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Author: Ares Lagae
Publisher: Springer Nature
ISBN: 3031795377
Category : Mathematics
Languages : en
Pages : 79
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Book Description
Many complex signals in computer graphics, such as point distributions and textures, cannot be efficiently synthesized and stored. This book presents tile-based methods based on Wang tiles and corner tiles to solve both these problems. Instead of synthesizing a complex signal when needed, the signal is synthesized beforehand over a small set of Wang tiles or corner tiles. Arbitrary large amounts of that signal can then efficiently be generated when needed by generating a stochastic tiling, and storing only a small set of tiles reduces storage requirements. A tile-based method for generating a complex signal consists of a method for synthesizing the signal over a set of Wang tiles or corner tiles, and a method for generating a stochastic tiling using the set of tiles. The method for generating a stochastic tiling using the set of tiles is independent of the signal. This book covers scanline stochastic tiling algorithms and direct stochastic tiling algorithms for Wang tiles and corner tiles. The method for synthesizing the signal over a set of tiles is dependent on the signal. This book covers tile-based methods for texture synthesis and for generating Poisson disk distributions. This book also explores several applications such as tile-based texture mapping and procedural modeling and texturing. Although the methods for constructing a complex signal over a set of Wang tiles or corner tiles are dependent on the signal, the general idea behind these methods generalizes to other kinds of signals. The methods presented in this book therefore have the potential to make the generation and storage of almost any complex signal efficient. Table of Contents: Introduction / Wang Tiles and Corner Tiles / Tiling Algorithms for Wang Tiles and Corner Tiles / Tile-Based Methods for Texture Synthesis / Tile-Based Methods Generating Poisson Disk Distributions / Applications of Poisson Disk Distributions
Author: Ares Lagae
Publisher: Springer Nature
ISBN: 3031795377
Category : Mathematics
Languages : en
Pages : 79
Get Book Here
Book Description
Many complex signals in computer graphics, such as point distributions and textures, cannot be efficiently synthesized and stored. This book presents tile-based methods based on Wang tiles and corner tiles to solve both these problems. Instead of synthesizing a complex signal when needed, the signal is synthesized beforehand over a small set of Wang tiles or corner tiles. Arbitrary large amounts of that signal can then efficiently be generated when needed by generating a stochastic tiling, and storing only a small set of tiles reduces storage requirements. A tile-based method for generating a complex signal consists of a method for synthesizing the signal over a set of Wang tiles or corner tiles, and a method for generating a stochastic tiling using the set of tiles. The method for generating a stochastic tiling using the set of tiles is independent of the signal. This book covers scanline stochastic tiling algorithms and direct stochastic tiling algorithms for Wang tiles and corner tiles. The method for synthesizing the signal over a set of tiles is dependent on the signal. This book covers tile-based methods for texture synthesis and for generating Poisson disk distributions. This book also explores several applications such as tile-based texture mapping and procedural modeling and texturing. Although the methods for constructing a complex signal over a set of Wang tiles or corner tiles are dependent on the signal, the general idea behind these methods generalizes to other kinds of signals. The methods presented in this book therefore have the potential to make the generation and storage of almost any complex signal efficient. Table of Contents: Introduction / Wang Tiles and Corner Tiles / Tiling Algorithms for Wang Tiles and Corner Tiles / Tile-Based Methods for Texture Synthesis / Tile-Based Methods Generating Poisson Disk Distributions / Applications of Poisson Disk Distributions
Author: Ares Lagae
Publisher: Morgan & Claypool Publishers
ISBN: 1598299654
Category : Computers
Languages : en
Pages : 92
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Book Description
Many complex signals in computer graphics, such as point distributions and textures, cannot be efficiently synthesized and stored. This book presents tile-based methods based on Wang tiles and corner tiles to solve both these problems. Instead of synthesizing a complex signal when needed, the signal is synthesized beforehand over a small set of Wang tiles or corner tiles. Arbitrary large amounts of that signal can then efficiently be generated when needed by generating a stochastic tiling, and storing only a small set of tiles reduces storage requirements. A tile-based method for generating a complex signal consists of a method for synthesizing the signal over a set of Wang tiles or corner tiles, and a method for generating a stochastic tiling using the set of tiles. The method for generating a stochastic tiling using the set of tiles is independent of the signal. This book covers scanline stochastic tiling algorithms and direct stochastic tiling algorithms for Wang tiles and corner tiles. The method for synthesizing the signal over a set of tiles is dependent on the signal. This book covers tile-based methods for texture synthesis and for generating Poisson disk distributions. This book also explores several applications such as tile-based texture mapping and procedural modeling and texturing. Although the methods for constructing a complex signal over a set of Wang tiles or corner tiles are dependent on the signal, the general idea behind these methods generalizes to other kinds of signals. The methods presented in this book therefore have the potential to make the generation and storage of almost any complex signal efficient. Table of Contents: Introduction / Wang Tiles and Corner Tiles / Tiling Algorithms for Wang Tiles and Corner Tiles / Tile-Based Methods for Texture Synthesis / Tile-Based Methods Generating Poisson Disk Distributions / Applications of Poisson Disk Distributions
