دانلود کتاب ریاضیات و کاربردهای گرافیک کامپیوتری

It is said that the origin of computer graphics (CG) dates back to the early 1960s when Ivan Sutherland, an American computer scientist, invented Sketchpad, which was a precursor to the graphical user interface (GUI). For a long time thereafter, computers were primarily used for scientific and technical calculations and back-office tasks. However, with the advent of personal computers and gaming consoles being used in our daily lives, a wide range of applications for entertainment purposes have been developed. As computer performance improved and the demand for creating images as if the real world was expanding on the screen increased, 3D CG became an indispensable technology. Today, various services based on 3D CG have been born in games, movies, advertisements, VR experiences, and more. Furthermore, with the advent of head-mounted displays, the range of applications has expanded due to the possibility of immersive experiences. More than 60 years after the birth of CG, computers have achieved dramatic performance improvements that would have been unimaginable at the time, and with the development of 3D CG technology, images with such realism that they are indistinguishable from live-action can now be generated almost in real time. Virtual reality, virtual space, cyberspace, metaverse, parallel world, and so on, terms representing activities in virtual spaces created by computers have appeared one after another, and the challenge to create a new world with 3D CG shows no signs of stopping. Perhaps humans inherently have a desire to create a new space with their own hands that is similar to the space they live in. If so, 3D CG will continue to evolve until that is achieved and will continue to be universally needed in the future. Now, such 3D CG technology did not appear overnight. There was a steady accumulation of technical development over a long period from the birth of computer graphics. We are now reaping the fruits of that effort. However, if you want to master 3D CG technology and contribute to its development, you need to understand the underlying technology. To meet this need, this book was written. This book explains the technologies that support 3DCG, divided into four chapters: “Geometry Processing with Surface Meshes,” “Rendering,” “Character Animation,” and “Physics Simulation.” Each of these is explained in a separate chapter. If we were to express these four technologies in simpler terms, we could say they are about creating shapes, creating images, creating movements, and reproducing the behavior of the natural world. In Chap. 1 (authored by Kenshi Takayama), we explain the theories for describing the shape of an object with a surface mesh and editing and processing it. In Chap. 2 (authored by Yoshinori Dobashi), we focus on the calculation of the appearance of the object’s surface and explain global illumination calculation methods for generating realistic images, fast image generation methods using pre-calculation, and physical phenomena such as light scattering necessary for improving realism. In Chap. 3 (authored by Tomohiko Mukai), we introduce the skeleton method, a standard technique in animation production, and explain various animation editing techniques for humanoid character models. Finally, in Chap. 4 (authored by Makoto Fujisawa), we explain methods for calculating the behavior of complex natural phenomena, including not only rigid objects but also fluid like water and air. The four themes mentioned here can indeed be said to be the fundamental elements that support 3DCG. Each chapter was written by researchers who are active at the forefront of each field. All the authors have remarkable achievements and are leading the development of 3DCG technology with their abundant experience and knowledge. The content covered in this book is the basics of 3DCG, but that does not mean it is simple. Compared to similar books, it contains mathematically advanced content. Specifically, basic knowledge of analysis and linear algebra, which is taught in college science and engineering courses, is required. Also, basic knowledge of continuum mechanics and fluid mechanics, and knowledge of mathematical optimization such as least squares method would make it easier to read. Therefore, the main target readers of this book are senior students in science and engineering courses or graduate students. This book is also recommended for a wide range of people, including high school students and professionals interested in the theory behind 3D computer graphics, engineers working at game development companies, and those considering 3D computer graphics as a research subject. We hope this book will be useful in understanding the technologies that support 3DCG.