Synopsis "Solid Angle Computation with Monte Carlo Methods"
Book DescriptionsWhat motivated me to write this book? The knowledge pertaining to solid angle and its computation is scattered in bits and parts in the scientific literature. It is my feeling that no such book exists that explains the concepts of solid angles explicitly and enunciates the ab initio computation methods. This motivated me to write a book about the solid angle.This book pictorially explains the concepts of solid angles and gives the salient features of solid angles along with the necessary mathematical development for computation. Why Monte Carlo methods?I have specifically chosen Monte Carlo methods to compute solid angles because the students are fascinated to learn Monte Carlo methods. Monte Carlo methods have been explained in a simple way starting with ab initio principles without involving too many mathematical jargons. This book not only provides an opportunity to readers to learn Monte Carlo methods but also. helps the readers to apply Monte Carlo methods in the field of their interest in addition to compute solid angles.What is RAHI method?Monte Carlo methods can be applied to determine solid angles not only by solving the intricate solutions of multidimensional integrals but also by shining light on the given surface and determining the solid angles. This has been termed as Ray Hitting (RAHI) method. RAHI method is simple to understand and simple to apply.MATLAB ProgramIn implementing Monte Carlo methods in solid angles computations, some rudimentary knowledge of programming like MATLAB is, however, required. The MATLAB programs have been given in its simplest forms to conduct simulation experiments with solid angle computations and apply in the various field of interest.Chapter wise book appraisal.This book contains step-by-step solved examples and easy to implement MATLAB programs. Chapter 1 "Solid Angle" gives a pictorial illustration of solid angles. It gives the salient features of solid angle, basics requirements for the formation of solid angles in 3D-space. Moreover, definitions and mathematical developments of solid angles are summarized.Chapter 2 "Monte Carlo Methods" gives an understanding of Monte Carlo methods from scratches. Explains the Golden Rule of Monte Carlo and Hit-or-Miss methods. It makes easy to understand and implement the methods. Examples are given for understanding the methods.Chapter 3 'Random Numbers" provide the users to review that how grandpa clock can fulfill your needs to generate random numbers.Chapter 4. "Integration with Monte Carlo" helps to solve step-by-step the single/double/triple and higher order integrals by Monte Carlo Methods. After explaining the method with simple examples, the MATLAB programs are appended.Chapter 5. "Solid Angle Computation" gives step by step examples of computing solid angles subtending with: (a) a point and Plane surface, (b) Disk, and (c) Cylinder. Several solved examples are given using MATLAB programs. Listing of simple MATLAB programs are provided. Applications of RAHI method are given for all cases.Finally, computation of solid angles between a Line and a Disk has been given with explanation. RAHI and triple integration methods have been employed.ConclusionsAfter learning basic rules and practicing examples from all five chapters, one may be able to compute solid angle with any situation including a solid angle with an irregular shaped surface.