Author: Craig Kaplan
Publisher: Springer Nature
ISBN: 3031795431
Category : Mathematics
Languages : en
Pages : 103
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Book Description
Tiling theory is an elegant branch of mathematics that has applications in several areas of computer science. The most immediate application area is graphics, where tiling theory has been used in the contexts of texture generation, sampling theory, remeshing, and of course the generation of decorative patterns. The combination of a solid theoretical base (complete with tantalizing open problems), practical algorithmic techniques, and exciting applications make tiling theory a worthwhile area of study for practitioners and students in computer science. This synthesis lecture introduces the mathematical and algorithmic foundations of tiling theory to a computer graphics audience. The goal is primarily to introduce concepts and terminology, clear up common misconceptions, and state and apply important results. The book also describes some of the algorithms and data structures that allow several aspects of tiling theory to be used in practice. Table of Contents: Introduction / Tiling Basics / Symmetry / Tilings by Polygons / Isohedral Tilings / Nonperiodic and Aperiodic Tilings / Survey
Author: Tomoyuki Nishita
Publisher: Springer Science & Business Media
ISBN: 354035638X
Category : Computers
Languages : en
Pages : 788
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Book Description
This is the refereed proceedings of the 24th Computer Graphics International Conference, CGI 2006. The 38 revised full papers and 37 revised short papers presented were carefully reviewed. The papers are organized in topical sections on rendering and texture, efficient modeling and deformation, digital geometry processing, shape matching and shape analysis, face, virtual reality, motion and image, as well as CAGD.
Author: Shiguang Liu
Publisher: Morgan & Claypool Publishers
ISBN: 1636393217
Category : Computers
Languages : en
Pages : 110
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Book Description
This book gives a broad overview of research on sound simulation driven by a variety of applications. Vibrating objects produce sound, which then propagates through a medium such as air or water before finally being heard by a listener. As a crucial sensory channel, sound plays a vital role in many applications. There is a well-established research community in acoustics that has studied the problems related to sound simulation for six decades. Some of the earliest work was motivated by the design of concert halls, theaters, or lecture rooms with good acoustic characteristics. These problems also have been investigated in other applications, including noise control and sound design for urban planning, building construction, and automotive applications. Moreover, plausible or realistic sound effects can improve the sense of presence in a virtual environment or a game. In these applications, sound can provide important clues such as source directionality and spatial size. The book first surveys various sound synthesis methods, including harmonic synthesis, texture synthesis, spectral analysis, and physics-based synthesis. Next, it provides an overview of sound propagation techniques, including wave-based methods, geometric-based methods, and hybrid methods. The book also summarizes various techniques for sound rendering. Finally, it surveys some recent trends, including the use of machine learning methods to accelerate sound simulation and the use of sound simulation techniques for other applications such as speech recognition, source localization, and computer-aided design.
Author: Ron Goldman
Publisher: Springer Nature
ISBN: 3031795490
Category : Mathematics
Languages : en
Pages : 157
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Book Description
Quaternion multiplication can be used to rotate vectors in three-dimensions. Therefore, in computer graphics, quaternions have three principal applications: to increase speed and reduce storage for calculations involving rotations, to avoid distortions arising from numerical inaccuracies caused by floating point computations with rotations, and to interpolate between two rotations for key frame animation. Yet while the formal algebra of quaternions is well-known in the graphics community, the derivations of the formulas for this algebra and the geometric principles underlying this algebra are not well understood. The goals of this monograph are to provide a fresh, geometric interpretation for quaternions, appropriate for contemporary computer graphics, based on mass-points; to present better ways to visualize quaternions, and the effect of quaternion multiplication on points and vectors in three dimensions using insights from the algebra and geometry of multiplication in the complex plane; to derive the formula for quaternion multiplication from first principles; to develop simple, intuitive proofs of the sandwiching formulas for rotation and reflection; to show how to apply sandwiching to compute perspective projections. In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover, we show how to avoid distortions due to floating point computations with rotations by using unit quaternions to represent rotations. We also derive the formula for spherical linear interpolation, and we explain how to apply this formula to interpolate between two rotations for key frame animation. Finally, we explain the role of quaternions in low-dimensional Clifford algebras, and we show how to apply the Clifford algebra for R3 to model rotations, reflections, and perspective projections. To help the reader understand the concepts and formulas presented here, we have incorporated many exercises in order to clarify and elaborate some of the key points in the text. Table of Contents: Preface / Theory / Computation / Rethinking Quaternions and Clif ford Algebras / References / Further Reading / Author Biography
Author: Tiago Etiene
Publisher: Springer Nature
ISBN: 3031025873
Category : Mathematics
Languages : en
Pages : 80
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Book Description
