rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Mathematical basics of motion and deformation in computer graphics
  title info:
    title: Synthesis digital library of engineering and computer science
  name:
    name part: Anjyo, Ken
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Ochiai, Hiroyuki
    name part: 1965-
    role:
      role term: author.
  type of resource: text
  genre: abstract or summary
  genre: Electronic books.
  origin info:
    place:
      place term: cau
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xii, 71 pages) : illustrations.
  abstract: 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: 1. Introduction --
  table of contents: 2. Rigid transformation -- 2.1 Translation in 2D -- 2.2 Rotation in 2D -- 2.3 Rigid transformation in 2D -- 2.4 Reflections in 2D -- 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 --
  table of contents: 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) --
  table of contents: 4. Exponential and logarithm of matrices -- 4.1 Exponential: 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 --
  table of contents: 5. 2D affine transformation between two triangles -- 5.1 Triangles and an affine transformation -- 5.2 Comparison of three interpolation methods --
  table of contents: 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 --
  table of contents: 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 --
  table of contents: 8. Further readings -- Bibliography -- Authors' biographies.
  target audience: specialized
  note: Ken Anjyo, Hiroyuki Ochiai.
  note: Abstract freely available; full-text restricted to subscribers or individual document purchasers.
  note: Also available in print.
  note: Mode of access: World Wide Web.
  note: System requirements: Adobe Acrobat Reader.
  note: Includes bibliographical references (pages 65-69).
  subject:
    topic: Computer animation
    topic: Mathematics
  subject:
    topic: Computer graphics
    topic: Mathematics
  subject:
    topic: Lie algebra
  subject:
    topic: Lie group
  subject:
    topic: deformation
  subject:
    topic: motion
  subject:
    topic: quaternion
  classification: T385 .A534 2014
  classification: 006.6869
  related item:
    title info:
      title: Synthesis lectures in computer graphics and animation ; # 17
  identifier: 9781627054454
  identifier: 9781627054447
  identifier: http://proxy.library.tamu.edu/login
  access condition: Abstract freely available; full-text restricted to subscribers or individual document purchasers.
  record info:
    record content source: CaBNVSL
    record creation date: 141119
    record change date: 20210728125142.0
    record identifier: in00003762147
    language of cataloging:
      language term: eng