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Nonmanifold Modeling: An Approach Based on Spatial Subdivision
, 1997
"... This paper deals with the problem of creating and maintaining a spatial ..."
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Cited by 22 (7 self)
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This paper deals with the problem of creating and maintaining a spatial
Maintenance Of Geometric Representations Through Space Decompositions
, 1997
"... The ability to transform between distinct geometric representations is the key to success of multiple-representation modeling systems. But the existing theory of geometric modeling does not directly address or support construction, conversion, and comparison of geometric representations. A study of ..."
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Cited by 11 (5 self)
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The ability to transform between distinct geometric representations is the key to success of multiple-representation modeling systems. But the existing theory of geometric modeling does not directly address or support construction, conversion, and comparison of geometric representations. A study of classical problems of CSG $ b-rep conversions, CSG optimization, and other representation conversions suggests a natural relationship between a representation scheme and an appropriate decomposition of space. We show that a hierarchy of space decompositions corresponding to different representation schemes can be used to enhance the theory and to develop a systematic approach to maintenance of geometric representations. 1. Motivation 1.1. Modern theory of representations The modern field of solid modeling owes much of its success to the theoretical foundations laid by members of the Production Automation Project at the University of Rochester in the 1970's. The history of these development...
Recognition of volumetric features from CAD models: Problem formalization and algorithms
, 1993
"... Automated recognition of features from CAD models has been attempted for a wide range of application domains in mechanical engineering. However, the absence of a clear mathematical formalism for the problem has made it di cult to develop a general approach|and thus most of these methods are limited ..."
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Cited by 9 (7 self)
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Automated recognition of features from CAD models has been attempted for a wide range of application domains in mechanical engineering. However, the absence of a clear mathematical formalism for the problem has made it di cult to develop a general approach|and thus most of these methods are limited in scope. In this paper, we develop a formalization of the problem of recognizing a class of machinable features expressed as MRSEVs (a PDES/STEP library of machining features) [19], and an algorithm for solving this problem. Some of the characteristics of this approach are: the algorithm handles a large variety ofholeandpocket features features along with elementary accessibility constraints and blends for those features� it is provably complete, even if the features intersect with each other in arbitrarily complex ways� it has O(n 4)worst-case time complexity. 1
Space decompositions: Theory and practice
- Instituto de Matemática Pura e Aplicada, Rio de Janeiro (RJ
, 1992
"... ..."
Recognition of Volumetric Features from CAD Models: Problem Formalization and Algorithms
"... Automated recognition of features from CAD models has been attempted for a wide range of application domains in mechanical engineering. However, the absence of a clear mathematical formalism for the problem has made it dicult to develop a general approach|and thus most of these methods are limited i ..."
Abstract
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Automated recognition of features from CAD models has been attempted for a wide range of application domains in mechanical engineering. However, the absence of a clear mathematical formalism for the problem has made it dicult to develop a general approach|and thus most of these methods are limited in scope. In this paper, we develop a formalization of the problem of recognizing a class of machinable features expressed as MRSEVs (a PDES/STEP library of machining features) [19], and an algorithm for solving this problem. Some of the characteristics of this approach are: the algorithm handles a large variety of hole and pocket features features along with elementary accessibility constraints and blends for those features; it is provably complete, even if the features intersect with each other in arbitrarily complex ways; it has O(n 4) worst-case time complexity. 1
Nonmanifold Modeling: An Approach Based on Spatial Subdivision
"... This paper deals with the problem of creating and maintaining a spa-tial subdivision, defined by a set of surface patches. The main goal is to create a set of functions which provides a layer of abstraction capable of hiding the geometric and topological problems which occur when one cre-ates and ma ..."
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This paper deals with the problem of creating and maintaining a spa-tial subdivision, defined by a set of surface patches. The main goal is to create a set of functions which provides a layer of abstraction capable of hiding the geometric and topological problems which occur when one cre-ates and manipulates spatial subdivisions. The study of arbitrary spatial subdivisions extends and unifies the techniques used in nonmanifold solid modeling and allows the modeling of heterogeneous objects.
