Mathematics and Applications of Computer Graphics

This book equips readers with the fundamentals of 3DCG that support the advanced technologies. The content of this book is divided into four categories: modeling, rendering, character animation, and physical simulation, and each is explained in a separate chapter. In simpler terms, these four technologies can be described as creating shapes, creating images, creating motion, and reproducing the behavior of the natural world. The "Modeling" chapter describes the theory behind describing the shape of an object using surface meshes and then editing and manipulating them. The chapter "Rendering" focuses on the calculation of the luminance of an object's surface, and describes methods for calculating global illumination and generating fast images using precomputation to produce realistic images. Physical phenomena such as light scattering, which is necessary to improve realism, are also explained. The "Character Animation" chapter introduces the skeleton method, a standard technique in animation production, and describes various animation editing techniques for humanoid character models. Finally, the chapter on "Physical Simulation" describes methods to compute the behavior of complex natural phenomena, including not only hard objects but also flowing objects such as water and air. The four topics listed here are the fundamental elements that support 3DCG. The chapters were written by researchers who are active at the forefront of their respective fields. Each of the authors has a remarkable track record and can be said to have led the development of 3DCG technology in Japan with their wealth of experience and knowledge.

To understand the mathematical content of this book, basic knowledge of analysis and linear algebra is required. This book is suitable for upper undergraduate and graduate students in computer science, engineering, and other fields in science, and is also useful for practitioners in game production and those who are interested in 3DCG.