Projective Geometric Algebra ILLUMINATEDの目次

Projective Geometric Algebra ILLUMINATEDの目次

Projective Geometric Algebra ILLUMINATEDは，ゲームプログラミングのための3Dグラフィックス数学の著者であるEric Lengyel先生による射影幾何代数の書籍です．

ざっと目を通した感じ，フルカラーで表紙にあるような図も使いながらの説明なので，理解を深められそうです．

書籍のページはこちら

• https://projectivegeometricalgebra.org/

Amazonのサンプルから目次の画像を見ることも可能ですが，テキストで欲しかったのでメモとして残します．

1. Preface
2. Conventional Mathematics
   1. The Cross Product
   2. Homogeneous Coordinates
   3. Lines and Planes
      1. Parametric Forms
      2. Implicit Forms
      3. Distance Between a Point and a Line
      4. Intersection of a Line and a Plane
      5. Intersection of Multiple Planes
      6. Reflection Across a Planes
      7. Homogeneous Formulas
      8. Plane Transformation
      9. Line Transformation
   4. Quaternions
      1. Quaternion Fundamentals
      2. Rotations With Quaternions
      3. Interpolating Quaternions
      4. Dual Quaternions
   5. Histroical Remarks
3. Flat Projective Geometry
   1. Algebraic Structure
      1. The Wedge Product
      2. Bivectors
      3. Trivectors
      4. Basis Elements
   2. Complements
   3. Antiproducts
   4. 3D Flat Geometry
      1. Points
      2. Lines
      3. Planes
   5. Join and Meet
   6. Duality
   7. Exomorphisms
   8. Metric Transformations
      1. The Metric
      2. The Animetric
      3. Bulk and Weight
      4. Attitude
   9. Inner Products
   10. Norms
       1. Bulk and Weight Norms
       2. Unitization
       3. The Geometric Norm
   11. Euclidean Distances
   12. Duals
   13. Interior Products
       1. Contractions
       2. Projection and Rejection
       3. Euclidean Angles
       4. Parametric Forms
       5. Expansions
       6. Geometric Projection
   14. 2D Flat Geometry
   15. Dependencies
   16. Historical Remarks
4. Rigid Transformations
   1. The Geometric Product
   2. Dual Numbers
   3. Reflection and Rotation
   4. Reversion
      1. Reverse and Antireverse
      2. Dual Identities
      3. Geometric Constraint
   5. Euclidean Isometries
      1. Reflection
      2. Rotation
      3. Translation
      4. Inversion
      5. Transflection
   6. Motors
      1. Motion Operator
      2. Parameterization
      3. Line to Line Motion
      4. Matrix Conversion
      5. Implementation
   7. Flectors
      1. Reflection Operator
      2. Matrix Conversion
      3. Implementation
   8. 2D Rigid Transformations
   9. Operator Duality
      1. Complement Isometries
      2. Transformation Groups
      3. Quaternions Revisited
   10. Historical Remarks
5. Round Projective Geometry
   1. Construction
   2. 3D Round Geometry
      1. Representations
      2. Duals
      3. Carriers
      4. Centers
      5. Containers
      6. Partners
      7. Attitude
   3. Norms
   4. Alignment
   5. Dot Products
      1. Round Points
      2. Spheres
      3. Partners
      4. Conjugates
   6. Containment
   7. Join and Meet
   8. Expansions
   9. 2D Round Geometry
   10. Degrees of Freedom
6. Conformal Transformations
   1. Generalized Operators
      1. Rigid Transformations
      2. Sphere Inversion
      3. Circle Rotation
   2. Dilation
   3. Duals and Complements
   4. 2D Conformal Transformations
7. Multiplication Tables (実際のページにはComformal Productsと書いてある)
8. Geometric Properties
   • Point (3D)
   • Line (3D)
   • Plane (3D)
   • Round Point (3D)
   • Sphere (3D)
   • Dipole (3D)
   • Circle (3D)
   • Point (2D)
   • Line (2D)
   • Round Point (2D)
   • Circle (2D)
   • Dipole (2D)
9. Notation Referencec
10. Bibliography (参考文献)
11. Index (索引)