Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
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
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
On the exact computation of the topology of real algebraic curves
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
An exact and efficient approach for computing a cell in an arrangement of quadrics
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Complete subdivision algorithms, I: intersection of Bezier curves
Proceedings of the twenty-second annual symposium on Computational geometry
Provably good sampling and meshing of Lipschitz surfaces
Proceedings of the twenty-second annual symposium on Computational geometry
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Complete numerical isolation of real zeros in zero-dimensional triangular systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Proceedings of the twenty-fifth annual symposium on Computational geometry
On the topology of planar algebraic curves
Proceedings of the twenty-fifth annual symposium on Computational geometry
Lower bounds for zero-dimensional projections
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
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
The DMM bound: multivariate (aggregate) separation bounds
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
A worst-case bound for topology computation of algebraic curves
Journal of Symbolic Computation
Arrangement computation for planar algebraic curves
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Non-local isotopic approximation of nonsingular surfaces
Computer-Aided Design
Journal of Symbolic Computation
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Given a real function f(X,Y), a box region B and ε0, we want to compute an ε-isotopic polygonal approximation to the curve C: f(X,Y)=0 within B. We focus on subdivision algorithms because of their adaptive complexity. Plantinga & Vegter (2004) gave a numerical subdivision algorithm that is exact when the curve C is non-singular. They used a computational model that relies only on function evaluation and interval arithmetic. We generalize their algorithm to any (possibly non-simply connected) region B that does not contain singularities of C. With this generalization as subroutine, we provide a method to detect isolated algebraic singularities and their branching degree. This appears to be the first complete numerical method to treat implicit algebraic curves with isolated singularities.