Reconciliation of Geometry and Perception in Radiation Physics

Author： Benoit Beckers  

Publisher： John Wiley & Sons Inc‎

Publication year： 2014

E-ISBN: 9781118984499

P-ISBN(Hardback):  9781848215832

Subject： O411.1 Mathematical Methods of Physics

Language： ENG

Access to resources Favorite

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Description

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 and the complexity of their interactions.

Chapter

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 ratio

2.2.1. 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. Azimuth

3.2.4. Orthodromes and loxodromes

3.2.5. Earth’s 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 projections

3.5.1. 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 sources

4.2.2. 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

The users who browse this book also browse


No browse record.