Offsetting operations in solid modelling

Rossignac, Jaroslaw R.; Requicha, Aristides A. G.

doi:10.1016/0167-8396(86)90017-8

Cited by 213 publications

(82 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In many applied fields, including tolerancing and metrology (Hillyard and Braid, 1978a;Hillyard and Braid, 1978b;Gossard et al, 1988;Jayaraman and Srinivasan, 1989;Srinivasan and Jayaraman, 1989;Rossignac and Requicha, 1986;Boyer and Stewart, 1991;Boyer and Stewart, 1992;Stewart, 1993), solid modeling (M~intyl~i, 1988, p.110), engineering design (Heisserman and Woodbury, 1992), finite element analysis (Kumar and Gossard, 1992), surface reconstruction (Hoppe et al, 1993), computer graphics (Edelsbrunner and Miicke, 1994), path planning in robotics (Latombe, 1991, p. 91), fairing procedures (Rando and Roulier, 1991), image analysis (Serra, 1982, p. 69), and medical imaging (Peters et al, 1992;Fuchs, 1977), it is natural to require that a perturbed object should have the same topological form as a given original object S.…”

Section: Introductionmentioning

confidence: 99%

Polyhedral perturbations that preserve topological form

Andersson

Dorney

Peters

et al. 1995

Computer Aided Geometric Design

View full text Add to dashboard Cite

The idea, that we are willing to accept variation in an object but that we insist it should retain its original topological form, has powerful intuitive appeal, and the concept appears in many applied fields. Some of the most important of these are tolerancing and metrology, solid modeling, engineering design, finite element analysis, surface reconstruction, computer graphics, path planning in robotics, fairing procedures, image analysis, and medical imaging. In this paper we focus on the field of tolerancing and metrology. The requirement that two objects or sets should have the same topological form requires a precise definition. We specify "same topological form" to mean that there exists a "space homeomorphism" from IR 3 onto IR 3 that carries a nominal object S onto another design object. In general, establishing the existence of such space homeomorphisms can be considerably more difficult than demonstrating classical topological equivalence by a homeomorphism. In the special case when the boundary of S is a polyhedral two-sphere in R 3, one of the authors has previously given a simple sufficient condition for the existence of a space homeomorphism mapping S onto another design object. This paper presents * Corresponding author. Email: tpeters@cse.uconn. 4 Acknowledges, with appreciation, partial funding for this work received under National Aeronautics and Space Administration (NASA) Grant Number NGT 40037 and under National Science Foundation Grant Number MI1-9308346. The views expressed herein are of this author, not of these funding agencies.5 The research of the fourth author was supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.0167-81396/95/$09.50 @ 1995 Elsevier Science B.V. All rights reserved SSD10167-8396(94) 00039-5 786 L.-E. Andersson et al./Computer Aided Geometric Design 12 (1995) [785][786][787][788][789][790][791][792][793][794][795][796][797][798][799] an analogous sufficient condition for the case when S is a finite polyhedron in R 3. The result relies upon a triangulation of the boundary and upon a dependent parameter that specifies the maximum size of permissible perturbations of the vertices of the polyhedron.

show abstract

Section: Introductionmentioning

confidence: 99%

Polyhedral perturbations that preserve topological form

Andersson

Dorney

Peters

et al. 1995

Computer Aided Geometric Design

View full text Add to dashboard Cite

show abstract

“…Offsetting has various important applications [69]. For example, if the inner surface of a piece is taken as the reference surface, the outer surface can be Fig.…”

Section: Offset Curves and Surfacesmentioning

confidence: 99%

Computational Methods for Geometric Processing. Applications to Industry

Iglesias

Gálvez

Puig-Pey

2001

Computational Science — ICCS 2001

View full text Add to dashboard Cite

show abstract

“…Several specific GOG systems have been studied by Rossignac: offset and blending nodes in CSG [Rossignac86a], constraints in CSG [Rossignac86b], and operations as general procedures [Rossignac89]. A GOG with constraints between coordinate systems and an underlying procedural programming language was described in [Emmerik90].…”

Section: Geometric Operation Graph Representationsmentioning

confidence: 99%

Breps as Displayable-Selectable Models in Interactive Design of Families of Geometric Objects

Rappoport

1997

Geometric Modeling: Theory and Practice

View full text Add to dashboard Cite

Abstract. In classical geometric modeling, the primary objects of interest are geometric pointsets, the primary representation scheme for which is the boundary representation (Brep). Modern geometric modeling focuses on parametric families of pointsets, defined using geometric operation graphs (GOGs), features and constraints. During interactive design of families of objects, users interact with an example object from the family. The example object is a pointset, hence is usually modeled using the Brep. In this paper we study the issue of which modeling scheme is most appropriate for the example object. We identify two major operations which such a modeling scheme must support: display and selection. Selection can be further decomposed into picking, invariant naming, and persistent naming. We introduce the term Displayable-Selectable Models (DSmodels) as a generic term for models providing display and selection functionality. We discuss the suitability of Breps to serve as DS-models and whether other, perhaps simpler, representations could also serve as DS-models.

show abstract

Offsetting operations in solid modelling

Cited by 213 publications

References 15 publications

Polyhedral perturbations that preserve topological form

Polyhedral perturbations that preserve topological form

Computational Methods for Geometric Processing. Applications to Industry

Breps as Displayable-Selectable Models in Interactive Design of Families of Geometric Objects

Contact Info

Product

Resources

About