652 research outputs found

    Robustness in solid modeling - a tolerance based, intuitionistic approach

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    Journal ArticleThis paper presents a new robustness method for geometric modeling operations. It computes geometric relations from the tolerances defined for geometric objects and dynamically updates the tolerances to preserve the properties of the relations, using an intuitionistic self-validation approach. Geometric algorithms using this approach are proved to be robust. A robust Boolean set operation algorithm using this robustness approach has been implemented and test examples are described in this paper as well

    A new approach to tolerance analysis

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    Journal ArticleTolerance analysis is seen as part of a more general problem, namely handling data with uncertainty. Uncertain geometric data arises when interpreting measured data, but also in solid modeling where floating point approximations are common, when representing design tolerances, or when dealing with limited manufacturing precision. The common question is whether parts with uncertain shape fulfill certain functional specification. The question is expressed as geometrical relationship between toleranced objects. Unfortunately, tolerance based relations are often inconsistent, unlike relations between exactly represented objects. In this paper we survey current tolerance representation and analysis methods. We then derive our method of intuitionistic tolerance handling from a method developed for robust solid modeling. A new representational framework is proposed, which serves as the basis for robust geometric modeling and tolerance analysis. We illustrate the framework with examples of assembly design

    The discretized polyhedra simplification (DPS): a framework for polyhedra simplification based on decomposition schemes

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    This work discusses simplification algorithms for the generation of a multiresolution family of solid representations from an initial polyhedral solid. We introduce the Discretized Polyhedra Simplification (DPS), a framework for polyhedra simplification using space decomposition models. The DPS is based on a new error measurement and provides a sound scheme for error-bounded, geometry and topology simplification while preserving the validity of the model. A method following this framework, Direct DPS, is presented and discussed. Direct DPS uses an octree for topology simplification and error control, and generates valid solid representations. Our method is also able to generate approximations which do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Unlike most of the current methods, our algorithm can deal and also produces faces with arbitrary complexity. An extension of the Direct method for appearance preservation, called Hybrid DPS, is also discussed

    Robustness in geometric modeling - an intuitionistic and tolerance-based approach

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    Journal ArticleAn intuitionistic geometry approach is taken to develop two tolerance-based methods for robust geometric computation. The so called analytic model method and the approximated model method are developed independently of a specific application or a geometric algorithm. Geometric robustness is formally defined. Geometric relations are computed based on tolerances defined for geometric objects. Dynamic tolerance updating rules are given to preserve properties of the geometric relations. The two methods differ in the definition of robustness and they use different tolerance updating rules, and hence, they preseve different properties and are suitable for different kinds of applications. To handle the possibly occuring ambiguities dynamic ambiguity handling methods are described as well

    Robust boolean set operations for manifold solids bounded by planar and natural quadric surfaces

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    Journal ArticleThis paper describes our latest effort in robust solid modeling. An algorithm for set operations on solids bounded by planar and natural quadric surfaces, that handles all geometrically degenerate cases robustly, is described. We identify as the main reason for the lack of robustness in geometric modeling, that dependent relations are handled inconsistently by disregarding the dependencies. Instead of using explicit reasoning to make dependent decisions consistent, we show that redundant computation can be avoided by correctly ordering the operations, and redundant data can be eliminated in the set operation algorithm, so that the result is guaranteed to be a valid two-manifold solid
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