An exact and efficient approach for computing a cell in an arrangement of quadrics

[1]  A. Tarski A Decision Method for Elementary Algebra and Geometry , 2023 .

[2]  Joseph F. Traub,et al.  On Euclid's Algorithm and the Theory of Subresultants , 1971, JACM.

[3]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[4]  George E. Collins,et al.  Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975, Automata Theory and Formal Languages.

[5]  Joshua Levin,et al.  A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces , 1976, CACM.

[6]  Joshua Z. Levin Mathematical models for determining the intersections of quadric surfaces , 1979 .

[7]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.

[8]  Bruno Buchberger,et al.  Computer algebra symbolic and algebraic computation , 1982, SIGS.

[9]  G. E. Collins,et al.  Real Zeros of Polynomials , 1983 .

[10]  George E. Collins,et al.  Cylindrical Algebraic Decomposition I: The Basic Algorithm , 1984, SIAM J. Comput..

[11]  George E. Collins,et al.  Cylindrical Algebraic Decomposition II: An Adjacency Algorithm for the Plane , 1984, SIAM J. Comput..

[12]  George E. Collins,et al.  An Adjacency Algorithm for Cylindrical Algebraic Decompositions of Three-Dimensional Space , 1985, J. Symb. Comput..

[13]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[14]  Stefan Arnborg,et al.  Algebraic decomposition of regular curves , 1986, SYMSAC '86.

[15]  David Prill On Approximations and Incidence in Cylindrical Algebraic Decompositions , 1986, SIAM J. Comput..

[16]  James R. Miller,et al.  Geometric approaches to nonplanar quadric surface intersection curves , 1987, TOGS.

[17]  Scott McCallum,et al.  A Polynomial-Time Algorithm for the Topological Type of a Real Algebraic Curve , 1984, J. Symb. Comput..

[18]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[19]  George E. Collins,et al.  An Adjacency Algorithm for Cylindrical Algebraic Decompositions of Three-Dimensional Space , 1988, J. Symb. Comput..

[20]  Chandrajit L. Bajaj,et al.  Computations with Algebraic Curves , 1988, ISSAC.

[21]  Christoph M. Hoffmann,et al.  Geometric and Solid Modeling: An Introduction , 1989 .

[22]  Ketan Mulmuley,et al.  A fast planar partition algorithm, II , 1989, JACM.

[23]  John Hershberger,et al.  Sweeping arrangements of curves , 1989, SCG '89.

[24]  Christoph M. Hoffmann,et al.  Geometric and Solid Modeling , 1989 .

[25]  Rida T. Farouki,et al.  Automatic parsing of degenerate quadric-surface intersections , 1989, TOGS.

[26]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[27]  John K. Johnstone,et al.  On the planar intersection of natural quadrics , 1991, SMA '91.

[28]  T. Sakkalis The topological configuration of a real algebraic curve , 1991, Bulletin of the Australian Mathematical Society.

[29]  Leonidas J. Guibas,et al.  A Singly Exponential Stratification Scheme for Real Semi-Algebraic Varieties and its Applications , 1991, Theor. Comput. Sci..

[30]  Ron Goldman,et al.  Using multivariate resultants to find the intersection of three quadric surfaces , 1991, TOGS.

[31]  Paul Pedersen Multivariate Sturm Theory , 1991, AAECC.

[32]  Ron Goldman,et al.  Combining algebraic rigor with geometric robustness for the detection and calculation of conic sections in the intersection of two natural quadric surfaces , 1991, SMA '91.

[33]  Keith O. Geddes,et al.  Algorithms for computer algebra , 1992 .

[34]  David A. Cox,et al.  Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics) , 2007 .

[35]  Ron Goldman,et al.  Geometric Algorithms for Detecting and Calculating All Conic Sections in the Intersection of Any 2 Natural Quadric Surfaces , 1995, CVGIP Graph. Model. Image Process..

[36]  Kurt Mehlhorn,et al.  LEDA: a platform for combinatorial and geometric computing , 1997, CACM.

[37]  Micha Sharir,et al.  Vertical decomposition of a single cell in a three-dimensional arrangement of surfaces and its applications , 1996, SCG '96.

[38]  John Canny,et al.  A toolkit for algebra and geometry , 1996 .

[39]  H. Hong An efficient method for analyzing the topology of plane real algebraic curves , 1996 .

[40]  Joseph O'Rourke,et al.  Handbook of Discrete and Computational Geometry, Second Edition , 1997 .

[41]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[42]  L. G. Lidia,et al.  A library for computational number theory , 1997 .

