Boolean operations of 2-manifolds through vertex neighborhood classification
ACM Transactions on Graphics (TOG)
IEEE Computer Graphics and Applications
Constructive solid geometry for polyhedral objects
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Numerical stability of geometric algorithms
SCG '87 Proceedings of the third annual symposium on Computational geometry
Partitioning Polyhedral Objects into Nonintersecting Parts
IEEE Computer Graphics and Applications
Verifiable implementation of geometric algorithms using finite precision arithmetic
Artificial Intelligence - Special issue on geometric reasoning
Recipes for geometry and numerical analysis - Part I: an empirical study
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Towards implementing robust geometric computations
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A geometric consistency theorem for a symbolic perturbation scheme
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Calculating approximate curve arrangements using rounded arithmetic
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Consistent calculations for solids modeling
SCG '85 Proceedings of the first annual symposium on Computational geometry
A Characterization of Ten Hidden-Surface Algorithms
ACM Computing Surveys (CSUR)
Robust Set Operations on Polyhedral Solids
IEEE Computer Graphics and Applications
Topologically reliable display of algebraic curves
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
A Paradigm for Robust Geometric Algorithms
A Paradigm for Robust Geometric Algorithms
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Error-free boundary evaluation using lazy rational arithmetic: a detailed implementation
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Obtaining robust Boolean set operations for manifold solids by avoiding and eliminating redundancy.
SMA '93 Proceedings on the second 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
Face-based data structure and its application to robust geometric modeling
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Consistent solid and boundary representations from arbitrary polygonal data
Proceedings of the 1997 symposium on Interactive 3D graphics
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
Matchmaker: manifold BReps for non-manifold r-sets
Proceedings of the fifth ACM symposium on Solid modeling and applications
Foundation of a computable solid modeling
Proceedings of the fifth ACM symposium on Solid modeling and applications
Use of topological constraints in construction and processing of robust solid models
Proceedings of the sixth ACM symposium on Solid modeling and applications
ESOLID---A System for Exact Boundary Evaluation
Proceedings of the seventh ACM symposium on Solid modeling and applications
Foundation of a computable solid modelling
Theoretical Computer Science
Removing Zero-Volume Parts from CAD Models for Layered Manufacturing
IEEE Computer Graphics and Applications
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Homotopy Conditions for Tolerant Geometric Queries
Reliable Implementation of Real Number Algorithms: Theory and Practice
ε-Topological formulation of tolerant solid modeling
Computer-Aided Design
Consensus sets for affine transformation uncertainty polytopes
Computers and Graphics
SGP '09 Proceedings of the Symposium on Geometry Processing
Point distance and orthogonal range problems with dependent geometric uncertainties
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Uncertain geometry with dependencies
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Uncertain geometry in computer vision
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Technical note: Uncertain lines and circles with dependencies
Computer-Aided Design
Geometric interoperability via queries
Computer-Aided Design
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A polyhedral solid modeler that operates on boundary representations of objects must infer topological information from numerical data. Unavoidable errors (due to limited precision) affect these calculations so that their use may produce ambiguous or contradictory results. These effects cause existing polyhedral modelers to fail when presented with objects that nearly align or barely intersect[10][7].An object description associating a tolerance with each of its topological features (vertices, edges, and faces) is introduced. The use of tolerances leads to a definition of topological consistency that is readily applied to boundary representations. The implications of using tolerances to aid in making consistent topological determinations from imprecise geometric data are explored and applied to the calculations of a polyhedral solid modeler. The resulting modeler produces a consistent polyhedral boundary when given consistent boundaries as input.