As we increase our reliance on computer-generated information, often using it as part of our decision-making process, we must devise tools to assess the correctness of that information. Consider, for example, software embedded on vehicles, used for simulating aircraft performance, or used in medical imaging. In those cases, software correctness is of paramount importance as there's little room for error. Software verification is one of the tools available to attain such goals. Verification is a well known and widely studied subfield of computer science and computational science and the goal is to help us increase confidence in the software implementation by verifying that the software does what it is supposed to do. The goal of this book is to introduce the reader to software verification in the context of visualization. In the same way we became more dependent on commercial software, we have also increased our reliance on visualization software. The reason is simple: visualization is the lens through which users can understand complex data, and as such it must be verified. The explosion in our ability to amass data requires tools not only to store and analyze data, but also to visualize it. This book is comprised of six chapters. After an introduction to the goals of the book, we present a brief description of both worlds of visualization (Chapter 2) and verification (Chapter 3). We then proceed to illustrate the main steps of the verification pipeline for visualization algorithms. We focus on two classic volume visualization techniques, namely, Isosurface Extraction (Chapter 4) and Direct Volume Rendering (Chapter 5). We explain how to verify implementations of those techniques and report the latest results in the field of verification of visualization techniques. The last chapter concludes the book and highlights new research topics for the future.
Author: Marcelo Kallmann
Publisher: Springer Nature
ISBN: 3031025881
Category : Mathematics
Languages : en
Pages : 181
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Book Description
Path planning and navigation are indispensable components for controlling autonomous agents in interactive virtual worlds. Given the growing demands on the size and complexity of modern virtual worlds, a number of new techniques have been developed for achieving intelligent navigation for the next generation of interactive multi-agent simulations. This book reviews the evolution of several related techniques, starting from classical planning and computational geometry techniques and then gradually moving toward more advanced topics with focus on recent developments from the work of the authors. The covered topics range from discrete search and geometric representations to planning under different types of constraints and harnessing the power of graphics hardware in order to address Euclidean shortest paths and discrete search for multiple agents under limited time budgets. The use of planning algorithms beyond path planning is also discussed in the areas of crowd animation and whole-body motion planning for virtual characters.
Author: Giuseppe Patanè
Publisher: Springer Nature
ISBN: 303102589X
Category : Mathematics
Languages : en
Pages : 129
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Book Description
New data acquisition techniques are emerging and are providing fast and efficient means for multidimensional spatial data collection. Airborne LIDAR surveys, SAR satellites, stereo-photogrammetry and mobile mapping systems are increasingly used for the digital reconstruction of the environment. All these systems provide extremely high volumes of raw data, often enriched with other sensor data (e.g., beam intensity). Improving methods to process and visually analyze this massive amount of geospatial and user-generated data is crucial to increase the efficiency of organizations and to better manage societal challenges. Within this context, this book proposes an up-to-date view of computational methods and tools for spatio-temporal data fusion, multivariate surface generation, and feature extraction, along with their main applications for surface approximation and rainfall analysis. The book is intended to attract interest from different fields, such as computer vision, computer graphics, geomatics, and remote sensing, working on the common goal of processing 3D data. To this end, it presents and compares methods that process and analyze the massive amount of geospatial data in order to support better management of societal challenges through more timely and better decision making, independent of a specific data modeling paradigm (e.g., 2D vector data, regular grids or 3D point clouds). We also show how current research is developing from the traditional layered approach, adopted by most GIS softwares, to intelligent methods for integrating existing data sets that might contain important information on a geographical area and environmental phenomenon. These services combine traditional map-oriented visualization with fully 3D visual decision support methods and exploit semantics-oriented information (e.g., a-priori knowledge, annotations, segmentations) when processing, merging, and integrating big pre-existing data sets.
Author: Novello Tiago
Publisher: Springer Nature
ISBN: 3031792122
Category : Mathematics
Languages : en
Pages : 112
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Book Description
This book explores the visualization of three-dimensional non-Euclidean spaces using ray-tracing techniques in Graphics Processing Unit (GPU). This is a trending topic in mathematical visualization that combines the mathematics areas of geometry and topology, with visualization concepts of computer graphics. Several conditions made this a special moment for such topic. On one hand, the development of mathematical research, computer graphics, and algorithms have provided the necessary theoretical framework. On the other hand, the evolution of the technologies and media allows us to be immersed in three-dimensional spaces using Virtual Reality. The content of this book serves both experts in the areas and students. Although this is a short book, it is self-contained since it considers all the ideas, motivations, references, and intuitive explanations of the required fundamental concepts.
