A generative theory of shape

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A generative theory of shape / Michael Leyton

資料種別:: 図書
出版情報:: Berlin : Springer, c2001
形態:: xvi, 554 p. ; 24 cm
シリーズ名:: Lecture notes in computer science ; 2145 <BA00009279>
著者名:: Leyton, Michael <DA06495143>
ISBN:: 9783540427179 [3540427171]
書誌ID:: BA54313422

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注記:

Bibliography: p. [541]-548
Includes index
"Tutorial"--on cover

主題:

Geometric programming; Shape theory (Topology)

言語:

英語

目次情報:

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

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：

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