Divided Spheres —— Geodesics and the Orderly Subdivision of the Sphere

----- 球体划分：测地线和球体的有序细分

ISBN: 9781466504295 出版年：2012 页码：525 Popko, Edward S CRC Press

Divided Spheres Working with Spheres Making a Point An Arbitrary Number Symmetry and Polyhedral Designs Spherical Workbenches Detailed Designs Other Ways to Use Polyhedra Summary Additional Resources Bucky's Dome Synergetic Geometry Dymaxion Projection Cahill and Waterman Projections Vector Equilibrium Icosa's The First Dome NC State and Skybreak Carolina Ford Rotunda Dome Marines in Raleigh University Circuit Radomes Kaiser's Domes Union Tank Car Covering Every Angle Summary Additional Resources Putting Spheres to Work Tammes Problem Spherical Viruses Celestial Catalogs Sudbury Neutrino Observatory Climate Models and Weather Prediction Cartography Honeycombs for Supercomputers Fish Farming Virtual Reality Modeling Spheres Dividing Golf Balls Spherical Throwable Panoramic Camera Hoberman's MiniSphere Rafiki's Code World Art and Expression Additional Resources Circular Reasoning Lesser and Great Circles Geodesic Subdivision Circle Poles Arc and Chord Factors Where Are We? Altitude-Azimuth Coordinates Latitude and Longitude Coordinates Spherical Trips Loxodromes Separation Angle Latitude Sailing Longitude Spherical Coordinates Cartesian Coordinates rho, phi, lambda Coordinates Spherical Polygons Excess and Defect Summary Additional Resources Distributing Points Covering Packing Volume Summary Additional Resources Polyhedral Frameworks What Is a Polyhedron? Platonic Solids Symmetry Archimedean Solids Additional Resources Golf Ball Dimples Icosahedral Balls Octahedral Balls Tetrahedral Balls Bilateral Symmetry Subdivided Areas Dimple Graphics Summary Additional Resources Subdivision Schemas Geodesic Notation Triangulation Number Frequency and Harmonics Grid Symmetry Class I: Alternates and Ford Class II: Triacon Class III: Skew Covering the Whole Sphere Additional Resources Comparing Results Kissing-Touching Sameness or Nearly So Triangle Area Face Acuteness Euler Lines Parts and T . 257 Convex Hull Spherical Caps Stereograms Face Orientation King Icosa Summary Additional Resources Computer-Aided Design A Short History CATIA Octet Truss Connector Spherical Design Three Class II Triacon Designs Panel Sphere Class II Strut Sphere Class II Parabolic Stellations Class I Ford Shell 31 Great Circles Class III Skew Additional Resources Advanced CAD Techniques Reference Models An Architectural Example Spherical Reference Models Prepackaged Reference and Assembly Models Local Axis Systems Assembly Review Design-in-Context Associative Geometry Design-in-Context versus Constraints Mirrored Enantiomorphs Power Copy Power Copy Prototype Macros Publication Data Structures CAD Alternatives: Stella and Antiprism Antiprism Summary Additional Resources Spherical Trigonometry Basic Trigonometric Functions The Core Theorems Law of Cosines Law of Sines Right Triangles Napier's Rule Using Napier's Rule on Oblique Triangles Polar Triangles Additional Resources Stereographic Projection Points on a Sphere Stereographic Properties A History of Diverse Uses The Astrolabe Crystallography and Geology Cartography Projection Methods Great Circles Lesser Circles Wulff Net Polyhedra Stereographics Polyhedra as Crystals Metrics and Interpretation Projecting Polyhedra Octahedron Tetrahedron Geodesic Stereographics Spherical Icosahedron Summary Additional Resources Geodesic Math Class I: Alternates and Fords Class II: Triacon Class III: Skew Characteristics of Triangles Storing Grid Points Additional Resources Schema Coordinates Coordinates for Class I: Alternates and Ford Coordinates for Class II: Triacon Coordinates for Class III: Skew Coordinate Rotations Rotation Concepts Direction and Sequences Simple Rotations Reflections Antipodal Points Compound Rotations Rotation around an Arbitrary Axis Polyhedra and Class Rotation Sequences Icosahedron Classes I and III Icosahedron Class Octahedron Classes I and III Octahedron Class Tetrahedron Classes I and III Tetrahedron Class Dodecahedron Class Cube Class Implementing Rotations Using Matrices Rotation Algorithms An Example Summary Additional Resources