S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerance-based intuitionistic approach. Computer-Aided Design, 25(9):567-577, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....robustness that do not rely on exact computation. For eliminating numerical errors in boundary evaluation on curved solids, the work has been much more limited. Yu has explored some theoretical bounds of exact computation [48] Fang et al. have explored tolerance methods for boundary evaluation [15], Hu et al. have explored interval computations and representations [23, 24] and Desaulniers and Stewart have given limited results on the interpretation of (possibly inconsistent) output [12] Requicha and Voelcker have listed and summarized many of the earliest solid modeling systems [39] ....

....have continued to be developed in recent years, such as the CSG based BRL CAD system from the Army Research Lab [14, 13] and research systems created to demonstrate new robustness techniques. Examples of those systems are ones by Fortune [16] Jackson [25] Benouamer et al. 2] Fang et al. [15], and Hu et al. 23, 24] A significant amount of work has been done on exact computation in computational geometry, solid modeling, and symbolic computation. Among the methods used to increase the efficiency of exact computations are those based on interval arithmetic [28, 26] floating point ....

Shiaofen Fang, Beat Bruderlin, and Xiaohong Zhu. Robustness in solid modeling: A tolerance-based intuitionistic approach. Computer Aided Design, 25(9):567--576, September 1993.

....robustness that do not rely on exact computation. For eliminating numerical errors in boundary evaluation on curved solids, the work has been much more limited. Yu has explored some theoretical bounds of exact computation [49] Fang et al. have explored tolerance methods for boundary evaluation [16], Hu et al. have explored interval computations and representations [24, 25] and Desaulniers and Stewart have given limited results on the interpretation of (possibly inconsistent) output [12] Requicha and Voelcker have listed and summarized many of the earliest solid modeling systems [40] ....

....developed in recent years, such as the CSG based BRL CAD system from the Army Research Lab [14, 13] and the IRIT system [15] and research systems created to demonstrate new robustness techniques. Examples of those systems are ones by Fortune [17] Jackson [26] Benouamer et al. 2] Fang et al. [16], and Hu et al. 24, 25] A significant amount of work has been done on exact computation in computational geometry, solid modeling, and symbolic computation. Among the methods used to increase the efficiency of exact computations are those based on interval arithmetic [29, 27] floating point ....

Shiaofen Fang, Beat Bruderlin, and Xiaohong Zhu. Robustness in solid modeling: A tolerance-based intuitionistic approach. Computer Aided Design, 25(9):567--576, September 1993.

....on using tolerances with floating point arithmetic [15] however it is hard to decide a global tolerance value for all computations. Other approaches for dealing with numerical error include adaptive tolerances [34] and interval arithmetic [14] Symbolic reasoning [12] and redundancy elimination [8] are among the other methods used to increase robustness in solid modeling applications. B rep computation algorithms involve accurate evaluation of the sign of arithmetic expressions, which can present problems for floating point arithmetic when the value of the expression is close to zero. If ....

S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerancebased intuitionistic approach. CAD, 25(9):567--576, 1993.

....arithmetic [Jac95] However, it is hard to decide a global tolerance value for all computations. To circumvent these problems, combinations of symbolic reasoning [HHK89] and adaptive tolerances [Seg90] have been proposed. Other algorithms include those based on redundancy elimination [FBZ93] Many algorithms based on exact arithmetic have been proposed for reliable numeric computation for polyhedra [SI89, For95, BMP94, Hof89] Sculptured Solids: The idea of using free form surfaces in solid modeling was introduced by Chiyokura et. al [CK83] It describes the implementation of a ....

S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerancebased intuitionistic approach. Computer-Aided Design, 25(9):567--576, 1993.

....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 ....

Fang, S., Bruderlin, B., and Zhu, X., Robustness in solid modeling: a tolerance-based intuitionistic approach, Computer Aided Design, 25, No. 9, 567-576, September 1993.

....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 yet been completely developed for CAD systems, but some initial steps have been taken [5, 6, 8, 10, 11, 12, 13, 18, 19, 20, 27, 35], where among these are some surface intersection algorithms which are capable of incorporating user specified tolerances [12, 20] The use of tolerances in modeling algorithms has received scant attention in the literature (Please see, for example [28] compared to their widespread use within ....

Fang, S., Bruderlin, B., and Zhu, X., Robustness in solid modeling: a tolerance-based intuitionistic approach, Computer Aided Design, 25, No. 9, 567-576, September 1993.

