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Visualizing Quaternions

Author: Andrew J. Hanson
Publisher: Elsevier
ISBN: 0080474772
Size: 75.55 MB
Format: PDF, ePub
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Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available. The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. Covers both non-mathematical and mathematical approaches to quaternions.

3d Math Primer For Graphics And Game Development

Author: Fletcher Dunn
Publisher: CRC Press
ISBN: 1498759890
Size: 29.78 MB
Format: PDF, Kindle
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This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for

Quaternion And Clifford Fourier Transforms And Wavelets

Author: Eckhard Hitzer
Publisher: Springer Science & Business Media
ISBN: 3034806035
Size: 54.70 MB
Format: PDF, ePub, Docs
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Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.

Physically Based Rendering

Author: Matt Pharr
Publisher: Morgan Kaufmann
ISBN: 0123750792
Size: 28.14 MB
Format: PDF, Docs
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Physically Based Rendering, 2nd Edition describes both the mathematical theory behind a modern photorealistic rendering system as well as its practical implementation. A method - known as 'literate programming'- combines human-readable documentation and source code into a single reference that is specifically designed to aid comprehension. The result is a stunning achievement in graphics education. Through the ideas and software in this book, you will learn to design and employ a full-featured rendering system for creating stunning imagery. New sections on subsurface scattering, Metropolis light transport, precomputed light transport, multispectral rendering, and much more. Includes a companion site complete with source code for the rendering system described in the book, with support for Windows, OS X, and Linux. Please visit, Code and text are tightly woven together through a unique indexing feature that lists each function, variable, and method on the page that they are first described.


Author: Canadian Human-Computer Communications Society
ISBN: 9780969533825
Size: 56.71 MB
Format: PDF, Mobi
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