Topics in algebraic geometry and geometric modeling : Workshop on Algebraic Geometry and Geometric Modeling, July 29-August 2, 2002, Vilnius University, Vilnius, Lithuania
著者
書誌事項
Topics in algebraic geometry and geometric modeling : Workshop on Algebraic Geometry and Geometric Modeling, July 29-August 2, 2002, Vilnius University, Vilnius, Lithuania
（Contemporary mathematics, 334）
American Mathematical Society, c2003
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture.The NSF sponsored the four-day 'Vilnius Workshop on Algebraic Geometry and Geometric Modeling', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, 'On the determination of the degree of an equation obtained by elimination', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.
目次
Modeling Curves and Surfaces: Polar forms in geometric modeling and algebraic geometry by R. Goldman Interference analysis of conics and quadrics by W. Wang and R. Krasauskas Geometrically continuous octahedron by R. Vidunas Multisided Patches: Smoothness, fairness and the need for better multi-sided patches by J. Peters Toric Bezier patches with depth by R. Krasauskas and R. Goldman On the uniqueness of barycentric coordinates by J. Warren Rational $M$-patches and tensor-border patches by K. Karciauskas Implicitization and Parametrization: Curves, surfaces, and syzygies by D. Cox Implicitizing rational surfaces with base points using the method of moving surfaces by J. Zheng, T. W. Sederberg, E.-W. Chionh, and D. A. Cox Overview of approximate implicitization by T. Dokken and J. B. Thomassen Algorithms for rational surfaces by J. Schicho Toric Varieties: What is a toric variety? by D. Cox Toric ideals, real toric varieties, and the moment map by F. Sottile Universal rational parametrizations and toric varieties by D. Cox, R. Krasauskas, and M. Mustata Real structures on smooth compact toric surfaces by C. Delaunay Mixed Volume and Resultants: Why polyhedra matter in non-linear equation solving by J. M. Rojas Using projection operators in computer aided geometric design by L. Buse, M. Elkadi, and B. Mourrain On combinatorial coefficients and the Gelfond-Khovanskii residue formula by I. Soprounov On the determination of the degree of an equation obtained by elimination by F. Minding Index.
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