....computation (as a way to increase robustness) is different from, although related to, the technical notion of tolerances in CAD design. Design tolerances in CAD are tolerance amounts specifically placed by the designer in order to account for such things as wear or manufacturing imprecision ([FBZ93]) Work is also being done on ways to represent true design tolerances in geometric solid modeling systems ( GT93] and in choosing appropriate design tolerances ( LJ93] At the same time, there are several drawbacks to the use of tolerances. First of all, unless a common tolerance value is used ....

....which is expanded as necessary to account for error buildup. The drawbacks to this approach are that several of the problems with tolerances remain, and in addition, the tolerance values can grow rather large. An approach by Fang et al. also uses various tolerances for various parts of the model ([FBZ93]) In this approach, multiple tolerances are kept, and decisions are made as to whether geometric objects are apart, coincident, intersecting, or ambiguous (which requires refinement of the interval) based on how the tolerance bounds overlap. A potential drawback to this approach is that setting ....

Shiaofen Fang, Beat Bruderlin, and Xiaohong Zhu. Robustness in solid modeling: A tolerance-based intuitionistic approach. Computer Aided Design, 25(9):567--576, September 1993.

....are considered incident. However, it is hard to decide a global tolerance value for all computations. To circumvent these problems, combinations of symbolic reasoning [HHK89] and adaptive tolerances [Seg90] have been proposed. Other algorithms include those based on redundancy elimination [RV89, FBZ93] B rep computation algorithms involve accurate evaluation of the sign of arithmetic expressions. Algorithms based on floating point arithmetic are at times ambiguous, when the value of the expression is close to zero. If this ambiguity is not properly addressed, the resulting algorithm becomes ....

S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerance-based intuitionistic approach. Computer-Aided Design, 25(9):567--576, 1993.

....floating point arithmetic [Jac95] however it is hard to decide a global tolerance value for all computations. To circumvent these problems, combinations of symbolic reasoning [HHK89] and adaptive tolerances [Seg90] have been proposed. Other algorithms include those based on redundancy elimination [FBZ93]. B rep computation algorithms involve accurate evaluation of the sign of arithmetic expressions, which can present problems for floating point arithmetic when the value of the expression is close to zero. If this problem is not properly addressed, the resulting algorithm becomes un reliable. ....

S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerance-based intuitionistic approach. Computer-Aided Design, 25(9):567-- 576, 1993.

....arithmetic [Jac95] However, it is hard to decide a global tolerance value for all computations. To circumvent these problems, combinations of symbolic reasoning [HHK89] and adaptive tolerances [Seg90] have been proposed. Other algorithms include those based on redundancy elimination [FBZ93] Many algorithms based on exact arithmetic have been proposed for reliable numeric computation for polyhedra [SI89, For95, BMP94, Hof89] Sculptured Solids: The idea of using free form surfaces in solid modeling was introduced by Chiyokura et. al [CK83] It describes the implementation of a ....

S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerancebased intuitionistic approach. Computer-Aided Design, 25(9):567--576, 1993.

....tolerances with floating point arithmetic [20] however, it is hard to decide a global tolerance value for all computations. Other approaches for dealing with numerical error include adaptive tolerances ( 37] and interval arithmetic ( 12] Symbolic reasoning ( 18] and redundancy elimination ([13]) are among the other methods used to increase robustness in solid modeling applications. Boundary computation algorithms rely on accurate evaluation of the sign of arithmetic expressions, which can present problems for floatingpoint implementations when the value of the expression is close to ....

S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerance-based intuitionistic approach. Computer-Aided Design, 25(9):567--576, 1993.

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S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerance-based intuitionistic approach. Computer-Aided Design, 25(9):567-577, 1993.

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Fang S, Bruderlin B, Zhu X. Robustness in solid modeling: a tolerance -based intuitionistic approach. Computer Aided Design 1993;25(9):567--76.

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S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerance-based intuitionistic approach. Computer-Aided Design, 25(9):567--576, 1993.

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S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerance-based intuitionistic approach. Computer-Aided Design, 25#9#:567#576, 1993.

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S. Fang, B. Bruderlin, and X. Zhu. Robustness in solid modeling: a tolerance-based intuitionistic approach. Computer-Aided Design, 25(9):567--576, 1993.

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