Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The Visual Computer: International Journal of Computer Graphics
Isotopic meshing of implicit surfaces
The Visual Computer: International Journal of Computer Graphics
Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization)
Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization)
Topology determination and isolation for implicit plane curves
Proceedings of the 2009 ACM symposium on Applied Computing
Complete numerical isolation of real roots in zero-dimensional triangular systems
Journal of Symbolic Computation
Root isolation for bivariate polynomial systems with local generic position method
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design
Determining the topology of real algebraic surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Homeomorphic approximation of the intersection curve of two rational surfaces
Computer Aided Geometric Design
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A complete method is proposed to compute an ambient isotopic meshing for an implicit algebraic surface with singularities. By ambient isotopic, we mean a meshing with correct topology and any given precision. We use symbolic computation to guarantee the correctness and use numerical computation whenever possible to enhance the efficiency. Nontrivial examples are given to show the effectiveness of the algorithm.