Journal Article10.1006/GMOD.2001.0543
Boundary Representation Model Rectification
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TL;DR: It is argued that a rectify-by-reconstruction approach is needed in order to reach the global optimal solution of manifold boundary models, and the restricted face boundary reconstruction problem is shown to be NP-hard.
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Abstract: Defects in boundary representation models often lead to system errors in modeling software and associated applications. This paper analyzes the model rectification problem of manifold boundary models, and argues that a rectify-by-reconstruction approach is needed in order to reach the global optimal solution. The restricted face boundary reconstruction problem is shown to be NP-hard. Based on this, the solid boundary reconstruction problem is also shown to be NP-hard.
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Citations
Error Analysis for Operations in Solid Modeling in the Presence of Uncertainty
TL;DR: A solution to the inconsistency problem is proposed and supported by theorems: it is based on the use of Whitney extension to define sets, called Quasi-NURBS sets, which are viewed as realizations of the inconsistent data provided to the numerical method.
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Analysis of boundary representation model rectification
Guoling Shen,Takis Sakkalis,Nicholas M. Patrikalakis +2 more
- 01 May 2001
TL;DR: It is argued that a rectify-by-reconstruction approach is needed in order to reach the global optimal solution of manifold boundary models, and the restricted face boundary reconstruction problem is shown to be NP-hard.
15
•Dissertation
Surface-surface intersection with validated error bounds
Harish Mukundan
- 01 Jan 2005
TL;DR: A method to achieve a continuous gapfree boundary with a definite numerically verified upper bound for the intersection curve error in parameter space is developed, which assists in defining robust boundary representation models of complex three-dimensional solids.
4
Intersections With Validated Error Bounds for Building Interval Solid Models
Harish Mukundan,Kwang Hee Ko,Nicholas M. Patrikalakis +2 more
- 01 Jan 2005
TL;DR: This paper explains that the validated ODE solver can be used in the construction of an interval B-rep solid model using such an error control, and concentrates on the issue of error control in model space using the validation of this solver.
A Rectification Algorithm for Manifold Boundary Representation Models
Guoling Shen,Takis Sakkalis,Nicholas M. Patrikalakis +2 more
- 01 Jan 2002
TL;DR: A boundary reconstruction methodology which builds a valid model in the neighborhood of an object described by a traditional boundary representation model with floating point specification, and converts an erroneous model into an interval model guaranteed to be gap-free.
1
References
Representations for Rigid Solids: Theory, Methods, and Systems
TL;DR: A coherent view, based on sound theoretical principles, of what is presently known about the representation of solids is provided by providing a simple mathematical framework for characterizing certain important aspects of representations, for example, their semantic (geometric) integrity.
•Book
An Introduction to Solid Modeling
Martti Mäntylä
- 01 Jun 1988
TL;DR: This is a very reasonable book that should be read as discussed by the authors and the following may offer you the way to get this book: When the other people must walk around and go outside to get the book in the book store, you can just be by visiting this site.
1.3K
•Book
Permutation Groups and Combinatorial Structures
Norman Biggs,Arthur T. White +1 more
- 27 Sep 1979
TL;DR: In this paper, the action of permutation groups on sets associated with combinatorial structures is discussed, and a theory of maps on orientable surfaces is developed within a combinatorical framework.
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