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Record Nr. |
UNINA9910825265603321 |
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Autore |
Beckers Benoit |
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Titolo |
Reconciliation of geometry and perception in radiation physics / / Benoit Beckers, Pierre Beckers |
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Pubbl/distr/stampa |
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London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 |
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©2014 |
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ISBN |
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1-118-98450-1 |
1-118-98448-X |
1-118-98449-8 |
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Descrizione fisica |
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1 online resource (182 p.) |
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Collana |
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Focus Numerical Methods in Engineering Series, , 2051-249X |
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Disciplina |
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Soggetti |
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Geometry, Projective |
Physics - Mathematical models |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Cover; Title Page; Copyright; Contents; Introduction; Chapter 1. Discovering the Central Perspective; 1.1. The musical scale; 1.2. The tonal system; 1.3. Nomenclature of the projections; 1.4. The central projection on the plane; 1.4.1. Principle; 1.4.2. Essential properties; 1.4.3. Basics; 1.5. Proportions and progressions; 1.5.1. Arithmetic progression: AB = CD =; 1.5.2. Geometric progression: BC/AB = CD/BC = r; 1.5.3. Harmonic progression: AB-BC-CD, 1/A, 1/B, 1/C; 1.6. The eighth proposal of Euclid; Chapter 2. Main Properties of Central Projections; 2.1. Straight lines and conics |
2.2. Coherence and cross ratio2.2.1. Calculation of cross ratio on a circle; 2.3. Harmonic relation and regularity; 2.4. The foreshortening; 2.4.1. Variations in positions on a straight line; 2.4.2. The critical experiment; 2.4.3. Detailed analysis; 2.5. Homogeneous coordinates; Chapter 3. Any Scene Carried to a Sphere and the Sphere To a Point; 3.1. General concepts; 3.1.1. Point and great circle; 3.1.2. Line and polygon; 3.1.3. Tilling of the sphere; 3.1.4. Areas and volumes; 3.1.5. Spherical trigonometry; 3.2. Cartography of the sphere; 3.2.1. Orthogonal net; 3.2.2. Latitude and longitude |
3.2.3. Azimuth3.2.4. Orthodromes and loxodromes; 3.2.5. Earth's |
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surface shape; 3.2.6. Alterations; 3.2.7. Properties of the projection; 3.3. Projection of the sphere on cylinders; 3.3.1. Central projection on the cylinder; 3.3.2. Lambert equal-area projection; 3.3.3. Mercator projection; 3.4. Projection on the plane; 3.4.1. Parallel projection; 3.4.2. Central projection; 3.4.3. Gnomonic projection; 3.4.4. Stereographic projection; 3.4.5. Stereography versus Mercator projection; 3.4.6. Postel projection; 3.4.7. Lambert projection; 3.4.8. Direct computation of azimuthal projections |
3.5. Pseudocylindrical projections3.5.1. Coordinates transformation from direct to transversal aspect; 3.5.2. Hammer projection; 3.5.3. Mollweide projection, another pseudo-cylindrical projection; 3.6. Hemisphere tilling; 3.6.1. Presentation of the method; 3.6.2. Exact fulfillment of the aspect ratio constraint; 3.6.3. Approximate fulfillment of the aspect ratio constraint; 3.6.4. Equal-area cells and constant aspect ratio on the hemisphere; 3.6.5. Conclusion; Chapter 4. Geometry And Physics: Radiative Exchanges; 4.1. Geometric wave propagation; 4.2. The radiosity equation |
4.2.1. Surface sources4.2.2. Lambert diffuse reflection; 4.2.3. Interactions between surfaces; 4.2.4. Discretization of the radiosity equation; 4.2.5. Properties of the radiosity matrix; 4.3. View factors; 4.4. Ray tracing; 4.4.1. Mesh quality; 4.4.2. Solid angle or view factor; 4.5. Specular reflection of light and sound; Conclusion; Bibliography; Index |
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Sommario/riassunto |
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Reconciliation of Geometry and Perception in Radiation Physics approaches the topic of projective geometry as it applies to radiation physics and attempts to negate its negative reputation. With an original outlook and transversal approach, the book emphasizes common geometric properties and their potential transposition between domains. After defining both radiation and geometric properties, authors Benoit and Pierre Beckers explain the necessity of reconciling geometry and perception in fields like architectural and urban physics, which are notable for the regularity of their forms an |
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