Computational geometry: an introduction
Computational geometry: an introduction
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th 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
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
Handbook of discrete and computational geometry
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Complete, exact, and efficient computations with cubic curves
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
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
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
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization)
Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization)
Complete subdivision algorithms, II: isotopic meshing of singular algebraic curves
Proceedings of the twenty-first 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
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
Certified computation of planar morse-smale complexes
Proceedings of the twenty-eighth annual symposium on Computational geometry
| Hi-index | 0.00 |
We consider domain subdivision algorithms for computing isotopic approximations of nonsingular curves represented implicitly by an equation f(X,Y)=0. Two algorithms in this area are from Snyder (1992) and Plantinga & Vegter (2004). We introduce a new algorithm that combines the advantages of these two algorithms: like Snyder, we use the parametrizability criterion for subdivision, and like Plantinga & Vegter we exploit non-local isotopy. We further extend our algorithm in two important and practical directions: first, we allow subdivision cells to be rectangles with arbitrary but bounded aspect ratios. Second, we extend the input domains to be regions R0 with arbitrary geometry and which might not be simply connected. Our algorithm halts as long as the curve has no singularities in the region, and intersects the boundary of R0 transversally. Our algorithm is also easy to implement exactly. We report on very encouraging preliminary experimental results, showing that our algorithms can be much more efficient than both Plantinga & Vegter's and Snyder's algorithms.