Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Polygonization of implicit surfaces
Computer Aided Geometric Design
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Contour generators of evolving implicit surfaces
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Isotopic implicit surface meshing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
An effective condition for sampling surfaces with guarantees
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Complete subdivision algorithms, I: intersection of Bezier curves
Proceedings of the twenty-second annual symposium on Computational geometry
Meshing skin surfaces with certified topology
Computational Geometry: Theory and Applications
Learning smooth shapes by probing
Computational Geometry: Theory and Applications
Reliable implicit surface polygonization using visibility mapping
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Provably good moving least squares
ACM Transactions on Algorithms (TALG)
Complete subdivision algorithms, II: isotopic meshing of singular algebraic curves
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Topology and arrangement computation of semi-algebraic planar curves
Computer Aided Geometric Design
Proceedings of the twenty-fifth annual symposium on Computational geometry
Exact numerical computation in algebra and geometry
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Computer Aided Geometric Design
The design of core 2: a library for exact numeric computation in geometry and algebra
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves
Journal of Symbolic Computation
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
Journal of Symbolic Computation
Arrangement computation for planar algebraic curves
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Empirical study of an evaluation-based subdivision algorithm for complex root isolation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Non-local isotopic approximation of nonsingular surfaces
Computer-Aided Design
Near optimal tree size bounds on a simple real root isolation algorithm
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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Implicit surfaces are defined as the zero set of a function F: R3 ← R. Although several algorithms exist for generating piecewise linear approximations, most of them are based on a user-defined stepsize or bounds to indicate the precision, and therefore cannot guarantee topological correctness. Interval arithmetic provides a mechanism to determine global properties of the implicit function. In this paper we present an algorithm that uses these properties to generate a piecewise linear approximation of implicit curves and surfaces, that is isotopic to the curve or surface itself. The algorithm is simple and fast, and is among the first to guarantee isotopy for implicit surface meshing.