[43]  Micha Sharir,et al.  Vertical Decomposition of a Single Cell in a Three-Dimensional Arrangement of Surfaces , 1997, Discret. Comput. Geom..

[44]  David A. Cox,et al.  Ideals, Varieties, and Algorithms , 1997 .

[45]  Frank Nielsen,et al.  An Output-Sensitive Convex Hull Algorithm for Planar Objects , 1995 .

[46]  Joachim von zur Gathen,et al.  Modern Computer Algebra , 1998 .

[47]  Iddo Hanniel,et al.  The Design and Implementation of Planar Maps in CGAL , 1999, WAE.

[48]  Jean-Daniel Boissonnat,et al.  Efficient algorithms for line and curve segment intersection using restricted predicates , 1999, SCG '99.

[49]  Dinesh Manocha,et al.  MAPC: a library for efficient and exact manipulation of algebraic points and curves , 1999, SCG '99.

[50]  Chee-Keng Yap,et al.  A core library for robust numeric and geometric computation , 1999, SCG '99.

[51]  Chee-Keng Yap,et al.  Fundamental problems of algorithmic algebra , 1999 .

[52]  Jean-Daniel Boissonnat,et al.  Robust Plane Sweep for Intersecting Segments , 2000, SIAM J. Comput..

[53]  Dinesh Manocha,et al.  Exact boundary evaluation for curved solids , 2000 .

[54]  Olivier Devillers,et al.  Algebraic methods and arithmetic filtering for exact predicates on circle arcs , 2000, SCG '00.

[55]  Timothy M. Chan Reporting curve segment intersections using restricted predicates , 2000, Comput. Geom..

[56]  Micha Sharir,et al.  Arrangements and Their Applications , 2000, Handbook of Computational Geometry.

[57]  J. Boissonnat,et al.  Efficient algorithms for line and curve segment intersection using restricted predicates , 1999, SCG '99.

[58]  J. Sack,et al.  Handbook of computational geometry , 2000 .

[59]  David Eisenbud,et al.  Resultants and Chow forms via exterior syzygies , 2001, math/0111040.

[60]  Elmar Schömer,et al.  Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually! , 2001, SCG '01.

[61]  M. Hemmer,et al.  The Convex Hull of Ellipsoids (Video) , 2001 .

[62]  Elmar Schömer,et al.  The convex hull of ellipsoids , 2001, SCG '01.

[63]  Dinesh Manocha,et al.  ESOLID---A System for Exact Boundary Evaluation , 2002, SMA '02.

[64]  Kurt Mehlhorn,et al.  A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons , 2002, ESA.

[65]  R. Gregory Taylor,et al.  Modern computer algebra , 2002, SIGA.

[66]  Ron Wein,et al.  High-Level Filtering for Arrangements of Conic Arcs , 2002, ESA.

[67]  Arno Eigenwillig Exact Arrangement Computation for Cubic Curves , 2003 .

[68]  Nicola Wolpert,et al.  Jacobi Curves : Computing the Exact Topology of Arrangements of Non-Singular Algebraic Curves , 2000 .

[69]  Sylvain Lazard,et al.  Near-Optimal Parameterization of the Intersection of Quadrics : III . Parameterizing Singular Intersections , 2005 .

[70]  Ioannis Z. Emiris,et al.  Comparing Real Algebraic Numbers of Small Degree , 2004, ESA.

[71]  Sylvain Lazard,et al.  Intersecting quadrics: an efficient and exact implementation , 2004, SCG '04.

[72]  Sylvain Pion,et al.  Towards and open curved kernel , 2004, SCG '04.

[73]  Elmar Schömer,et al.  Complete, exact, and efficient computations with cubic curves , 2004, SCG '04.

[74]  Dinesh Manocha,et al.  ESOLID - A system for exact boundary evaluation , 2004 .

[75]  E. Berberich,et al.  Exact Arrangements of Quadric Intersection Curves , 2004 .

[76]  Bud Mishra,et al.  Computational Real Algebraic Geometry , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[77]  Bernard Mourrain,et al.  On the computation of an arrangement of quadrics in 3D , 2005, Comput. Geom..

[78]  Chandrajit L. Bajaj,et al.  Convex Hull of Objects Bounded by Algebraic Curves , 2013 .

[79]  Elmar Schömer,et al.  An Exact, Complete and Efficient Implementation for Computing Planar Maps of Quadric Intersection Curves * , 2005 .

[80]  David P. Dobkin,et al.  Computational geometry in a curved world , 1990, Algorithmica.

[81]  Knut Lage Sundet Singular points of algebraic curves , 2018, Geometry of Curves.