Contents

This is the table of contents for Projective Geometric Algebra Illuminated.

• Preface
• 1 Conventional Mathematics
  • 1.1 The Cross Product
  • 1.2 Homogeneous Coordinates
  • 1.3 Lines and Planes
    • 1.3.1 Parametric Forms
    • 1.3.2 Implicit Forms
    • 1.3.3 Distance Between a Point and a Line
    • 1.3.4 Intersection of a Line and a Plane
    • 1.3.5 Intersection of Multiple Planes
    • 1.3.6 Reflection Across a Plane
    • 1.3.7 Homogeneous Formulas
    • 1.3.8 Plane Transformation
    • 1.3.9 Line Transformation
  • 1.4 Quaternions
    • 1.4.1 Quaternion Fundamentals
    • 1.4.2 Rotations With Quaternions
    • 1.4.3 Interpolating Quaternions
    • 1.4.4 Dual Quaternions
  • Historical Remarks
• 2 Flat Projective Geometry
  • 2.1 Algebraic Structure
    • 2.1.1 The Wedge Product
    • 2.1.2 Bivectors
    • 2.1.3 Trivectors
    • 2.1.4 Basis Elements
  • 2.2 Complements
  • 2.3 Antiproducts
  • 2.4 3D Flat Geometry
    • 2.4.1 Points
    • 2.4.2 Lines
    • 2.4.3 Planes
  • 2.5 Join and Meet
  • 2.6 Duality
  • 2.7 Exomorphisms
  • 2.8 Metric Transformations
    • 2.8.1 The Metric
    • 2.8.2 The Antimetric
    • 2.8.3 Bulk and Weight
    • 2.8.4 Attitude
  • 2.9 Inner Products
  • 2.10 Norms
    • 2.10.1 Bulk and Weight Norms
    • 2.10.2 Unitization
    • 2.10.3 The Geometric Norm
  • 2.11 Euclidean Distances
  • 2.12 Duals
  • 2.13 Interior Products
    • 2.13.1 Contractions
    • 2.13.2 Projection and Rejection
    • 2.13.3 Euclidean Angles
    • 2.13.4 Parametric Forms
    • 2.13.5 Expansions
    • 2.13.6 Geometric Projection
  • 2.14 2D Flat Geometry
  • 2.15 Dependencies
  • Historical Remarks
• 3 Rigid Transformations
  • 3.1 The Geometric Product
  • 3.2 Dual Numbers
  • 3.3 Reflection and Rotation
  • 3.4 Reversion
    • 3.4.1 Reverse and Antireverse
    • 3.4.2 Dual Identities
    • 3.4.3 Geometric Constraint
  • 3.5 Euclidean Isometries
    • 3.5.1 Reflection
    • 3.5.2 Rotation
    • 3.5.3 Translation
    • 3.5.4 Inversion
    • 3.5.5 Transflection
  • 3.6 Motors
    • 3.6.1 Motion Operator
    • 3.6.2 Parameterization
    • 3.6.3 Line to Line Motion
    • 3.6.4 Matrix Conversion
    • 3.6.5 Implementation
  • 3.7 Flectors
    • 3.7.1 Reflection Operator
    • 3.7.2 Matrix Conversion
    • 3.7.3 Implementation
  • 3.8 2D Rigid Transformations
  • 3.9 Operator Duality
    • 3.9.1 Complement Isometries
    • 3.9.2 Transformation Groups
    • 3.9.3 Quaternions Revisited
  • Historical Remarks
• 4 Round Projective Geometry
  • 4.1 Construction
  • 4.2 3D Round Geometry
    • 4.2.1 Representations
    • 4.2.2 Duals
    • 4.2.3 Carriers
    • 4.2.4 Centers
    • 4.2.5 Containers
    • 4.2.6 Partners
    • 4.2.7 Attitude
  • 4.3 Norms
  • 4.4 Alignment
  • 4.5 Dot Products
    • 4.5.1 Round Points
    • 4.5.2 Spheres
    • 4.5.3 Partners
    • 4.5.4 Conjugates
  • 4.6 Containment
  • 4.7 Join and Meet
  • 4.8 Expansions
  • 4.9 2D Round Geometry
  • 4.10 Degrees of Freedom
• 5 Conformal Transformations
  • 5.1 Generalized Operators
    • 5.1.1 Rigid Transformations
    • 5.1.2 Sphere Inversion
    • 5.1.3 Circle Rotation
  • 5.2 Dilation
  • 5.3 Duals and Complements
  • 5.4 2D Conformal Transformations
• A Multiplication Tables
• B Geometric Properties
• C Notation Reference
• Bibliography
• Index

See Also

• PGA Illuminated on Amazon.com
• Exercises