MAPC: a library for efficient and exact manipulation of algebraic points and curves
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Look — a Lazy Object-Oriented Kernel for geometric computation
Proceedings of the sixteenth annual symposium on Computational geometry
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A new constructive root bound for algebraic expressions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Dynamic maintenance of molecular surfaces under conformational changes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
An adaptable and extensible geometry kernel
Computational Geometry: Theory and Applications
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs
Computational Geometry: Theory and Applications
Computing the arrangement of circles on a sphere, with applications in structural biology
Computational Geometry: Theory and Applications
Sweeping and maintaining two-dimensional arrangements on surfaces: a first step
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Comments on "algorithms for reporting and counting geometric intersections"
IEEE Transactions on Computers
Computational and structural advantages of circular boundary representation
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Computing the arrangement of circles on a sphere, with applications in structural biology
Computational Geometry: Theory and Applications
Exact geometric and algebraic computations in CGAL
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
PRIB'11 Proceedings of the 6th IAPR international conference on Pattern recognition in bioinformatics
Robust and efficient delaunay triangulations of points on or close to a sphere
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
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This paper presents a cgal kernel for algorithms manipulating 3D spheres, circles, and circular arcs. The paper makes three contributions. First, the mathematics underlying two non-trivial predicates are presented. Second, the design of the kernel concept is developed, and the connexion between the mathematics and this design is established. In particular, we show how two different frameworks can be combined: one for the general setting, and one dedicated to the case where all the objects handled lie on a reference sphere. Finally, an assessment about the efficacy of the 3D Spherical Kernel is made through the calculation of the exact arrangement of circles on a sphere. On average while computing arrangements with few degeneracies (on sample molecular models), it is shown that certifying the result incurs a modest factor of two with respect to calculations using a plain double arithmetic.