Design of the CGAL 3D spherical kernel and application to arrangements of circles on a sphere

DOI10.1016/j.comgeo.2008.10.003zbMath1169.65021OpenAlexW2083598506MaRDI QIDQ924069

Monique Teillaud, Sébastien Loriot, Frédéric Cazals, Pedro Machado Manhães de Castro

Publication date: 27 July 2009

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.comgeo.2008.10.003

zbMATH Keywords

algorithmsnumerical examplerobustnessspheresconstructionscircular arcsgeneric programmingcurved objectspredicatesCGAL kernelgeometric kernels

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items

Arrangements on parametric surfaces. I: General framework and infrastructure ⋮ Arrangements on parametric surfaces. II: Concretizations and applications ⋮ Computing the arrangement of circles on a sphere, with applications in structural biology ⋮ 3D spherical kernel

Uses Software

• CGAL
• LOOK
• MAPC
• Qsplat
• 2D Arrangement
• Powercrust

Cites Work

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• Collision detection for deforming necklaces
• On the computation of an arrangement of quadrics in 3D
• Computing the arrangement of circles on a sphere, with applications in structural biology
• Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs
• Computing the volume of the union of spheres
• Recent progress in exact geometric computation
• An adaptable and extensible geometry kernel
• Classroom examples of robustness problems in geometric computations
• Algorithms for Reporting and Counting Geometric Intersections
• Sweeping and Maintaining Two-Dimensional Arrangements on Surfaces: A First Step
• Computational and Structural Advantages of Circular Boundary Representation
• Comments on “algorithms for reporting and counting geometric intersections”
• EXACT ALGORITHMS FOR CIRCLES ON THE SPHERE
• The computational geometry algorithms library CGAL
• Look — a Lazy Object-Oriented Kernel for geometric computation
• Towards and open curved kernel
• Dynamic maintenance of molecular surfaces under conformational changes
• An exact, complete and efficient implementation for computing planar maps of quadric intersection curves
• The power crust, unions of balls, and the medial axis transform