Modeling spaces for toleranced objects
International Journal of Robotics Research
Imperfect form tolerancing on manifold objects: a metric approach
International Journal of Robotics Research
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Polyhedral perturbations that preserve topological form
Computer Aided Geometric Design
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Towards robust interval solid modeling of curved objects
Towards robust interval solid modeling of curved objects
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Approximating curves via alpha shapes
CVGIP: Graphical Models and Image Processing
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Topological and geometric properties of interval solid models
Graphical Models
Computational topology: ambient isotopic approximation of 2-manifolds
Theoretical Computer Science - Topology in computer science
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
A condition for isotopic approximation
Graphical Models - Solid modeling theory and applications
A condition for isotopic approximation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Computational topology for isotopic surface reconstruction
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
Modeling time and topology for animation and visualization with examples on parametric geometry
Theoretical Computer Science
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Given a nonsingular compact 2-manifold F without boundary, we present methods for establishing a family of surfaces which can approximate F so that each approximant is ambient isotopic to F. The current state of the art in surface reconstruction is that both theory and practice are limited to generating a piecewise linear (PL) approximation. The methods presented here offer broader theoretical guidance for a rich class of ambient isotopic approximations. They are also used to establish sufficient conditions for an interval solid to be ambient isotopic to the solid it is approximating.The methods are based on global theoretical considerations and are compared to existing local methods. Practical implications of these methods are also presented. For the global case, a differential surface analysis is performed to find a positive number ρ so that the offsets Fo(± ρ) of F at distances ± ρ are nonsingular. In doing so, a normal tubular neighborhood, F(ρ), of F is constructed. Then, each approximant of F lies inside F(ρ). Comparisons between these global and local constraints are given.