الصفحة 1
الصفحة 1
Writing mental ray shaders : A Perceptual Introduction
The word "render" isn't unique to the vocabulary of computer graphics. We can talk about a "watercolor rendering," a "musical rendering" or a "poetic rendering." In each of these, there is a transformation from one domain to another: from the landscape before the painter to color on paper, from musical notation to sound, from the associations in a poet's mind to a book of poetry. But the type of rendering that may come closest to what we mean when we talk about rendering in computer graphics is in architecture. Geometric blueprints and technical specifications of building materials are transformed in the architectural rendering into a picture of the building 1 Introduction as it will appear when construction is complete. In addition to the designs of the building's geometry and its visual characteristics, the artist chooses a point of view to depict the scene in perspective. This is a transformation of a description of imagined space into a picture of that space.
Worlds Out of Nothing : A Course in the History of Geometry in the 19th Century
Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How - if at all - was it appreciated? What new questions did it generate?
WALCOM: Algorithms and Computation ; 2nd International Workshop, WALCOM 2008, Dhaka, Bangladesh, February 7-8, 2008. Proceedings
This book features original research in the areas of algorithms and data structures, combinatorial algorithms, graph drawings and graph algorithms, parallel and distributed algorithms, string algorithms, computational geometry, graphs in bioinformatics and computational biology. The book is organized in topical sections on bioinformatics algorithms, computational geometry and graph drawing, graph algorithms, and algorithm engineering.
Visualization, Explanation and Reasoning Styles in Mathematics
Contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc.
Visualization and Processing of Tensor Fields
This book is the first edited volume that presents the state-of-the-art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before.
Vector Analysis for Computer Graphics
Divided into eleven chapters covering the history of vector analysis, linear equations, vector algebra, vector products, differentiating vector-valued functions, vector differential operators, tangent and normal vectors, straight lines, planes, intersections and rotating vectors.
Variational, geometric, and level set methods in computer vision ; 3rd International Workshop, VLSM 2005, Beijing, China, October 16, 2005, Proceedings
Mathematical methods has been a dominant research path in computational vision leading to a number of areas like ?ltering, segmentation, motion analysis and stereo reconstruction.
Variation et optimisation de formes : Une analyse géométrique = Variation and optimization of shapes : A geometric analysis
An introduction to modern approaches to the mathematical optimization of shapes. It is based solely on first-year Master's level mathematics knowledge, but already allows readers to address open questions in this rapidly evolving field. It develops the methodology as well as the mathematical analysis and geometric tools necessary for studying domain variations. It includes a systematic study of geometric questions associated with the Laplace operator, classical capacity, and differentiation with respect to a shape, as well as a FAQ on common topologies of domains and on the geometric properties of optimal shapes, including what happens when they do not exist, all accompanied by a substantial bibliography.
Variable-length Codes for Data Compression
Most data compression methods that are based on variable-length codes employ the Huffman or Golomb codes. However, there are a large number of less-known codes that have useful properties and these can be useful. This book brings this large set of codes to the attention of workers in the field and for students of computer science.
Vanishing and Finiteness Results in Geometric Analysis : A Generalization of the Bochner Technique
This book presents very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods from spectral theory and qualitative properties of solutions of PDEs to comparison theorems in Riemannian geometry and potential theory.
Using the Borsuk-Ulam Theorem : Lectures on Topological Methods in Combinatorics and Geometry
Matousek's lively little textbook now shows that Lovász' insight as well as beautiful work of many others (such as Vrecica and Zivaljevic, and Sarkaria) have opened up an exciting area of mathematics that connects combinatorics, graph theory, algebraic topology and discrete geometry.
Using Algebraic Geometry
In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gröbner bases and resultants.
Universal Algebra
Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science.
Unitals in Projective Planes
This clearly written text is the first book on unitals embedded in finite projective planes. Unitals are key structures in square order projective planes, and have connections with other structures in algebra. They provide a link between groups and geometries. There is a considerable number of research articles concerning unitals, and there also exist many open problems. This book is a thorough survey of the research literature on embedded unitals which collects this material in book form for the first time.
Two Algebraic Byways from Differential Equations : Gröbner Bases and Quivers
Presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types.Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line.
Tropical Algebraic Geometry
Tropical geometry is algebraic geometry over the semifield of tropical numbers, i.e., the real numbers and negative infinity enhanced with the (max,+)-arithmetics. Geometrically, tropical varieties are much simpler than their classical counterparts. Yet they carry information about complex and real varieties.These notes present an introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject.
Triangulations and Applications
This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate triangulations. In particular, we make a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. We also discuss various data structures used for the representation of triangulations.
Trauma - An Engineering Analysis : With Medical Case Studies Investigation
The purpose of this book is to bring together experts from the medical and engineering fields in which trauma acts as a fulcrum in understanding the engineering approach to medical cases. The emphasis of this book is on the retrospective study of medical scenarios as seen from the engineering perspective. An in-depth study is required to ensure the accuracy of both medical and engineering data. Where static, dynamic, temperature and impact loads and velocities/accelerations are unknown; they are evaluated using the material properties and fracture geometry of case studies. From the analytical techniques, a prospective study would assist in predicting the outcome of post-trauma damage. Generally, the book covers a wide spectrum of trauma case studies and could be used in medico-legal test cases. The medical opinion can be translated into the engineering analysis there by validating or invalidating the total medical decisions.
Transportation engineering : A practical approach to highway design, traffic analysis, and systems operation
Explains the many aspects of transportation systems planning, design, operation, and maintenance. Explores key topics, including geometric design for roadway alignment; traffic demand, flow, and control; and highway and intersection capacity. Emerging issues such as livable streets, automated vehicles, and smart cities are also discussed. You will get real-world case studies that highlight practical applications as well as valuable diagrams and tables that define transportation engineering terms and acronyms. Coverage includes: introduction to transportation engineering / Geometric design / Traffic flow theory / Traffic control / Capacity and level of service / Highway safety / Transportation demand / Transportation systems management and operations / Emerging topics
Transport Equations and Multi-D Hyperbolic Conservation Laws
The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. Geometric and measure theoretic tools play a key role to obtain some fundamental advances: the well-posedness theory of linear transport equations with irregular coefficients, and the study of the BV-like structure of bounded entropy solutions to multi-dimensional scalar conservation laws.
