Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
A fast planar partition algorithm, I
Journal of Symbolic Computation
An implementation for maintaining arrangements of polygons
Proceedings of the eleventh annual symposium on Computational geometry
Static analysis yields efficient exact integer arithmetic for computational geometry
ACM Transactions on Graphics (TOG)
Interval arithmetic yields efficient dynamic filters for computational geometry
Proceedings of the fourteenth annual symposium on Computational geometry
Handbook of discrete and computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
MAPC: a library for efficient and exact manipulation of algebraic points and curves
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Look — a Lazy Object-Oriented Kernel for geometric computation
Proceedings of the sixteenth annual symposium on Computational geometry
A new constructive root bound for algebraic expressions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Polygon decomposition for efficient construction of Minkowski sums
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
On-Line Zone Construction in Arrangements of Lines in the Plane
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
A Separation Bound for Real Algebraic Expressions
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Controlled perturbation for arrangements of circles
Proceedings of the nineteenth annual symposium on Computational geometry
Continuous path verification in multi-axis NC-machining
SCG '04 Proceedings of the twentieth annual symposium on Computational 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
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The visibility--voronoi complex and its applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The predicates of the Apollonius diagram: algorithmic analysis and implementation
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
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
An approximate arrangement algorithm for semi-algebraic curves
Proceedings of the twenty-second annual symposium on Computational geometry
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
The visibility-Voronoi complex and its applications
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Exact and approximate construction of offset polygons
Computer-Aided Design
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improving the topology computation of an arrangement of cubics
Computational Geometry: Theory and Applications
The predicates of the Apollonius diagram: Algorithmic analysis and implementation
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
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
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
Precise global collision detection in multi-axis NC-machining
Computer-Aided Design
Computing the topology of an arrangement of quartics
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Exact geometric and algebraic computations in CGAL
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Journal of Symbolic Computation
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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Many computational geometry algorithms involve the construction and maintenance of planar arrangements of conic arcs. Implementing a general, robust arrangement package for conic arcs handles most practical cases of planar arrangements covered in literature. A possible approach for implementing robust geometric algorithms is to use exact algebraic number types -- yet this may lead to a very slow, inefficient program. In this paper we suggest a simple technique for filtering the computations involved in the arrangement construction: when constructing an arrangement vertex, we keep track of the steps that lead to its construction and the equations we need to solve to obtain its coordinates. This construction history can be used for answering predicates very efficiently, compared to a na茂ve implementation with an exact number type. Furthermore, using this representation most arrangement vertices may be computed approximately at first and can be refined later on in cases of ambiguity. Since such cases are relatively rare, the resulting implementation is both efficient and robust.