Geometry Illuminated

Geometry Illuminated

Author: Matthew Harvey

Publisher: The Mathematical Association of America

ISBN: 9781939512116

Category: Mathematics

Page: 561

View: 859

Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.

Real-Time Rendering, Fourth Edition

Real-Time Rendering, Fourth Edition

Author: Tomas Akenine-Mo ̈ller

Publisher: CRC Press

ISBN: 9781351816151

Category: Computers

Page: 1198

View: 715

Thoroughly updated, this fourth edition focuses on modern techniques used to generate synthetic three-dimensional images in a fraction of a second. With the advent of programmable shaders, a wide variety of new algorithms have arisen and evolved over the past few years. This edition discusses current, practical rendering methods used in games and o

Conformally Invariant Metrics and Quasiconformal Mappings

Conformally Invariant Metrics and Quasiconformal Mappings

Author: Parisa Hariri

Publisher: Springer Nature

ISBN: 9783030320683

Category: Mathematics

Page: 502

View: 132

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

TERRA: Return of the Divine Feminine

TERRA: Return of the Divine Feminine

Author: Keith David Henry

Publisher: Keith David Henry

ISBN: 9781448682096

Category:

Page: 154

View: 306

The world today is faced with the gravest dilemmas of all time. Every major system is beginning to disintegrate. This global phenomenon is happening across social, political, financial, religious, environmental, and moral lines. The artificially masculine - that contrived patriarchal and oligarchic paradigm in which we currently live - is in large part responsible for this breakdown. This book, the third in the series, examines the role that the renewed respect for and acceptance of the Divine Feminine integrated with the true Divine Masculine will play during this age. It also delves into the science and esotery behind the Mayan calendar, our progression of consciousness as a species, and their implications for humanity's post-2012 existence as our solar system moves into the next 26,000-year Mayan calendar astronomical cycle known commonly as the Aquarian Age.

Numerical Methods in Photonics

Numerical Methods in Photonics

Author: Andrei V. Lavrinenko

Publisher: CRC Press

ISBN: 9781351832007

Category: Science

Page: 206

View: 720

Simulation and modeling using numerical methods is one of the key instruments in any scientific work. In the field of photonics, a wide range of numerical methods are used for studying both fundamental optics and applications such as design, development, and optimization of photonic components. Modeling is key for developing improved photonic devices and reducing development time and cost. Choosing the appropriate computational method for a photonics modeling problem requires a clear understanding of the pros and cons of the available numerical methods. Numerical Methods in Photonics presents six of the most frequently used methods: FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green’s function, and FEM. After an introductory chapter outlining the basics of Maxwell’s equations, the book includes self-contained chapters that focus on each of the methods. Each method is accompanied by a review of the mathematical principles in which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATLAB® is used throughout the text. This book provides a solid basis to practice writing your own codes. The theoretical formulation is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools.

Old and New Unsolved Problems in Plane Geometry and Number Theory

Old and New Unsolved Problems in Plane Geometry and Number Theory

Author: Victor Klee

Publisher: American Mathematical Soc.

ISBN: 9781470454616

Category: Education

Page: 333

View: 510

Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.

