polygon mesh processing

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Polygon Mesh Processing

Author : Mario Botsch
ISBN : 9781568814261
Genre : Computers
File Size : 84. 93 MB
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Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.

Polygon Mesh Processing

Author : Mario Botsch
ISBN : 9781439865316
Genre : Computers
File Size : 38. 72 MB
Format : PDF, ePub
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Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.

Delaunay Mesh Generation

Author : Siu-Wing Cheng
ISBN : 9781584887317
Genre : Computers
File Size : 62. 66 MB
Format : PDF
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Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why these meshing algorithms work. The book is one of the first to integrate a vast amount of cutting-edge material on Delaunay triangulations. It begins with introducing the problem of mesh generation and describing algorithms for constructing Delaunay triangulations. The authors then present algorithms for generating high-quality meshes in polygonal and polyhedral domains. They also illustrate how to use restricted Delaunay triangulations to extend the algorithms to surfaces with ridges and patches and volumes with smooth surfaces. For researchers and graduate students, the book offers a rigorous theoretical analysis of mesh generation methods. It provides the necessary mathematical foundations and core theoretical results upon which researchers can build even better algorithms in the future. For engineers, the book shows how the algorithms work well in practice. It explains how to effectively implement them in the design and programming of mesh generation software.

Isosurfaces

Author : Rephael Wenger
ISBN : 9781466571020
Genre : Computers
File Size : 54. 20 MB
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Ever since Lorensen and Cline published their paper on the Marching Cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data. Yet there is no book exclusively devoted to isosurfaces. Isosurfaces: Geometry, Topology, and Algorithms represents the first book to focus on basic algorithms for isosurface construction. It also gives a rigorous mathematical perspective on some of the algorithms and results. In color throughout, the book covers the Marching Cubes algorithm and variants, dual contouring algorithms, multilinear interpolation, multiresolution isosurface extraction, isosurfaces in four dimensions, interval volumes, and contour trees. It also describes data structures for faster isosurface extraction as well as methods for selecting significant isovalues. For designers of visualization software, the book presents an organized overview of the various algorithms associated with isosurfaces. For graduate students, it provides a solid introduction to research in this area. For visualization researchers, the book serves as a reference to the vast literature on isosurfaces.

Computational Geometry

Author : Mark de Berg
ISBN : 9783540779735
Genre : Computers
File Size : 26. 61 MB
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This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Geometry And Topology For Mesh Generation

Author : Herbert Edelsbrunner
ISBN : 0521793092
Genre : Mathematics
File Size : 28. 92 MB
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The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The original motivation for these topics was the difficulty faced (both conceptually and in the technical execution) in any attempt to combine elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains recent breakthrough solutions to meshing that fit into this category.The book should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, useful, and interesting.

Foundations Of Multidimensional And Metric Data Structures

Author : Hanan Samet
ISBN : 0123694469
Genre : Computers
File Size : 73. 24 MB
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Samet offers a thorough treatment of multidimensional point data, object and image-based representations, intervals and small rectangles, and high-dimensional datasets. This work includes a thorough introduction; a comprehensive survey to spatial and multidimensional data structures and algorithms; and implementation details for the most useful data structures.

A Sampler Of Useful Computational Tools For Applied Geometry Computer Graphics And Image Processing

Author : Daniel Cohen-Or
ISBN : 9781498706308
Genre : Computers
File Size : 83. 65 MB
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A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing shows how to use a collection of mathematical techniques to solve important problems in applied mathematics and computer science areas. The book discusses fundamental tools in analytical geometry and linear algebra. It covers a wide range of topics, from matrix decomposition to curvature analysis and principal component analysis to dimensionality reduction. Written by a team of highly respected professors, the book can be used in a one-semester, intermediate-level course in computer science. It takes a practical problem-solving approach, avoiding detailed proofs and analysis. Suitable for readers without a deep academic background in mathematics, the text explains how to solve non-trivial geometric problems. It quickly gets readers up to speed on a variety of tools employed in visual computing and applied geometry.

Discrete And Computational Geometry

Author : Satyan L. Devadoss
ISBN : 1400838983
Genre : Mathematics
File Size : 69. 66 MB
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Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only). To obtain access, please e-mail: [email protected]

Generalized Barycentric Coordinates In Computer Graphics And Computational Mechanics

Author : Kai Hormann
ISBN : 9781498763615
Genre : Computers
File Size : 64. 1 MB
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In Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics, eminent computer graphics and computational mechanics researchers provide a state-of-the-art overview of generalized barycentric coordinates. Commonly used in cutting-edge applications such as mesh parametrization, image warping, mesh deformation, and finite as well as boundary element methods, the theory of barycentric coordinates is also fundamental for use in animation and in simulating the deformation of solid continua. Generalized Barycentric Coordinates is divided into three sections, with five chapters each, covering the theoretical background, as well as their use in computer graphics and computational mechanics. A vivid 16-page insert illustrates the stunning applications of this fascinating research area.

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