Computational geometry: an introduction
Computational geometry: an introduction
Generic programming and the STL: using and extending the C++ Standard Template Library
Generic programming and the STL: using and extending the C++ Standard Template Library
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
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th 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
Complete, exact, and efficient computations with cubic curves
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Intersecting quadrics: an efficient and exact implementation
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
Boolean operations on 3D selective Nef complexes: optimized implementation and experiments
Proceedings of the 2005 ACM symposium on Solid and physical modeling
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
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
An exact, complete and efficient computation of arrangements of Bézier curves
Proceedings of the 2007 ACM symposium on Solid and physical modeling
The voronoi diagram of three lines
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm
Journal of Symbolic Computation
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The visual hull of piecewise smooth objects
Computer Vision and Image Understanding
Computing the Voronoi cells of planes, spheres and cylinders in R3
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Exact arrangements on tori and Dupin cyclides
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Using signature sequences to classify intersection curves of two quadrics
Computer Aided Geometric Design
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
Computer Aided Geometric Design
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: 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
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Sweeping and maintaining two-dimensional arrangements on surfaces: a first step
ESA'07 Proceedings of the 15th annual European conference on Algorithms
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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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We present the first exact, complete and efficient implementation that computes for a given set P=p1,...,pn of quadric surfaces the planar map induced by all intersection curves p1∩ pi, 2 ≤ i ≤ n, running on the surface of p1. The vertices in this graph are the singular and x-extreme points of the curves as well as all intersection points of pairs of curves. Two vertices are connected by an edge if the underlying points are connected by a branch of one of the curves. Our work is based on and extends ideas developed in [20] and [9].Our implementation is complete in the sense that it can handle all kind of inputs including all degenerate ones where intersection curves have singularities or pairs of curves intersect with high multiplicity. It is exact in that it always computes the mathematical correct result. It is efficient measured in running times.