記錄 10 之 13
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作者 Anjyo, Ken, author
書名 Mathematical basics of motion and deformation in computer graphics / Ken Anjyo, Hiroyuki Ochiai
出版項 [San Rafael, California] : Morgan & Claypool, 2017
國際標準書號 9781627056977 print
9781627059848 ebook
國際標準號碼 10.2200/S00766ED1V01Y201704VCP027 doi
版本 Second edition
說明 1 online resource (xvi, 79 pages) : illustrations
text rdacontent
electronic isbdmedia
online resource rdacarrier
系列 Synthesis lectures on visual computing, 2469-4223 ; # 27
Synthesis lectures on visual computing ; # 27. 2469-4223
Synthesis digital library of engineering and computer science
附註 Part of: Synthesis digital library of engineering and computer science
Includes bibliographical references (pages 73-77)
8. Further readings -- A. Formula derivation -- Several versions of Rodrigues formula -- Rodrigues type formula for motion group -- Proof of the energy formula -- Bibliography -- Authors' biographies
7. Parametrizing 3D positive affine transformations -- 7.1 The parametrization map and its inverse -- 7.2 Deformer applications -- 7.3 Integrating with Poisson mesh editing -- 7.3.1 The Poisson edits -- 7.3.2 Harmonic guidance -- 7.3.3 The parametrization map for Poisson mesh editing --
6. Global 2D shape interpolation -- 6.1 Local to global -- 6.2 Formulation -- 6.3 Error function for global interpolation -- 6.4 Examples of local error functions -- 6.5 Examples of constraint functions --
5. 2D affine transformation between two triangles -- 5.1 Triangles and an affine transformation -- 5.2 Comparison of three interpolation methods --
4. Exponential and logarithm of matrices -- 4.1 Definitions and basic properties -- 4.2 Lie algebra -- 4.3 Exponential map from Lie algebra -- 4.4 Another definition of Lie algebra -- 4.5 Lie algebra and decomposition -- 4.6 Loss of continuity: singularities of the exponential map -- 4.7 The field of blending --
3. Affine transformation -- 3.1 Several classes of transformations -- 3.2 Semidirect product -- 3.3 Decomposition of the set of matrices -- 3.3.1 Polar decomposition -- 3.3.2 Diagonalization of positive definite symmetric matrix -- 3.3.3 Singular value decomposition (SVD) --
Preface -- Preface to the second edition -- Symbols and notations -- 1. Introduction --
2. Rigid transformation -- 2.1 2D translation -- 2.2 2D rotation -- 2.3 2D rigid transformation -- 2.4 2D reflection -- 2.5 3D rotation: axis-angle -- 2.6 3D rotation: Euler angle -- 2.7 3D rotation: quaternion -- 2.8 Dual quaternion -- 2.9 Using complex numbers -- 2.10 Dual complex numbers -- 2.11 Homogeneous expression of rigid transformations --
Abstract freely available; full-text restricted to subscribers or individual document purchasers
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System requirements: Adobe Acrobat Reader
Mode of access: World Wide Web
This synthesis lecture presents an intuitive introduction to the mathematics of motion and deformation in computer graphics. Starting with familiar concepts in graphics, such as Euler angles, quaternions, and affine transformations, we illustrate that a mathematical theory behind these concepts enables us to develop the techniques for efficient/effective creation of computer animation. This book, therefore, serves as a good guidepost to mathematics (differential geometry and Lie theory) for students of geometric modeling and animation in computer graphics. Experienced developers and researchers will also benefit from this book, since it gives a comprehensive overview of mathematical approaches that are particularly useful in character modeling, deformation, and animation
Also available in print
Title from PDF title page (viewed on April 18, 2017)
鏈接 Print version: 9781627056977
主題 Computer animation -- Mathematics
Computer graphics -- Mathematics
Lie group
Lie algebra
quaternion
deformation
motion
Alt Author Ochiai, Hiroyuki, 1965- author
記錄 10 之 13
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