10, 11, 20] modeling and the calculation of convex hulls [17] and other problems in plane geometry [15] Karasick [11] has the most practical result to date, an ultra reliable polyhedral modeling system that is provably safe: it will not generate a topologically inconsistent ....

Mark Segal and Carlo H. Sequin. Consistent calculations for solids modeling. In Proceedings of the Symposium on Computational Geometry, pages 29--37, ACM, June 1985.

....below. For the purpose of this paper, we shall only give the outlines of a (non exhaustive) classification. 1. Solutions based on pure floating point arithmetic (a) Numerical solutions i. Epsilons (popular folklore) ii. Finite exact precision ( 4] 9] 18] 19] iii. Epsilon geometry ( 8] [25]) b) Geometrical solutions i. Adaptive geometry ( 7] 18] 20] ii. Robust geometry ( 10] 13] 18] iii. Constructive geometry ( 11] iv. Symbolic geometry ( 18] 2. Solutions based on an exact library 3. Perturbation techniques ( 5] 26] 4. Mixed solutions (a) Solutions based on one exact ....

M. Segal and C.H. S'equin. Consistent calculations for solids modeling. In Proceedings of the 1st ACM Symposium on Computational Geometry, pages 29-- 38, 1985.

....input. The author has also created line arrangement and plane arrangement algorithms that satisfy this definition [10] For a discussion of the more general problem of improving the reliability geometric computations using rounded arithmetic, see [4, 5] Problems addressed include polygon [13, 9] and polyhedron [6, 7, 14] modeling and the calculation of convex hulls [12] and other problems in plane geometry [11] Karasick [7] has the most practical result to date, an ultra reliable polyhedral modeling system that is provably safe: either it generates a topologically consistent result or ....

Mark Segal and Carlo H. Sequin. Consistent calculations for solids modeling. In Proceedings of the Symposium on Computational Geometry, pages 29--37, ACM, June 1985.

....hulls and maintaining triangulations of the plane [5] but the precision required by these grows with the number of inputs. For a discussion of the more general problem of improving the reliability of geometric computations using rounded arithmetic, see [9, 10] Problems addressed include polygon [21, 16] and polyhedron [11, 12, 22] modeling, algebraic curves [14] and other problems in plane geometry [20] Karasick [12] has the most practical three dimensional result to date, a polyhedral modeling system that is provably safe: either it generates a topologically consistent result or it indicates ....

Mark Segal and Carlo H. Sequin. Consistent calculations for solids modeling. In Proceedings of the Symposium on Computational Geometry, pages 29--37, ACM, June 1985.

....for simplicity) which induces fundamentally different topologies. their results. Is it possible to consider using lazy arithmetic packages when data are represented by intervals only In Computational Geometry, a few similar situations have been studied by authors like M. Segal and C.H. S equin ([38]) Z. Li and V. Milenkovic ( 27] More recently, C. Barber ( 1] studied this problem from a very theoretical point of view in the case of the construction of 3 D convex hulls for sets of fuzzy points. He suggests very involved methods for defining and constructing such objects consistently, ....

M. Segal and C.H. S'equin. Consistent calculations for solids modeling. In Proceedings of the 1st ACM Symposium on Computational Geometry, pages 29--38, 1985.

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M. Segal and C. Séquin, "Consistent Calculation for Solid Modeling", ACM Annual Symposium on Computational Geometry, pp. 29-37, June 1985.

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