| Transfer / 1： |
| Introduction / 1.1： |
| Complex Shape Generation / 1.2： |
| Object-Oriented Theory of Geometry / 1.3： |
| Human Perception / 1.4： |
| Serial-Link Manipulators / 1.6： |
| Object-Oriented Inheritance / 1.7： |
| Design / 1.8： |
| Cognition and Transfer / 1.10： |
| Transfer in Differential Equations / 1.11： |
| Scientific Structure / 1.12： |
| Maximization of Transfer / 1.13： |
| Primitive-Breaking / 1.14： |
| The Algebraic Description of Machines / 1.15： |
| Agent Self-Substitution / 1.16： |
| RigorousDefinition of Shape / 1.17： |
| RigorousDefinition of Aesthetics / 1.18： |
| Shape Generation by Group Extensions / 1.19： |
| Recoverability / 2.： |
| Geometry and Memory / 2.1： |
| Practical Need for Recoverability / 2.2： |
| Theoretical Need for Recoverability / 2.3： |
| Data Sets / 2.4： |
| The Fundamental Recovery Rules / 2.5： |
| Design as Symmetry-Breaking / 2.6： |
| Computational Vision and Symmetry-Breaking / 2.7： |
| Occupancy / 2.8： |
| External vs. Internal Inference / 2.9： |
| Exhaustiveness and Internal Inference / 2.10： |
| Externalization Principle / 2.11： |
| Choice of Metric in the Externalization Principle / 2.12： |
| Externalization Principle and Environmental Dimensionality / 2.13： |
| History Symmetrization Principle / 2.14： |
| Symmetry-to-Trace Conversion / 2.15： |
| Roots / 2.16： |
| Inferred Order of the Generative Operations / 2.17： |
| Symmetry-Breaking vs. Asymmetry-Building / 2.18： |
| Against the Erlanger Program / 2.19： |
| Memory / 2.20： |
| Regularity / 2.21： |
| Aesthetics / 2.22： |
| The Definition of Shape / 2.23： |
| Mathematical Theory of Transfer, I / 3.： |
| The Importance of n-Cubes in Computational Vision and CAD / 3.1： |
| Stage 1: Defining Fibers and Control / 3.3： |
| Stage 2: Defining the Fiber-Group Product / 3.4： |
| The Fiber-Group Product as a Symmetry Group / 3.5： |
| Defining the Action of the Fiber-Group Product on the Data Set 84 / 3.6： |
| Stage 3: Action of G(C) on the Fiber-Group Product / 3.7： |
| Transfer as an Automorphism Group / 3.8： |
| Stage 4: Splitting Extension of the Fiber-Group Product by the Control Group / 3.9： |
| Wreath Products / 3.10： |
| The Universal Embdedding Theorems / 3.11： |
| Nesting vs. Control-Nesting / 3.12： |
| Stage 5: Defining the Action of G(F)$$G(C)on F x C / 3.13： |
| Control-GroupIndexes / 3.14： |
| Up-Keeping Effect of the Transfer Automorphisms / 3.15： |
| The Direct vs. the Indirect Representation / 3.16： |
| Transfer asConjugation / 3.17： |
| Conjugation and Recoverability / 3.18： |
| Infinite Control Sets / 3.19： |
| The Full Structure / 3.20： |
| The FiveGroupActions / 3.21： |
| Mathematical Theory of Transfer, II / 4.： |
| The Iterated Wreath Product / 4.1： |
| Opening Up / 4.3： |
| The Group TheoryofHierarchicalDetection / 4.4： |
| Control-Nested t-Automorphisms / 4.5： |
| The Wreath Modifier / 4.6： |
| Iso-Regular Groups / 4.7： |
| Canonical Plans / 4.8： |
| Wreath Poly A Groups / 4.9： |
| WreathCovering / 4.10： |
| Theory of Grouping / 5.： |
| Grouping from Wreath Products / 5.1： |
| Grouping as Algebraic Action / 5.3： |
| Generative Crystallography / 5.4： |
| Using the Law of Grouping / 5.5： |
| Hierarchical Detection in Grouping / 5.6： |
| Perceptual Relationship between Similar Groupings / 5.7： |
| Product Ordering / 5.8： |
| Local-to-Global in a Wreath Product / 5.9： |
| Perceptual Effect of Inclusion and Omission of Levels / 5.10： |
| Non-iso-regular Groups / 5.11： |
| Robot Manipulators / 6.： |
| Three Algebraic Conditions / 6.1： |
| Object-Centered FramesasTransfer / 6.2： |
| The Serial-Link Manipulator / 6.3： |
| The Full Group of a Serial-Link Manipulator / 6.4： |
| Transfer in the Serial-Link Manipulator / 6.5： |
| The Full Group of a General-Linked Manipulator / 6.6： |
