The algebraic eigenvalue problem
The algebraic eigenvalue problem
Geometric tolerancing: 1. Virtual boundary requirements
IBM Journal of Research and Development
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Imperfect form tolerancing on manifold objects: a metric approach
International Journal of Robotics Research
Computing convex hull in a floating point arithmetic
Computational Geometry: Theory and Applications
The NURBS book
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Topological and geometric properties of interval solid models
Graphical Models
Sculptured Surface Shapes using Inner and Outer Bounded Models
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
Heterogeneous material modeling with distance fields
Computer Aided Geometric Design
Epsilon-Regular Sets and Intervals
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Accuracy and semantics in shape-interrogation applications
Graphical Models - Solid modeling theory and applications
Set Membership Classification: A Unified Approach to Geometric Intersection Problems
IEEE Transactions on Computers
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
Trimming for subdivision surfaces
Computer Aided Geometric Design
A New Approach to Point Membership Classification in B-rep Solids
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
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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Two major approaches to defining the semantics of inaccurate boundary representations have been proposed in the literature. They are referred to here as single-set semantics, and class-of-sets semantics, respectively. Our description of the distinction between these two approaches focuses on the nature of the topological regularity on which they are based (classical regularity vs.@e-regularity). It is shown in this note that both approaches may be useful, depending on what information is available. As an illustrative example, an elementary result is given, for a point-membership-classification algorithm, that is sufficiently general to be of practical interest but sufficiently special to be transparent.