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Modular functions --- Polyhedral functions --- Group theory --- Substitutions, Linear
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Lattice theory --- Polyhedral functions --- Convex sets --- Number Theory
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Filters (Mathematics) --- Ideals (Algebra) --- Polyhedral functions --- Rings (Algebra)
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An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.
Geometry -- Data processing -- Congresses. --- Geometry, Algebraic -- Congresses. --- Polyhedral functions -- Congresses. --- Geometry --- Geometry, Algebraic --- Polyhedral functions --- Mathematics --- Physical Sciences & Mathematics --- Data processing --- Nonlinear programming --- Numerical analysis --- Mathematics. --- Algebraic geometry. --- Algebra. --- Computer mathematics. --- Geometry. --- Algebraic Geometry. --- Computational Mathematics and Numerical Analysis. --- General Algebraic Systems. --- Programming (Mathematics) --- Geometry, algebraic. --- Computer science --- Mathematical analysis --- Euclid's Elements --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algebraic geometry --- Computational geometry --- Nonlinear geometry
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Polyhedral functions. --- Discretization (Mathematics) --- Earth sciences --- Mathematics. --- Geosciences --- Environmental sciences --- Physical sciences --- Differential equations --- Functions, Polyhedral --- Modular functions --- Numerical solutions --- Ciències de la Terra --- Matemàtica --- Matemàtiques (Ciència) --- Ciència --- Alfabetisme matemàtic --- Àlgebra --- Anàlisi matemàtica --- Aritmètica --- Axiomes --- Biomatemàtica --- Congruències (Geometria) --- Congruències i residus --- Constants matemàtiques --- Descomposició (Matemàtica) --- Dinàmica --- Estadística --- Factorització (Matemàtica) --- Filtres (Matemàtica) --- Formes (Matemàtica) --- Formes normals (Matemàtica) --- Geometria --- Geografia matemàtica --- Inducció (Matemàtica) --- Infinit --- Lògica matemàtica --- Matemàtica aplicada --- Matemàtica japonesa --- Màxims i mínims --- Nombres --- Quarta dimensió --- Successions (Matemàtica) --- Teoria de conjunts --- Teoria de l'índex (Matemàtica) --- Teoria de la computació --- Variables (Matemàtica) --- Didàctica de la matemàtica --- Ensenyament de la matemàtica --- Història de la matemàtica --- Matemàtics --- Geociències --- Ciències ambientals --- Ciències del mar --- Edafologia --- Geobiologia --- Geofísica --- Geografia --- Geologia --- Geomàtica --- Geoquímica --- Hidrologia --- Meteorologia --- Ciències naturals
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