Читать книгу Mathematical Basics of Motion and Deformation in Computer Graphics - Ken Anjyo - Страница 7
ОглавлениеContents
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
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)
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
5 2D Affine Transformation between Two Triangles
5.1 Triangles and an Affine Transformation
5.2 Comparison of Three Interpolation Methods
6 Global 2D Shape Interpolation
6.2 Formulation
6.3 Error Function for Global Interpolation
6.4 Examples of Local Error Functions
6.5 Examples of Constraint Functions
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
A.1 Several Versions of Rodrigues Formula
A.2 Rodrigues Type Formula for Motion Group
A.3 Proof of the Energy Formula