| Semi-Rigid Groups |
| Including Manipulator Shape / 6.8： |
| Algebraic Theory of Inheritance / 7.： |
| Inheritance / 7.1： |
| Geometric Inheritance / 7.2： |
| Theory of Inheritance / 7.3： |
| Relating Inheritance Diagrams to Algebra / 7.4： |
| Class Inheritance / 7.5： |
| Reference Frames / 8.： |
| Reference Objects / 8.1： |
| Non-coordinate-free Geometry / 8.2： |
| Processes andPhases / 8.3： |
| TheoryofReference Objects / 8.4： |
| The Necessity of Reference Frames / 8.5： |
| Structure of the 2D Reference Frame / 8.6： |
| Canonical Plan from the 2D Reference Frame / 8.7： |
| Organizing Role of the Cartesian Reference Frame / 8.8： |
| Orientation-and-Form / 8.9： |
| Cartesian Frame Bundle / 8.10： |
| External Actions on Frames: Decomposition / 8.11： |
| The3DReferenceFrame / 8.12： |
| Assigning Triple-Reflection Structures to Surfaces / 8.13： |
| ConstructionPlane / 8.14： |
| Relative Motion / 9.： |
| Theory of Relative Motion / 9.1： |
| Induced Motion / 9.3： |
| Inheritance via Extra Frames / 9.4： |
| Physics / 9.5： |
| Surface Primitives / 10.： |
| Defining and Classifying Primitives / 10.1： |
| Level-ContinuousPrimitives / 10.2： |
| Sphere and Torus / 10.3： |
| Cylinder and Cone / 10.4： |
| Level-Discrete Primitives / 10.5： |
| Formulation of Primitives to Maximize Transfer and Recoverability / 10.6： |
| Externalization / 10.7： |
| Unfolding Groups, I / 11.： |
| Symmetry Group of a Complex Environment / 11.1： |
| Concatenation asSymmetry-Breaking / 11.2： |
| Concatenation asAsymmetry-Building / 11.3： |
| Serial-Link Manipulators as Telescope Groups / 11.4： |
| Constructive Solid Geometry(CSG) / 11.5： |
| Boolean Operations as Symmetry-Breaking / 11.6： |
| Boolean Operations as Telescope Groups / 11.7： |
| Spatial Group Equivalence of Boolean Operations / 11.8： |
| Unfolding Groups, II / 12.： |
| Importance of Selection in Generativity / 12.1： |
| Super-Local Unfolding / 12.2： |
| Establishing a Target for Super-Local Unfolding / 12.3： |
| Super-Local Unfolding and Wreath Coverings / 12.4： |
| The Symmetry Group of a Complex Object / 12.5： |
| Exploitation of Existing Structure / 12.6： |
| Cross-Hierarchy in Super-Local Unfolding / 12.7： |
| Unfolding Groups, III / 13.： |
| Symmetry Group of an Apartment / 13.1： |
| Wreath-Direct Groups / 13.3： |
| Canonical Unfoldings / 13.4： |
| Incorporating the Symmetry of Referents / 13.5： |
| Why Internal Symmetry Groups / 13.6： |
| Base and Subsidiary Alignment Kernels / 13.7： |
| Cloning / 13.8： |
| The Inference Structure / 13.9： |
| Group Elements / 13.10： |
| Adding the Anomaly / 13.11： |
| Adding more Primitives / 13.12： |
| Multi-index Notation / 13.13： |
| Symmetry Streaming / 13.14： |
| Mechanical Design and Manufacturing / 13.15： |
| Parametric, Feature-Based, Solid Modeling / 14.1： |
| A Generative Theory of Physical Features / 14.3： |
| Datum Features / 14.4： |
| Parent-Child Structures as Wreath Products / 14.5： |
| Review of Part Design / 14.6： |
| Complex Parts / 14.8： |
| A Theory of Resolution / 14.9： |
| A Theory of Sketching / 14.10： |
| A Mathematical Theory of the Designer's Mental Analysis / 14.11： |
| Constraints and Unfolding / 14.12： |
| Theory of the Sketch Plane / 14.13： |
| Solidity / 14.14： |
| A Comment on Resolution / 14.15： |
| Adding Features / 14.16： |
| Model Structure / 14.17： |
| Intent Manager / 14.18： |
| Intent Managers: Gestalt Principles / 14.19： |
| Slicing asUnfolding / 14.20： |
| Assembly: Symmetry-Breaking Theory / 14.21： |
| Unfolding Groups, Boolean Operations, and Assembly / 14.22： |
| The Designer's Conceptual Planning / 14.23： |
| Holesthrough Several Layers / 14.24： |
| Analogy with Quantum Mechanics / 14.25： |
| Fiber-Relative Actions / 14.26： |
