{"title":"A mathematical model for boundary representations of n-dimensional geometric objects","authors":"A. Gomes, A. Middleditch, C. Reade","doi":"10.1145/304012.304039","DOIUrl":"https://doi.org/10.1145/304012.304039","url":null,"abstract":"The major purpose of this paper is to introduce a general theory within which previous boundary representations (Breps) are a special case. Basically, this theory combines sub-analyt,ic geometry and theory of stratifications. The sub-analyt,ic geometry covers almost, all geometric engineering artefacts, and it is a generalisation of the semi-analytic geometry, which in turn is a generalisation of the semialgebraic geometry used by most geometric kernels. On the other hand, the theory of stratifications provides the most general manifold structures for geometric objects that it is possible to consider in geometric modelling. Whitney stratifications are particularly useful in geometric modelling because they provide a general abstraction for the #structure of boundary representations of objects in IV’. Remarkably, it is well-known in mathematics that sub-analytic objects are Whitney stratifiable, and this mathematically matches and validates the usual geometry-structure design of boundary representation data structures. Thus, the general B-rep introduced here represents Whitney-stratified sub-analytic objects, though the global design of the data structure is classical: the geometry (sub-analytic geometry) separated from the structure (Whitney stratification). 1 Theoretical evolution of boundary repre-","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"28 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120934726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Offsetting operations on non-manifold boundary representation models with simple geometry","authors":"Sang-Hun Lee","doi":"10.1145/304012.304017","DOIUrl":"https://doi.org/10.1145/304012.304017","url":null,"abstract":"This paper describes non-manifold offsetting operations that add or remove a uniform thickness from a given non-manifold object with simple ge:ometry. Each offsetting operation for wireframes, sheets and solids is applicable to different engineering areas with a great potential usefulness. However, the representation schemes of conventional geometric modeling systems have not described all of the wireframes, sheets and solids together; each offsetting capability has been developed and applied separately in each .system. In recent years, non-manifold geometric modelers have been developed and more widely spread. Since they can manipulate different levels of models with a unified data structure, these three types of offsetting operations can be integrated into one. Moreover, non-manifold offsetting operations can be used to give flesh to abstract model!s that are generated as a mixture of wireframes and sheets in conceptual design. Therefore, in this paper, the mathematical definitions and properties of the non-manifold offsetting operations are described first and then an offset algorithm using the non-manifold Euler and Boolean operations is suggested. In this algorithm, o&et models for all or a subset of the vertices, edges and faces of a given nonmanifold model are generated first. Then, they are united into one body using the non-manifold Boolean operations. Finally, all topological entities that are within offset distance are dei.ected and removed in turn. In addition to the general offset algorithm, this paper discusses its variations for wireframes and sheets to provide the more practical offset solids for pipelines, plastic parts and sheet metal parts.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"725 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132337888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Manufacturable feature recognition and its integration with process planning","authors":"Junghyun Han, Inho Han","doi":"10.1145/304012.304023","DOIUrl":"https://doi.org/10.1145/304012.304023","url":null,"abstract":"Despite the long history of research on feature recognition, its research results have rarely been transferred into indu:stry. One of the reasons may be the separation of feature recognition and process planning. This paper proposes to integrate the two activities, and presents efforts towards it: feature recognition for manufacturability and setup minimization, feature dependency construction, and generation of an optimal featurebased machining sequence.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114781132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error classification and recovery within CAD model reconstruction","authors":"Massimo M. Ficco, F. Mandorli, H. Otto","doi":"10.1145/304012.304056","DOIUrl":"https://doi.org/10.1145/304012.304056","url":null,"abstract":"With ever increasing demands from international markets and responding industries for a quick transfer as well as processing of CAD and product data between different computer aided applications, within as well as between a product's life cycle stages, activities dedicated to the development and standardization of data representations and exchange formats are more critical than ever before. However, in practice, before complete standards and developed models and systems succeed and become reality, interim solutions are required to bridge certain gaps. One application field, requiring such interim solutions until robust methods are found, to correct error causing processes, is the exchange and consequent repair of geometric models. Due to subtle errors in geometric models and their representations, caused by design mistakes, programming errors or model evaluation failures, irrational behavior of CAD systems and other, post design related systems exchanging as well as accessing CAD data, are becoming a frequently observed situation, causing a severe break in the process of computer aided product development. To recover from such a rather undesirable situation, we propose an interim solution, aimed at bridging the gap between generation of corrupted CAD data and model exchanging post design applications. An approach, that is based on an error classification driven systematic recovery of corrupted CAD data being subject to model reconstruction. The approach taken includes a classification scheme for face adjacency errors, missing faces and curve adjacency errors for which dedicated individual methods and solutions were developed and related to. Practical work used to support as well as provide parameters for validation and assessment of proposed solutions was carried out using an implemented testbed, which is based on spatial model point distance tolerances driven face sewing. During experimental work exchange format used for model import/export were limited to IGES. Investigated models imported through these standardized data exchange formats were mainly taken from mechanical engineering.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134177217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implicit functions with guaranteed differential properties","authors":"V. Shapiro, I. Tsukanov","doi":"10.1145/304012.304038","DOIUrl":"https://doi.org/10.1145/304012.304038","url":null,"abstract":"Theory of R-functions [12] provides the methodology for constructing exact implicit functions for any semianalytic set. This paper systematically explores and compares the known constructions in terms of their differential properties and explains how such functions may be constructed automatically from CSG and boundary representations of solids. The constructed functions may be automatically differentiated and integrated and have many important applications in meshfree engineering analysis, motion planning, and scientific visualization.