MAPC

MAPC is a C++ library for manipulating algebraically defined points and curves in the plane. MAPC represents points and curves exactly, and makes use of a number of approaches to increase the efficiency of manipulation on these points. MAPC is meant to provide a usable implementation of points and curves in the plane. It is meant to provide a way to represent points and curves without having to worry about the details of how these are implemented underneath. MAPC provides C++ classes for representing and manipulating the following: Multivariate polynomials with floating-point, multiprecision integer, or multiprecision rational coefficients. Algebraic numbers represented as the roots of polynomials within an interval. One and two dimensional points whose coordinates are defined as either algebraic numbers or as rational numbers. Sections of algebraic plane curves. One and two dimensional ”boxes.” MAPC implements 3 new algorithms which provide the following functions: Rapidly finding the sign of a determinant of arbitrary size, with entries that are arbitrary size integers. Isolating all intersections of two algebraic plane curves in a region. Decomposing a plane algebraic curve into monotonic subsections. The current implementation of MAPC is built on top of the LiDIA library, which provides exact rational number support, and makes use of the LAPACK library, which implements various numerical algorithms in floating point.


References in zbMATH (referenced in 22 articles )

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  1. Gao, Ben; Chen, Yufu: Finding the topology of implicitly defined two algebraic plane curves (2012)
  2. Hemmer, Michael; Dupont, Laurent; Petitjean, Sylvain; Schömer, Elmar: A complete, exact and efficient implementation for computing the edge-adjacency graph of an arrangement of quadrics (2011)
  3. de Castro, Pedro M.M.; Cazals, Frédéric; Loriot, Sébastien; Teillaud, Monique: Design of the CGAL 3D spherical kernel and application to arrangements of circles on a sphere (2009)
  4. Wein, Ron; Fogel, Efi; Zukerman, Baruch; Halperin, Dan: Advanced programming techniques applied to CGAL’s arrangement package (2007)
  5. Eigenwillig, Arno; Kettner, Lutz; Schömer, Elmar; Wolpert, Nicola: Exact, efficient, and complete arrangement computation for cubic curves (2006)
  6. Schömer, Elmar; Wolpert, Nicola: An exact and efficient approach for computing a cell in an arrangement of quadrics (2006)
  7. Berberich, Eric; Eigenwillig, Arno; Hemmer, Michael; Hert, Susan; Kettner, Lutz; Mehlhorn, Kurt; Reichel, Joachim; Schmitt, Susanne; Schömer, Elmar; Wolpert, Nicola: EXACUS: Efficient and exact algorithms for curves and surfaces (2005)
  8. Emiris, Ioannis Z.; Tsigaridas, Elias P.: Real solving of bivariate polynomial systems (2005)
  9. Culver, Tim; Keyser, John; Manocha, Dinesh: Exact computation of the medial axis of a polyhedron (2004)
  10. Fogel, Efi; Wein, Ron; Halperin, Dan: Code flexibility and program efficiency by genericity: Improving Cgal’s arrangements (2004)
  11. Kaltofen, Erich; Villard, Gilles: Computing the sign or the value of the determinant of an integer matrix, a complexity survey. (2004)
  12. Morgado, José F.M.; Gomes, Abel J.P.: A derivative-free tracking algorithm for implicit curves with singularities (2004)
  13. Culver, Tim; Keyser, John; Manocha, Dinesh; Krishnan, Shankar: A hybrid approach for determinant signs of moderate-sized matrices. (2003)
  14. Karavelas, Menelaos I.; Emiris, Ioannis Z.: Root comparison techniques applied to computing the additively weighted Voronoi diagram (2003)
  15. Wolpert, Nicola: Jacobi curves: computing the exact topology of arrangements of non-singular algebraic curves (2003)
  16. Berberich, Eric; Eigenwillig, Arno; Hemmer, Michael; Hert, Susan; Mehlhorn, Kurt; Schömer, Elmar: A computational basis for conic arcs and boolean operations on conic polygons (2002)
  17. Wein, Ron: High-level filtering for arrangements of conic arcs (Extended abstract) (2002)
  18. Krishnan, S.; Manocha, D.; Gopi, M.; Culver, T.; Keyser, J.: Boole: a boundary evaluation system for Boolean combinations of sculptured solids (2001)
  19. Flato, Eyal; Halperin, Dan; Hanniel, Iddo; Nechushtan, Oren; Ezra, Eti: The design and implementation of planar maps in CGAL (2000)
  20. Keyser, J.; Culver, T.; Manocha, D.; Krishnan, S.: Efficient and exact manipulation of algebraic points and curves (2000)

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