System requirements: Adobe Acrobat Reader.

Mode of access: World Wide Web.

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 --

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INSPEC

Compendex

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).