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130635291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rational bisectors of CSG primitives","authors":"G. Elber, Myung-Soo Kim","doi":"10.1145/304012.304028","DOIUrl":"https://doi.org/10.1145/304012.304028","url":null,"abstract":"The bisector surface of two rational surfaces in R3 is non-rational, in general. However, in some special cases, the bisector surfaces can have rational parameterization. This paper classifies some of these special cases that are related to constructive solid geometry (CSG). We consider the bisector surfaces between points, lines, planes, spheres, cylinders, cones, and tori. Many cases are shown to yield rational bisector surfaces, while several other cases are still left as open questions.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116762348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Foundation of a computable solid modeling","authors":"A. Edalat, A. Lieutier","doi":"10.1145/304012.304040","DOIUrl":"https://doi.org/10.1145/304012.304040","url":null,"abstract":"Solid modelling and computational geometry are based on classical topology and geometry in which the basic predicates and operations, such as membership, subset inclusion, union and intersection, are not continuous and therefore not computable. But a sound computational framework for solids and geometry can only be built in a framework with computable predicates and operations. In practice, correctness of algorithms in computational geometry is usually proved using the unrealistic Real RAM machine model of computation, which allows comparison of real numbers, with the undesirable result that correct algorithms, when implemented, turn into unreliable programs. Here, we use a domain-theoretic approach to recursive analysis to develop the basis of an e3ective and realistic framework for solid modelling. This framework is equipped with a well de5ned and realistic notion of computability which re6ects the observable properties of real solids. The basic predicates and operations on solids are computable in this model which admits regular and non-regular sets and supports a design methodology for actual robust algorithms. Moreover, the model is able to capture the uncertainties of input data in actual CAD situations. c 2002 Elsevier Science B.V. All rights reserved.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126679086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Robert L. Blanding, C. Brooking, M. Ganter, D. Storti
{"title":"A skeletal-based solid editor","authors":"Robert L. Blanding, C. Brooking, M. Ganter, D. Storti","doi":"10.1145/304012.304026","DOIUrl":"https://doi.org/10.1145/304012.304026","url":null,"abstract":"This paper explores the concept of using skeletons as the basis for constructing a solid-editing system. Skeletal data (i.e., the skeleton and the associated maximal sphere radii) offers a valid solid representation scheme, and we examine the capability of the skeletal representation to support shape editing operations. In addition to general discussion of the capabilities of skeletalbased methods, we also present concrete examples of editing operations reahzed in a recent implementation of a skeletonbased solid editor. The im lemented skeletal-based editor imports polyhedral solids or po yhedral approximations of solids) by I, p computing their s eletal data. The editor then displays the skeletal data and provides a simple interface for editing both the skeleton and the sphere radii. The edited skeleton is then “refleshed”, based on the edited skeletal data, to reconstruct the edited solid. The reconstructed solid is represented as the halfspace associated with an implicit tinction, and polygonization methods can be applied to produce output that, like the input, is polyhedral. Editing operations illustrated correspond to stretching, bending, rounding, and uniform or non-uniform thickening of the solid. Discussions of the key enabling technologies including skeletonization, and polygonization are also presented. refleshing,","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123241536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Surface feature constraint deformation for free-form and interactive design","authors":"J. M. Zheng, K. W. Chan, I. Gibson","doi":"10.1145/304012.304035","DOIUrl":"https://doi.org/10.1145/304012.304035","url":null,"abstract":"There is an increasing demand in the conceptual design for more intuitive methods for creating and modifying free-form curves and sueaces in CAD ,nodeling systems. The methods should be based not on1.v on the change of the mathematical parameters but almy on the user’s specified constraints and shapes. Thrs paper presents a new surface representation model for ,%ee-form sur$ace deformation representation. The moa’el is a combination of two functions: a displacement fun,:tion and a function for representing an existing NURBS sur$ace called parent sur$ace. Based on the suvace msdel, the authors develop three deformation methods which are named SingleDef(Single-point constraint based deformation method), MultiDef(Multiple-points constraints based deformation method), and FeatDe,f(Feature constraint based deformation method}. The techniques for free-form surface deformation allow conceptual designers to modify a parent surface by directly applyrng point constraints or a sur$ace constraint to the paren,’ surface. The deformation methods are implemented in an experimental CAD system. The results show that designers can easily and intuitively control the sueace shapt!. &?yWOrdS: computer aided geometric design, jke-form deformation, modeling","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123463692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fine level feature editing for subdivision surfaces","authors":"A. Khodakovsky, P. Schröder","doi":"10.1145/304012.304033","DOIUrl":"https://doi.org/10.1145/304012.304033","url":null,"abstract":"In many industrial design modeling scenarios the designer wishes to edit small feature lines-such as variable width and height creases--on otherwise smooth surface patches. When the path of such a feature does not align with an iso-parameter line or crosses patch boundaries it becomes increasingly difficult to maintain good editing semantics of the underlying surface. In this paper we describe \u0000an algorithm and implementation allowing the interactive \u0000creation and manipulation of fine scale feature curves on subdivision surfaces. In particular, our approach addresses the problem of defining the path of such feature curves independent of the location of surface iso-parameter lines and global patch boundaries. The feature lines are modeled as swept displacement curves with variable profiles, providing a rich toolbox of shapes. Furthermore, \u0000the hierarchical editing semantics of subdivision surface based representations carry through to our extended setting, ensuring “good” behavior of the feature lines under coarse scale surface edits.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125224826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}