Introduction to Solid Modeling
Introduction to Solid Modeling
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
What is a parametric family of solids?
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Solving geometric constraints by homotopy
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Polyhedral perturbations that preserve topological form
Computer Aided Geometric Design
The generic geometric complex (GGC): a modeling scheme for families of decomposed pointsets
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
IEEE Transactions on Visualization and Computer Graphics
Consistent updates in dual representation systems
Proceedings of the fifth ACM symposium on Solid modeling and applications
Models and representations for families of parts
From geometric modeling to shape modeling
Topological framework for part families
Proceedings of the seventh ACM symposium on Solid modeling and applications
A survey of the persistent naming problem
Proceedings of the seventh ACM symposium on Solid modeling and applications
Constrained modifications of non-manifold B-reps
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
A small feature suppression/unsuppression system for preparing B-rep models for analysis
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Geometric modeling and representation based on sweep mathematical morphology
Information Sciences—Informatics and Computer Science: An International Journal
Constructive topological representations
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Solving topological constraints for declarative families of objects
Proceedings of the 2006 ACM symposium on Solid and physical modeling
History based reactive objects for immersive CAD
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Tracking topological changes in feature models
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Solving topological constraints for declarative families of objects
Computer-Aided Design
Maintaining associativity between form feature models
Computer-Aided Design
Tracking topological changes in parametric models
Computer Aided Geometric Design
Solid modelling based on sixth order partial differential equations
Computer-Aided Design
Geometric interoperability via queries
Computer-Aided Design
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One of the major unsolved problems in parametric solid modeling is a robust update (regeneration) of the solid's boundary representation, given a specified change in the solid's parameter values. The fundamental difficulty lies in determining the mapping between boundary representations for solids in the same parametric family. Several heuristic approaches have been proposed for dealing with this problem, but the formal properties of such mappings are not well understood. We propose a formal definition for boundary representation. (BR-)deformation for solids in the same parametric family, based on the assumption of continuity: small changes in solid parameter values should result in small changes in the solid's boundary reprentation, which may include local collapses of cells in the boundary representation. The necessary conditions that must be satisfied by any BR-deforming mappings between boundary representations are powerful enough to identify invalid updates in many (but not all) practical situations, and the algorithms to check them are simple. Our formulation provides a formal criterion for the recently proposed heuristic approaches to “persistent naming,” and explains the difficulties in devising sufficient tests for BR-deformation encountered in practice. Finally our methods are also applicable to more general cellular models of pointsets and should be useful in developing universal standards in parametric modeling.