| The Full Group of the Robot Serial-Link Manipulator / 14.27： |
| Machining / 14.28： |
| A Mathematical Theory of Architecture / 15.： |
| The Design Process / 15.1： |
| Massing Studies / 15.3： |
| Mass Elements / 15.4： |
| The Hierarchy of Mass Groups / 15.5： |
| Symmetry Group of a Massing Structure / 15.6： |
| Massing Structure and Generativity / 15.7： |
| Slicing the Massing Study to Create Floorplates / 15.8： |
| Space Planning: Unfolding of Space Volumes / 15.9： |
| Space Planning: Unfolding the Boundary and Void Spaces / 15.10： |
| Unfolding the Room Volumes / 15.11： |
| Unfolding the Wall Structure / 15.12： |
| Complex Slicing / 15.13： |
| Design Development Phase / 15.14： |
| Choice of Materials / 15.15： |
| Doorsand Windows / 15.16： |
| Structural Column Grid / 15.17： |
| Ceiling Grid / 15.18： |
| Stairs / 15.19： |
| Shafts / 15.20： |
| Roof / 15.21： |
| Development of Accuracy / 15.22： |
| Construction Documents / 15.23： |
| Sectionsand Elevations / 15.24： |
| Conclusion / 15.25： |
| Summary of a Mathematical Theory of Architecture / 15.26： |
| Solid Structure / 16.： |
| The Solid Primitives / 16.1： |
| The Solid n-Cube / 16.3： |
| The Hyperoctahedral Wreath Hyperplane Group / 16.4： |
| CubesasCartesian Frames / 16.5： |
| The Symmetry Group of the Solid n-Cube / 16.6： |
| Solid Interval and Solid Square / 16.7： |
| The Other Solid Primitives / 16.8： |
| The Solid Sphere / 16.9： |
| The Solid Cross-Section Cylinder / 16.10： |
| The Solid Ruled Cylinder / 16.11： |
| TheSolidCross-SectionBlock / 16.12： |
| TheSolidRuledorPlanarBlock / 16.13： |
| The Full Set of Solid Primitives / 16.14： |
| Externalization in the Solid Primitives / 16.15： |
| The Unfolding Group of a Solid / 16.16： |
| Wreath Formulation of Splines / 17.： |
| TheGoalofThisChapter / 17.1： |
| CurvesasMachines / 17.2： |
| Cubic Hermite Curves / 17.3： |
| Parametrized SurfacesasMachines / 17.4： |
| Bicubic Hermite Surfaces / 17.5： |
| Parametrized 3-SolidsasMachines / 17.6： |
| Tricubic Hermite Solid / 17.7： |
| Final Comment / 17.8： |
| Wreath Formulation of Sweep Representations / 18.： |
| Sweep Representations / 18.1： |
| Aesthetics and Sweep Representations / 18.2： |
| Ray Representations / 18.3： |
| Multiple Sweeping / 18.4： |
| Process Grammar / 19.： |
| Inference from a Single Shape / 19.1： |
| Intervening History / 19.3： |
| Other Literature / 19.4： |
| Conservation Laws of Physics / 20.： |
| Wreath Products and Commutators / 20.1： |
| Transfer in Quantum Mechanics / 20.2： |
| Symmetriesof the Schrodinger Equation / 20.3： |
| Space-Time Transfer in Quantum Mechanics / 20.4： |
| Non-solvability of the Galilean Lie Algebra / 20.5： |
| Semisimple Lie Algebras in Quantum Mechanics / 20.6： |
| Music / 21.： |
| Motival Material / 21.1： |
| Modulation as a Wreath Product / 21.3： |
| Psychological Studies of Sequential Structure / 21.4： |
| Transfer in Musical Sequence Structure / 21.5： |
| Meter / 21.6： |
| AlgebraicTheoryofMeter / 21.7： |
| TheoryofMetricalMovement(Pulse) / 21.8： |
| Algebraic Structure of Grouping / 21.9： |
| The Generative Structure of Quadrilaterals / 22.： |
| Non-coordinate-freedom / 22.4： |
| Theorem-Proving in Geometry / 22.5： |
| The Geometry Hierarchy / 22.6： |
| Projective Asymmetrization: Extrinsic View / 22.7： |
| Deriving Projective CoordinateSystems / 22.8： |
| Non-transitivity of the Geometry Group / 22.9： |
| Regular Translation Structure / 22.10： |
| 3D ProjectiveAsymmetrization / 22.11： |
| Against the Erlanger Program: Summary / 22.12： |
| Semi-direct Products / A.： |
| Normal Subgroups / A.1： |
| The Extending Group H as an Automorphism Group / A.2： |
| Multiplication in a Semi-direct Product / A.4： |
| Direct Products / A.5： |
| Symbols / B.： |
| References |
| Index |
図書