GPU-based Techniques for Global Illumination Effects

GPU-based Techniques for Global Illumination Effects

Author: László Szirmay-Kalos

Publisher: Morgan & Claypool Publishers

ISBN: 9781598295597

Category: Computers

Page: 275

View: 543

This book presents techniques to render photo-realistic images by programming the Graphics Processing Unit (GPU). We discuss effects such as mirror reflections, refractions, caustics, diffuse or glossy indirect illumination, radiosity, single or multiple scattering in participating media, tone reproduction, glow, and depth of field. The book targets game developers, graphics programmers, and also students with some basic understanding of computer graphics algorithms, rendering APIs like Direct3D or OpenGL, and shader programming. In order to make the book self-contained, the most important concepts of local illumination and global illumination rendering, graphics hardware, and Direct3D/HLSL programming are reviewed in the first chapters. After these introductory chapters we warm up with simple methods including shadow and environment mapping, then we move on toward advanced concepts aiming at global illumination rendering. Since it would have been impossible to give a rigorous review of all approaches proposed in this field, we go into the details of just a few methods solving each particular global illumination effect. However, a short discussion of the state of the art and links to the bibliography are also provided to refer the interested reader to techniques that are not detailed in this book. The implementation of the selected methods is also presented in HLSL, and we discuss their observed performance, merits, and disadvantages. In the last chapter, we also review how these techniques can be integrated in an advanced game engine and present case studies of their exploitation in games. Having gone through this book, the reader will have an overview of the state of the art, will be able to apply and improve these techniques, and most importantly, will be capable of developing brand new GPU algorithms. Table of Contents: Global Illumintation Rendering / Local Illumination Rendering Pipeline of GPUs / Programming and Controlling GPUs / Simple Improvements of the Local Illumination Model / Ray Casting on the GPU / Specular Effects with Rasterization / Diffuse and Glossy Indirect Illumination / Pre-computation Aided Global Illumination / Participating Media Rendering / Fake Global Illumination / Postprocessing Effects / Integrating GI Effects in Games and Virtual Reality Systems / Bibliography

Billmeyer and Saltzman's Principles of Color Technology

Billmeyer and Saltzman's Principles of Color Technology

Author: Roy S. Berns

Publisher: John Wiley & Sons

ISBN: 9781119366683

Category: Science

Page: 272

View: 701

This book offers detailed coverage of color, colorants, the coloring of materials, and reproducing the color of materials through imaging. It combines the clarity and ease of earlier editions with significant updates about the advancement in color theory and technology. Provides guidance for how to use color measurement instrumentation, make a visual assessment, set a visual tolerance, and select a formulation Supplements material with numerical examples, graphs, and illustrations that clarify and explain complex subjects Expands coverage of topics including spatial vision, solid-state lighting, cameras and spectrophotometers, and translucent materials

Modern Textile Characterization Methods

Modern Textile Characterization Methods

Author: Mastura Raheel

Publisher: Routledge

ISBN: 9781351430494

Category: Science

Page: 576

View: 344

This work details current advances in assessing the characteristics of polymers, single fibres and fibrous systems, and associated processes based on evolving theories in the physical, chemical and mechanical sciences. It focuses on recent develpments in selected characterization methods - such as Fourier transform infrared spectroscopy, Fourier transform nuclear magnetic resonance, electron diffraction, x-ray diffraction and electron microscopy - applicatble to polymers, fibres and textiles.

Office Hours with a Geometric Group Theorist

Office Hours with a Geometric Group Theorist

Author: Matt Clay

Publisher: Princeton University Press

ISBN: 9780691158662

Category: Mathematics

Page: 456

View: 635

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.

The Manual of Photography and Digital Imaging

The Manual of Photography and Digital Imaging

Author: Elizabeth Allen

Publisher: CRC Press

ISBN: 9781136091100

Category: Photography

Page: 608

View: 398

The tenth edition of The Manual of Photography is an indispensable textbook for anyone who is serious about photography. It is ideal if you want to gain insight into the underlying scientific principles of photography and digital imaging, whether you are a professional photographer, lab technician, researcher or student in the field, or simply an enthusiastic amateur. This comprehensive guide takes you from capture to output in both digital and film media, with sections on lens use, darkroom techniques, digital cameras and scanners, image editing techniques and processes, workflow, digital file formats and image archiving. This iconic text was first published in 1890 and has aided many thousands of photographers in developing their own techniques and understanding of the medium. Now in full colour, The Manual of Photography still retains its clear, reader-friendly style and is filled with images and illustrations demonstrating the key principles. Not only giving you the skills and know-how to take stunning photographs, but will also allowing you to fully understand the science behind the creation of great images.