Ebook: Nonlinear Computational Geometry
- Tags: Algebraic Geometry, Computational Mathematics and Numerical Analysis, Geometry, General Algebraic Systems
- Series: The IMA Volumes in Mathematics and its Applications 151
- Year: 2010
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages 1-8
Spectral Techniques to Explore Point Clouds in Euclidean Space, with Applications to Collective Coordinates in Structural Biology....Pages 1-34
Rational Parametrizations, Intersection Theory, and Newton Polytopes....Pages 35-50
Some Discrete Properties of the Space of Line Transversals to Disjoint Balls....Pages 51-83
Algebraic Geometry and Kinematics....Pages 85-107
Rational Offset Surfaces and their Modeling Applications....Pages 109-135
A List of Challenges for Real Algebraic Plane Curve Visualization Software....Pages 137-164
A Subdivision Method for Arrangement Computation of Semi-Algebraic Curves....Pages 165-187
Invariant-Based Characterization of the Relative Position of Two Projective Conics....Pages 189-220
A Note on Planar Hexagonal Meshes....Pages 221-233
List of Workshop Participants....Pages 235-239
Back Matter....Pages 1-5
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.
Content:
Front Matter....Pages 1-8
Spectral Techniques to Explore Point Clouds in Euclidean Space, with Applications to Collective Coordinates in Structural Biology....Pages 1-34
Rational Parametrizations, Intersection Theory, and Newton Polytopes....Pages 35-50
Some Discrete Properties of the Space of Line Transversals to Disjoint Balls....Pages 51-83
Algebraic Geometry and Kinematics....Pages 85-107
Rational Offset Surfaces and their Modeling Applications....Pages 109-135
A List of Challenges for Real Algebraic Plane Curve Visualization Software....Pages 137-164
A Subdivision Method for Arrangement Computation of Semi-Algebraic Curves....Pages 165-187
Invariant-Based Characterization of the Relative Position of Two Projective Conics....Pages 189-220
A Note on Planar Hexagonal Meshes....Pages 221-233
List of Workshop Participants....Pages 235-239
Back Matter....Pages 1-5
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