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Mathematical Basics of Motion and Deformation in Computer Graphics [electronic resource] / by Ken Anjyo, Hiroyuki Ochiai.

By: Anjyo, Ken [author.].
Contributor(s): Ochiai, Hiroyuki [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Computer Graphics and Animation: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Edition: 1st ed. 2017.Description: XVI, 101 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031795619.Subject(s): Mathematics | Image processing -- Digital techniques | Computer vision | Mathematics | Computer Imaging, Vision, Pattern Recognition and GraphicsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 510 Online resources: Click here to access online
Contents:
Preface -- Symbols and Notations -- Introduction -- Rigid Transformation -- Affine Transformation -- Exponential and Logarithm of Matrices -- 2D Affine Transformation between Two Triangles -- Global 2D Shape Interpolation -- Parametrizing 3D Positive Affine Transformations -- Further Readings -- Bibliography -- Authors' Biographies .
In: Springer Nature eBookSummary: 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. Table of Contents: Preface / Symbols and Notations / Introduction / Rigid Transformation / Affine Transformation / Exponential and Logarithm of Matrices / 2D Affine Transformation between Two Triangles / Global 2D Shape Interpolation / Parametrizing 3D Positive Affine Transformations / Further Readings / Bibliography / Authors' Biographies.
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Preface -- Symbols and Notations -- Introduction -- Rigid Transformation -- Affine Transformation -- Exponential and Logarithm of Matrices -- 2D Affine Transformation between Two Triangles -- Global 2D Shape Interpolation -- Parametrizing 3D Positive Affine Transformations -- Further Readings -- Bibliography -- Authors' Biographies .

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. Table of Contents: Preface / Symbols and Notations / Introduction / Rigid Transformation / Affine Transformation / Exponential and Logarithm of Matrices / 2D Affine Transformation between Two Triangles / Global 2D Shape Interpolation / Parametrizing 3D Positive Affine Transformations / Further Readings / Bibliography / Authors' Biographies.

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