Offsetting operations in solid modelling
Computer Aided Geometric Design
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
On the representation and manipulation of rigid solids
On the representation and manipulation of rigid solids
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Modeling spaces for toleranced objects
International Journal of Robotics Research
Filling gaps in the boundary of a polyhedron
Computer Aided Geometric Design
Polyhedral modelling with exact arithmetic
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Boundary representation modelling with local tolerances
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Handbook of logic in computer science (vol. 3)
Consistent solid and boundary representations from arbitrary polygonal data
Proceedings of the 1997 symposium on Interactive 3D graphics
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic
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)
Computable analysis: an introduction
Computable analysis: an introduction
Analysis of boundary representation model rectification
Proceedings of the sixth ACM symposium on Solid modeling and applications
Topological and geometric properties of interval solid models
Graphical Models
RSVP: A Geometric Toolkit for Controlled Repair of Solid Models
IEEE Transactions on Visualization and Computer Graphics
Generating Topological Structures for Surface Models
IEEE Computer Graphics and Applications
A topology-based approach for shell-closure
Selected and Expanded Papers from the IFIP TC5/WG5.2 Working Conference on Geometric Modeling for Product Realization
A Paradigm for Robust Geometric Algorithms
A Paradigm for Robust Geometric Algorithms
Epsilon-Regular Sets and Intervals
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Set Membership Classification: A Unified Approach to Geometric Intersection Problems
IEEE Transactions on Computers
Homotopy Conditions for Tolerant Geometric Queries
Reliable Implementation of Real Number Algorithms: Theory and Practice
On the long-term retention of geometry-centric digital engineering artifacts
Computer-Aided Design
Geometric interoperability via queries
Computer-Aided Design
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Classical theory of solid modeling relies on the notion of regular sets and presupposes exactness in both geometric data and algorithms. In contrast, modeling, exchange and translation of geometric models in engineering applications usually involve data approximations and algorithms with different numerical precisions. We argue that an appropriate formulation of these geometric modeling problems require finite size neighborhoods, leading to the notion of @e-topological operations. These operations are then used to formulate the definitions of @e-regularity and @e-solid that extend and subsume the corresponding classical concepts as exact special cases. Furthermore, the proposed theory suggests how the classical solid modeling paradigm should be extended in order to deal with the outstanding problems in geometric robustness, validation, and data translation. In particular, it explains why the current methods for validating boundary representaetions are not always sufficient and demonstrates that widely adapted geometric repairs are often unnecessary for maintaining solidity in the presence of numerical inaccuracies.